Tootfinder

This https://arxiv.org/abs/2405.03437 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csCE_…

pyCFS-data: Data Processing Framework in Python for openCFS
Many numerical simulation tools have been developed and are on the market, but there is still a strong need for appropriate tools capable of simulating multi-field problems, especially in aeroacoustics. Therefore, openCFS provides an open-source framework for implementing partial differential equations using the finite element method. Since 2000, the software has been developed continuously. The result is openCFS (before 2020, known as CFS++ Coupled Field Simulations written in C++). In this pa…

This https://arxiv.org/abs/2506.05678 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csLG_…

Numerical Investigation of Sequence Modeling Theory using Controllable Memory Functions
The evolution of sequence modeling architectures, from recurrent neural networks and convolutional models to Transformers and structured state-space models, reflects ongoing efforts to address the diverse temporal dependencies inherent in sequential data. Despite this progress, systematically characterizing the strengths and limitations of these architectures remains a fundamental challenge.In this work, we propose a synthetic benchmarking framework to evaluate how effectively different sequenc…

Calibration of Quantum Devices via Robust Statistical Methods
Alexandra Ram\^oa, Raffaele Santagati, Nathan Wiebe
https://arxiv.org/abs/2507.06941 https://…

Calibration of Quantum Devices via Robust Statistical Methods
Bayesian inference is a widely used technique for real-time characterization of quantum systems. It excels in experimental characterization in the low data regime, and when the measurements have degrees of freedom. A decisive factor for its performance is the numerical representation of the Bayesian probability distributions. In this work, we explore advanced statistical methods for this purpose, and numerically analyze their performance against the state-of-the-art in quantum parameter learnin…

This https://arxiv.org/abs/2005.11205 has been replaced.
link: https://scholar.google.com/scholar?q=a

The Cauchy Problem for Non-Isentropic compressible Navier-Stokes/Allen-Cahn system with Degenerate Heat-Conductivity
The Cauchy problem for non-isentropic compressible Navier-Stokes/Allen-Cahn system with degenerate heat-conductivity $κ(θ)=\tildeκθ^β$ in 1-d is discussed in this paper. This system is widely used to describe the motion of immiscible two-phase flow in numerical simulation. The wellposedness for strong solution of this problem is established with the $H^1$ initial data for density, temperature, velocity, and the $H^2$ initial data for phase field. The result shows that no discontinuity of t…

Imposing the Fundamental Dynamical Constraint of Hydrostatic Balance to Improve Global ML Weather Prediction
Akshay Subramaniam, Dale Durran, David Pruitt, Nathaniel Cresswell-Clay, William Yik
https://arxiv.org/abs/2506.08285

Imposing the Fundamental Dynamical Constraint of Hydrostatic Balance to Improve Global ML Weather Prediction
Forecasting weather accurately and efficiently is a critical capability in our ability to adapt to climate change. Data driven approaches to this problem have enjoyed much success recently providing forecasts with accuracy comparable to physics based numerical prediction models but at significantly reduced computational expense. However, these models typically do not incorporate any physics priors. In this work, we demonstrate improved skill of data driven weather prediction approaches by incor…

Physics-Informed Gaussian Process Inference of Liquid Structure from Scattering Data
Harry W. Sullivan, Brennon L. Shanks, Matej Cervenka, Michael P. Hoepfner
https://arxiv.org/abs/2507.07948

Physics-Informed Gaussian Process Inference of Liquid Structure from Scattering Data
We present a nonparametric Bayesian framework to infer radial distribution functions from experimental scattering measurements with uncertainty quantification using non-stationary Gaussian processes. The Gaussian process prior mean and kernel functions are designed to mitigate well-known numerical challenges with the Fourier transform, including discrete measurement binning and detector windowing, while encoding fundamental yet minimal physical knowledge of liquid structure. We demonstrate unce…

Determining $\alpha_s(m_Z)$ from the Heavy Jet Mass distribution
Miguel A. Benitez
https://arxiv.org/abs/2506.07723 https://arxiv.org…

Determining $α_s(m_Z)$ from the Heavy Jet Mass distribution
We present a state-of-the-art analysis on determining the strong coupling constant $α_s(m_Z)$ from available $e^+e^-$ data for the Heavy Jet Mass (HJM) distribution. Dijet resummation is supplemented with additional resummation of shoulder logarithms appearing around the symmetric 3-jet configuration of the HJM spectrum. In addition to $α_s(m_Z)$ we further obtain numerical results for two non-perturbative parameters, $Ω_1^ρ$ and $Θ_1$, encompassing effects from dijet and trijet hadronizat…

Ideal incompressible axisymmetric MHD: Uncovering finite-time singularities
Venkata Sai Swetha Kolluru, Rahul Pandit
https://arxiv.org/abs/2507.06842 https…

Ideal incompressible axisymmetric MHD: Uncovering finite-time singularities
We provide compelling numerical evidence for the development of (potential) finite-time singularities in the three-dimensional (3D) axisymmetric, ideal, incompressible magnetohydrodynamic (IMHD) equations, in a wall-bounded cylindrical domain, starting from smooth initial data, for the velocity and magnetic fields. We demonstrate that the nature of the singularity depends crucially on the relative strength C of the velocity and magnetic fields at the time of initialisation: (i) if C < 1, then t…

Numerical and data-driven modeling of spall failure in polycrystalline ductile materials
Indrashish Saha, Lori Graham-Brady
https://arxiv.org/abs/2507.03706

Numerical and data-driven modeling of spall failure in polycrystalline ductile materials
Developing materials with tailored mechanical performance requires iteration over a large number of proposed designs. When considering dynamic fracture, experiments at every iteration are usually infeasible. While high-fidelity, physics-based simulations can potentially reduce experimental efforts, they remain computationally expensive. As a faster alternative, key dynamic properties can be predicted directly from microstructural images using deep-learning surrogate models. In this work, the sp…

Global Solutions to the Discrete Nonlinear Breakage Equations without Mass Transfer
Mashkoor Ali (LAMA), Philippe Lauren\c{c}ot (LAMA)
https://arxiv.org/abs/2507.06685

Global Solutions to the Discrete Nonlinear Breakage Equations without Mass Transfer
Global existence of mild solutions to the discrete collisional breakage equations is established for a broad class of collision kernels, without imposing any growth assumptions. In addition, classical solutions are constructed, and uniqueness is proved for an appropriate class of kinetic coefficients and initial data. The large time behavior of solutions is also discussed, and numerical simulations are presented to support the theoretical results.

Bilinear Quadratic Output Systems and Balanced Truncation
Heike Fa{\ss}bender (Institute for Numerical Analysis, TU Braunschweig), Serkan Gugercin (Department of Mathematics and Division of Computational Modeling and Data Analytics, Academy of Data Science, Virginia Tech), Till Peters (Institute for Numerical Analysis, TU Braunschweig)
https://

Bilinear Quadratic Output Systems and Balanced Truncation
Dynamical systems with quadratic outputs have recently attracted significant attention. In this paper, we consider bilinear dynamical systems, a special class of weakly nonlinear systems, with a quadratic output. We develop various primal-dual formulations for these systems and define the corresponding system Gramians. Conditions for the existence and uniqueness of these Gramians are established, and the generalized Lyapunov equations they satisfy are derived. Using these Gramians and their tru…

Prospective Learning in Retrospect
Yuxin Bai, Cecelia Shuai, Ashwin De Silva, Siyu Yu, Pratik Chaudhari, Joshua T. Vogelstein
https://arxiv.org/abs/2507.07965 https://arxiv.org/pdf/2507.07965 https://arxiv.org/html/2507.07965
arXiv:2507.07965v1 Announce Type: new
Abstract: In most real-world applications of artificial intelligence, the distributions of the data and the goals of the learners tend to change over time. The Probably Approximately Correct (PAC) learning framework, which underpins most machine learning algorithms, fails to account for dynamic data distributions and evolving objectives, often resulting in suboptimal performance. Prospective learning is a recently introduced mathematical framework that overcomes some of these limitations. We build on this framework to present preliminary results that improve the algorithm and numerical results, and extend prospective learning to sequential decision-making scenarios, specifically foraging. Code is available at: https://github.com/neurodata/prolearn2.
toXiv_bot_toot

Data-driven ANN model for estimating unfrozen water content in the thermo-hydraulic simulation of frozen soils
Mingpeng Liu, Peizhi Zhuang, Raul Fuentes
https://arxiv.org/abs/2508.01902

Data-driven ANN model for estimating unfrozen water content in the thermo-hydraulic simulation of frozen soils
This study integrates a data-driven model for estimating the unfrozen water content into the thermo-hydraulic coupling simulation of frozen soils. An artificial neural network (ANN) was employed to develop this data-driven model using a dataset from the literature. Thereafter, a numerical algorithm was developed to implement the data-driven model into the thermo-hydraulic simulation. In the numerical algorithm, the frozen and unfrozen zones are distinguished first according to the freezing temp…

This is the first numerical problem I ever did. It demonstrates the
power of computers:
Enter lots of data on calorie & nutritive content of foods. Instruct
the thing to maximize a function describing nutritive content, with a
minimum level of each component, for fixed caloric content. The
results are that one should eat each day:
1/2 chicken
1 egg
1 glass of skim milk
27 heads of lettuce.
-- Rev. Adrian Melott

Resonant leptogenesis in inverse see-saw framework with modular $S_4$ symmetry
Abhishek, V. Suryanarayana Mummidi
https://arxiv.org/abs/2507.06610 https://…

Resonant leptogenesis in inverse see-saw framework with modular $S_4$ symmetry
This work introduces a model for lepton mass generation and flavor mixing, realized through a (2,3) inverse seesaw structure within a modular \( S_4 \) symmetry framework. The model employs modular forms to construct the lepton Yukawa couplings, thereby significantly simplifying the model by reducing its complexity. A detailed numerical analysis demonstrates consistency with current neutrino oscillation data, yielding constrained predictions for the mixing angles and CP-violating phases. The Di…

Efficiency of turbulence
A Lopez (SPEC - UMR3680), A Barral (SPEC - UMR3680), G Costa (SPEC - UMR3680), Q Pikeroen (SPEC - UMR3680), V Shukla (SPEC - UMR3680), B\'ereng\`ere Dubrulle (SPEC - UMR3680)
https://arxiv.org/abs/2508.05686

Efficiency of turbulence
We consider the efficiency of turbulence, a dimensionless parameter that characterises the fraction of the input energy stored into a turbulent flow field. We first show that the inverse of the efficiency provides an upper bound for the dimensionless energy injection in a turbulent flow. We analyse the efficiency of turbulence for different flows using numerical and experimental data. Our analysis suggests that efficiency is bounded from above, and, in some cases, saturates following a power la…

Efficient Conformance Checking of Rich Data-Aware Declare Specifications (Extended)
Jacobo Casas-Ramos, Sarah Winkler, Alessandro Gianola, Marco Montali, Manuel Mucientes, Manuel Lama
https://arxiv.org/abs/2507.00094

Efficient Conformance Checking of Rich Data-Aware Declare Specifications (Extended)
Despite growing interest in process analysis and mining for data-aware specifications, alignment-based conformance checking for declarative process models has focused on pure control-flow specifications, or mild data-aware extensions limited to numerical data and variable-to-constant comparisons. This is not surprising: finding alignments is computationally hard, even more so in the presence of data dependencies. In this paper, we challenge this problem in the case where the reference model is …

Task-Based Programming for Adaptive Mesh Refinement in Compressible Flow Simulations
Anjiang Wei, Hang Song, Mert Hidayetoglu, Elliott Slaughter, Sanjiva K. Lele, Alex Aiken
https://arxiv.org/abs/2508.05020

Task-Based Programming for Adaptive Mesh Refinement in Compressible Flow Simulations
High-order solvers for compressible flows are vital in scientific applications. Adaptive mesh refinement (AMR) is a key technique for reducing computational cost by concentrating resolution in regions of interest. In this work, we develop an AMR-based numerical solver using Regent, a high-level programming language for the Legion programming model. We address several challenges associated with implementing AMR in Regent. These include dynamic data structures for patch refinement/coarsening, mes…

Drag modelling for flows through assemblies of spherical particles with machine learning: A comparison of approaches
Julia Reuter, Hani Elmestikawy, Sanaz Mostaghim, Berend van Wachem
https://arxiv.org/abs/2507.05983

Drag modelling for flows through assemblies of spherical particles with machine learning: A comparison of approaches
Drag forces on particles in random assemblies can be accurately estimated through particle-resolved direct numerical simulations (PR-DNS). Despite its limited applicability to relatively small assemblies, data obtained from PR-DNS has been the driving force for the development of drag closures for much more affordable simulation frameworks, such as Eulerian-Lagrangian point particle methods. Recently, more effort has been invested in the development of deterministic drag models that account for…

Case Studies of Generative Machine Learning Models for Dynamical Systems
Nachiket U. Bapat, Randy C. Paffenroth, Raghvendra V. Cowlagi
https://arxiv.org/abs/2508.04459 https://

Case Studies of Generative Machine Learning Models for Dynamical Systems
Systems like aircraft and spacecraft are expensive to operate in the real world. The design, validation, and testing for such systems therefore relies on a combination of mathematical modeling, abundant numerical simulations, and a relatively small set of real-world experiments. Due to modeling errors, simplifications, and uncertainties, the data synthesized by simulation models often does not match data from the system's real-world operation. We consider the broad research question of whether …

This https://arxiv.org/abs/2505.23667 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csAI_…

Fortune: Formula-Driven Reinforcement Learning for Symbolic Table Reasoning in Language Models
Tables are a fundamental structure for organizing and analyzing data, making effective table understanding a critical capability for intelligent systems. While large language models (LMs) demonstrate strong general reasoning abilities, they continue to struggle with accurate numerical or symbolic reasoning over tabular data, especially in complex scenarios. Spreadsheet formulas provide a powerful and expressive medium for representing executable symbolic operations, encoding rich reasoning patt…

A multi-stage Bayesian approach to fit spatial point process models
Rachael Ren, Mevin B. Hooten, Toryn L. J. Schafer, Nicholas M. Calzada, Benjamin Hoose, Jamie N. Womble, Scott Gende
https://arxiv.org/abs/2508.02922

A multi-stage Bayesian approach to fit spatial point process models
Spatial point process (SPP) models are commonly used to analyze point pattern data, including presence-only data in ecology. Current methods for fitting these models are computationally expensive because they require numerical quadrature and algorithm supervision (i.e., tuning) in the Bayesian setting. We propose a flexible and efficient multi-stage recursive Bayesian approach to fitting SPP models that leverages parallel computing resources to estimate point process model coefficients and deri…

A Non-leveled and Reliable Approximate FHE Framework through Binarized Polynomial Rings
Baigang Chen, Dongfang Zhao
https://arxiv.org/abs/2508.02943 https://

A Non-leveled and Reliable Approximate FHE Framework through Binarized Polynomial Rings
Homomorphic encryption (HE) enables secure computation on encrypted data, safeguarding user privacy in domains such as cloud computing, healthcare, and finance. Among fully homomorphic encryption (FHE) schemes, CKKS is notable for supporting approximate arithmetic over complex numbers, a key requirement for machine-learning and numerical workloads. However, CKKS incurs rapid noise growth, complex parameter tuning, and relies on costly modulus switching. We propose a binary variant of CKKS that …

Table-r1: Self-supervised and Reinforcement Learning for Program-based Table Reasoning in Small Language Models
Rihui Jin, Zheyu Xin, Xing Xie, Zuoyi Li, Guilin Qi, Yongrui Chen, Xinbang Dai, Tongtong Wu, Gholamreza Haffari
https://arxiv.org/abs/2506.06137

Table-r1: Self-supervised and Reinforcement Learning for Program-based Table Reasoning in Small Language Models
Table reasoning (TR) requires structured reasoning over semi-structured tabular data and remains challenging, particularly for small language models (SLMs, e.g., LLaMA-8B) due to their limited capacity compared to large LMs (LLMs, e.g., GPT-4o). To narrow this gap, we explore program-based TR (P-TR), which circumvents key limitations of text-based TR (T-TR), notably in numerical reasoning, by generating executable programs. However, applying P-TR to SLMs introduces two challenges: (i) vulnerabi…

ESWC 2025 has just started with the presentation of the submission numbers to the individual tracks:
research track: 98 papers
resource track: 36 papers
in-use track: 22 papers
Looking forward to great presentations and discussions!
#eswc2025 #semweb

XPPLORE: Import, visualize, and analyze XPPAUT data in MATLAB
Matteo Martin, Anna Kishida Thomas, George Bard Ermentrout
https://arxiv.org/abs/2507.02709 h…

XPPLORE: Import, visualize, and analyze XPPAUT data in MATLAB
The analysis of ordinary differential equation (ODE) dynamical systems, particularly in applied disciplines such as mathematical biology and neuroscience, often requires flexible computational workflows tailored to model-specific questions. XPPAUT is a widely used tool combining numerical integration and continuation methods. Various XPPAUT toolboxes have emerged to customize analyses, however, they typically rely on summary '.dat' files and cannot parse the more informative '.auto' files, whic…

The Fourier Spectral Transformer Networks For Efficient and Generalizable Nonlinear PDEs Prediction
Beibei Li
https://arxiv.org/abs/2507.05584 https://

The Fourier Spectral Transformer Networks For Efficient and Generalizable Nonlinear PDEs Prediction
In this work we propose a unified Fourier Spectral Transformer network that integrates the strengths of classical spectral methods and attention based neural architectures. By transforming the original PDEs into spectral ordinary differential equations, we use high precision numerical solvers to generate training data and use a Transformer network to model the evolution of the spectral coefficients. We demonstrate the effectiveness of our approach on the two dimensional incompressible Navier-St…

Reasoning-Table: Exploring Reinforcement Learning for Table Reasoning
Fangyu Lei, Jinxiang Meng, Yiming Huang, Tinghong Chen, Yun Zhang, Shizhu He, Jun Zhao, Kang Liu
https://arxiv.org/abs/2506.01710

Reasoning-Table: Exploring Reinforcement Learning for Table Reasoning
Table reasoning, encompassing tasks such as table question answering, fact verification, and text-to-SQL, requires precise understanding of structured tabular data, coupled with numerical computation and code manipulation for effective inference. Supervised fine-tuning (SFT) approaches have achieved notable success but often struggle with generalization and robustness due to biases inherent in imitative learning. We introduce Reasoning-Table, the first application of reinforcement learning (RL)…

GP-Recipe: Gaussian Process approximation to linear operations in numerical methods
Christopher DeGrendele, Dongwook Lee
https://arxiv.org/abs/2506.03471 h…

GP-Recipe: Gaussian Process approximation to linear operations in numerical methods
We introduce new Gaussian Process (GP) high-order approximations to linear operations that are frequently used in various numerical methods. Our method employs the kernel-based GP regression modeling, a non-parametric Bayesian approach to regression that operates on the probability distribution over all admissible functions that fit observed data. We begin in the first part with discrete data approximations to various linear operators applied to smooth data using the most popular squared expone…

Numerical Errors in Quantitative System Analysis With Decision Diagrams
Sebastiaan Brand, Arend-Jan Quist, Richard M. K. van Dijk, Alfons Laarman
https://arxiv.org/abs/2508.02673

Numerical Errors in Quantitative System Analysis With Decision Diagrams
Decision diagrams (DDs) are a powerful data structure that is used to tackle the state-space explosion problem, not only for discrete systems, but for probabilistic and quantum systems as well. While many of the DDs used in the probabilistic and quantum domains make use of floating-point numbers, this is not without challenges. Floating-point computations are subject to small rounding errors, which can affect both the correctness of the result and the effectiveness of the DD's compression. In t…

Analytic Regression of Feynman Integrals from High-Precision Numerical Sampling
Oscar Barrera, Aur\'elien Dersy, Rabia Husain, Matthew D. Schwartz, Xiaoyuan Zhang
https://arxiv.org/abs/2507.17815

Analytic Regression of Feynman Integrals from High-Precision Numerical Sampling
In mathematics or theoretical physics one is often interested in obtaining an exact analytic description of some data which can be produced, in principle, to arbitrary accuracy. For example, one might like to know the exact analytical form of a definite integral. Such problems are not well-suited to numerical symbolic regression, since typical numerical methods lead only to approximations. However, if one has some sense of the function space in which the analytic result should lie, it is possib…

Explaining the "too massive" high-redshift galaxies in JWST data: numerical study of three effects and a simple relation
Joshua J. Ziegler, Katherine Freese, Jonathan Lozano, Gabriele Montefalcone
https://arxiv.org/abs/2507.21409

Explaining the "too massive" high-redshift galaxies in JWST data: numerical study of three effects and a simple relation
The James Webb Space Telescope has discovered high luminosity galaxies that appear to be "too many" and "too massive" compared to predictions of the Standard LCDM cosmology, suggesting that star formation in the early universe is more rapid than previously anticipated. In this paper we examine in detail the following three effects which can instead provide alternative explanations for these observations: (1) a "top heavy" initial mass function (IMF) for the stars, (2) a variety of star formatio…

Dynamic film thickness measurement in a rolling bearing using numerical elastohydrodynamic-acoustic modelling to interpret reflected ultrasound data
Pan Dou, Yayu Li, Suhaib Ardah, Tonghai Wu, Min Yu, Tom Reddyhoff, Yaguo Lei, Daniele Dini
https://arxiv.org/abs/2506.22618

Dynamic film thickness measurement in a rolling bearing using numerical elastohydrodynamic-acoustic modelling to interpret reflected ultrasound data
The thickness of the lubricating film plays a vital role in the operational efficiency and reliability of rolling bearings. Ultrasonic reflection techniques offer a promising non-invasive approach for in situ evaluation of lubricant films.However, accurately identifying the central film thickness remains challenging due to several complex factors, including dynamic fluctuations, localized elastic deformation, cavitation effects, and variations in oil supply. This study presents a comprehensive …

Jacobi-accelerated FFT-based solver for smooth high-contrast data
Martin Ladeck\'y, Ivana Pultarov\'a, Fran\c{c}ois Bignonnet, Indre J\"odicke, Jan Zeman, Lars Pastewka
https://arxiv.org/abs/2508.02613

Jacobi-accelerated FFT-based solver for smooth high-contrast data
The computational efficiency and rapid convergence of fast Fourier transform (FFT)-based solvers render them a powerful numerical tool for periodic cell problems in multiscale modeling. On regular grids, they tend to outperform traditional numerical methods. However, we show that their convergence slows down significantly when applied to microstructures with smooth, highly-contrasted coefficients. To address this loss of performance, we introduce a Green-Jacobi preconditioner, an enhanced succe…

Multilevel Stochastic Gradient Descent for Optimal Control Under Uncertainty
Niklas Baumgarten, David Schneiderhan
https://arxiv.org/abs/2506.02647 https:/…

Multilevel Stochastic Gradient Descent for Optimal Control Under Uncertainty
We present a multilevel stochastic gradient descent method for the optimal control of systems governed by partial differential equations under uncertain input data. The gradient descent method used to find the optimal control leverages a parallel multilevel Monte Carlo method as stochastic gradient estimator. As a result, we achieve precise control over the stochastic gradient's bias, introduced by numerical approximation, and its sampling error, arising from the use of incomplete gradients, wh…

Pitfalls and Limits in Automatic Dementia Assessment
Franziska Braun, Christopher Witzl, Andreas Erzigkeit, Hartmut Lehfeld, Thomas Hillemacher, Tobias Bocklet, Korbinian Riedhammer
https://arxiv.org/abs/2508.04512

Pitfalls and Limits in Automatic Dementia Assessment
Current work on speech-based dementia assessment focuses on either feature extraction to predict assessment scales, or on the automation of existing test procedures. Most research uses public data unquestioningly and rarely performs a detailed error analysis, focusing primarily on numerical performance. We perform an in-depth analysis of an automated standardized dementia assessment, the Syndrom-Kurz-Test. We find that while there is a high overall correlation with human annotators, due to cert…

Neural Drift Estimation for Ergodic Diffusions: Non-parametric Analysis and Numerical Exploration
Simone Di Gregorio, Francesco Iafrate
https://arxiv.org/abs/2505.24383

Neural Drift Estimation for Ergodic Diffusions: Non-parametric Analysis and Numerical Exploration
We take into consideration generalization bounds for the problem of the estimation of the drift component for ergodic stochastic differential equations, when the estimator is a ReLU neural network and the estimation is non-parametric with respect to the statistical model. We show a practical way to enforce the theoretical estimation procedure, enabling inference on noisy and rough functional data. Results are shown for a simulated Itô-Taylor approximation of the sample paths.

Towards Explainable Sequential Learning
Giacomo Bergami, Emma Packer, Kirsty Scott, Silvia Del Din
https://arxiv.org/abs/2505.23624 https://

Towards Explainable Sequential Learning
This paper offers a hybrid explainable temporal data processing pipeline, DataFul Explainable MultivariatE coRrelatIonal Temporal Artificial inTElligence (EMeriTAte+DF), bridging numerical-driven temporal data classification with an event-based one through verified artificial intelligence principles, enabling human-explainable results. This was possible through a preliminary a posteriori explainable phase describing the numerical input data in terms of concurrent constituents with numerical pay…

Multimodal Behavioral Patterns Analysis with Eye-Tracking and LLM-Based Reasoning
Dongyang Guo, Yasmeen Abdrabou, Enkeleda Thaqi, Enkelejda Kasneci
https://arxiv.org/abs/2507.18252

Multimodal Behavioral Patterns Analysis with Eye-Tracking and LLM-Based Reasoning
Eye-tracking data reveals valuable insights into users' cognitive states but is difficult to analyze due to its structured, non-linguistic nature. While large language models (LLMs) excel at reasoning over text, they struggle with temporal and numerical data. This paper presents a multimodal human-AI collaborative framework designed to enhance cognitive pattern extraction from eye-tracking signals. The framework includes: (1) a multi-stage pipeline using horizontal and vertical segmentation alo…

MountainLion: A Multi-Modal LLM-Based Agent System for Interpretable and Adaptive Financial Trading
Siyi Wu, Zhaoyang Guan, Leyi Zhao, Xinyuan Song, Xinyu Ying, Hanlin Zhang, Michele Pak, Yangfan He, Yi Xin, Jianhui Wang, Tianyu Shi
https://arxiv.org/abs/2507.20474

MountainLion: A Multi-Modal LLM-Based Agent System for Interpretable and Adaptive Financial Trading
Cryptocurrency trading is a challenging task requiring the integration of heterogeneous data from multiple modalities. Traditional deep learning and reinforcement learning approaches typically demand large training datasets and encode diverse inputs into numerical representations, often at the cost of interpretability. Recent progress in large language model (LLM)-based agents has demonstrated the capacity to process multi-modal data and support complex investment decision-making. Building on t…

ByteGen: A Tokenizer-Free Generative Model for Orderbook Events in Byte Space
Yang Li, Zhi Chen
https://arxiv.org/abs/2508.02247 https://arxiv.org/pdf/2508…

ByteGen: A Tokenizer-Free Generative Model for Orderbook Events in Byte Space
Generative modeling of high-frequency limit order book (LOB) dynamics is a critical yet unsolved challenge in quantitative finance, essential for robust market simulation and strategy backtesting. Existing approaches are often constrained by simplifying stochastic assumptions or, in the case of modern deep learning models like Transformers, rely on tokenization schemes that affect the high-precision, numerical nature of financial data through discretization and binning. To address these limitat…

Finite-time gradient blow-up and shock formation in Israel-Stewart theory: Bulk, shear, and diffusion regimes
F\'abio S. Bemfica
https://arxiv.org/abs/2508.04717 https://

Finite-time gradient blow-up and shock formation in Israel-Stewart theory: Bulk, shear, and diffusion regimes
We present the first demonstration of finite-time gradient blow-ups in Israel-Stewart (IS) theories with 1+1D plane symmetry, mathematically showing the existence of smooth initial data that can evolve into shocks across three regimes: pure bulk viscosity, shear viscosity, and diffusion. Through numerical simulations of bulk-viscous fluids, we verify that these shocks satisfy Rankine-Hugoniot conditions, exhibit characteristic velocity crossing (Mach number obeys $\mathcal{M}_u > 1 > \mathcal{M…

Analysis of A Mixed Finite Element Method for Poisson's Equation with Rough Boundary Data
Huadong Gao, Yuhui Huang, Wen Xie
https://arxiv.org/abs/2507.00697

Analysis of A Mixed Finite Element Method for Poisson's Equation with Rough Boundary Data
This paper is concerned with finite element methods for Poisson's equation with rough boundary data. Conventional methods require that the boundary data $g$ of the problem belongs to $H^{1/2} (\partial Ω)$. However, in many applications one has to consider the case when $g$ is in $L^2(\partial Ω)$ only. To this end, very weak solutions are considered to establish the well-posedness of the problem. Most previously proposed numerical methods use regularizations of the boundary data. The main pu…

A Closed-Form Approach to Oscillatory Integrals in Level-Crossing Physics
Maseim B. Kenmoe, Anicet D. Kammogne
https://arxiv.org/abs/2506.23385 https://

A Closed-Form Approach to Oscillatory Integrals in Level-Crossing Physics
We present a closed-form, exact analytical solution, valid at finite times, to a class of multiple integrals with highly oscillatory kernels. Our approach leverages the intimate connection between these integrals and the minimal level-crossing model, namely the Landau-Zener model. Benchmarking against data from numerical simulations demonstrates excellent agreement validating our analytical method. Impacts of our results in level-crossing dynamics are also discussed. A dedicated Mathematica pac…

This https://arxiv.org/abs/2502.16356 has been replaced.
initial toot: https://mastoxiv.page/@ar…

Analysis of In-cylinder Flow Structures and Turbulence in a Laboratory Scale Engine using Direct Numerical Simulations
In-cylinder flow structures and turbulence characteristics are investigated using direct numerical simulations (DNS) in a laboratory-scale engine at technically relevant engine speeds (1500 and 2500 rpm at full load). The data is computed for 12 compression-expansion cycles at each engine speed with initial conditions derived from precursor large eddy simulations (LES) validated against experimental data. Analysis of the tumble ratio indicates significant cycle-to-cycle variation, with lower va…

This https://arxiv.org/abs/2504.04375 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csCE_…

Self-Guided Diffusion Model for Accelerating Computational Fluid Dynamics
Machine learning methods, such as diffusion models, are widely explored as a promising way to accelerate high-fidelity fluid dynamics computation via a super-resolution process from faster-to-compute low-fidelity input. However, existing approaches usually make impractical assumptions that the low-fidelity data is down-sampled from high-fidelity data. In reality, low-fidelity data is produced by numerical solvers that use a coarser resolution. Solver-generated low-fidelity data usually sacrific…

SIP-IFVM: An observation-based magnetohydrodynamic model of coronal mass ejection
Haopeng Wang, Jinhan Guo, Stefaan Poedts, Andrea Lani, Luis Linan, Tinatin Baratashvili, Liping Yang, Hyun-Jin Jeong, Wenwen Wei, Caixia Li, Yun Yang, Yucong Li, Hao Wu, Yang Guo, Brigitte Schmieder
https://arxiv.org/abs/2506.19711

SIP-IFVM: An observation-based magnetohydrodynamic model of coronal mass ejection
Currently, achieving a balance between computational efficiency, accuracy, and numerical stability in CME simulations, particularly in the sub-Alfv{'e}nic coronal region, remains a significant challenge. This paper aims to address the challenge by integrating observational data and developing advanced numerical algorithms, focusing on reproducing large-scale CME evolutions that are consistent with observations in the coronal region. Based on the recently developed fully implicit thermodynamic M…

QC-OT: Optimal Transport with Quasiconformal Mapping
Yuping Lv, Qi Zhao, Xuebin Chang, Wei Zeng
https://arxiv.org/abs/2507.01456 https://

QC-OT: Optimal Transport with Quasiconformal Mapping
The optimal transport (OT) map offers the most economical way to transfer one probability measure distribution to another. Classical OT theory does not involve a discussion of preserving topological connections and orientations in transmission results and processes. Existing numerical and geometric methods for computing OT seldom pays specific attention on this aspect. Especially, when dealing with the triangular mesh data, the known semi-discrete geometric OT (sd-OT) method employs critical op…

DATA-DRIVEN PRONTO: a Model-free Solution for Numerical Optimal Control
Marco Borghesi, Lorenzo Sforni, Giuseppe Notarstefano
https://arxiv.org/abs/2506.15465

DATA-DRIVEN PRONTO: a Model-free Solution for Numerical Optimal Control
This article addresses the problem of data-driven numerical optimal control for unknown nonlinear systems. In our scenario, we suppose to have the possibility of performing multiple experiments (or simulations) on the system. Experiments are performed by relying on a data-driven tracking controller able to steer the system towards a desired reference. Our proposed DATA-DRIVEN PRONTO algorithm iteratively refines a tentative solution of the optimal control problem by computing an approximate des…

Ocean-E2E: Hybrid Physics-Based and Data-Driven Global Forecasting of Extreme Marine Heatwaves with End-to-End Neural Assimilation
Ruiqi Shu, Yuan Gao, Hao Wu, Ruijian Gou, Yanfei Xiang, Fan Xu, Qingsong Wen, Xian Wu, Xiaomeng Huang
https://arxiv.org/abs/2505.22071

Ocean-E2E: Hybrid Physics-Based and Data-Driven Global Forecasting of Extreme Marine Heatwaves with End-to-End Neural Assimilation
This work focuses on the end-to-end forecast of global extreme marine heatwaves (MHWs), which are unusually warm sea surface temperature events with profound impacts on marine ecosystems. Accurate prediction of extreme MHWs has significant scientific and financial worth. However, existing methods still have certain limitations, especially in the most extreme MHWs. In this study, to address these issues, based on the physical nature of MHWs, we created a novel hybrid data-driven and numerical MH…

Binary black holes in the heat of merger
Samanwaya Mukherjee, Sayak Datta, Sukanta Bose, Khun Sang Phukon
https://arxiv.org/abs/2506.22363 https://

Binary black holes in the heat of merger
A black hole binary approaching merger undergoes changes in its inspiral rate as energy and angular momentum are lost from the orbits into the horizons. This effect strengthens as the black holes come closer. We use numerical relativity data to model this so-called tidal heating in the strong gravity regime. We present a frequency-domain approximant for nonspinning black hole binaries that accounts for tidal heating effects up to the merger frequency. The approximant includes horizon parameters…

From Interviews to Equations: A Multi-Phase System Dynamics Model of Engineering Student Engagement
Mohammed A. Alrizqi
https://arxiv.org/abs/2507.00382 ht…

From Interviews to Equations: A Multi-Phase System Dynamics Model of Engineering Student Engagement
This study presents a systematic approach for converting qualitative data into quantitative parameters within a system dynamics (SD) framework, focusing on modeling engineering student engagement. Although SD typically relies on numerical inputs, important "soft" factors such as motivation, confidence, and a sense of belonging have often been neglected due to the challenge of measurement. Semi-structured interviews were conducted with mechanical engineering students in a Learning Studio environ…

Compact representation and long-time extrapolation of real-time data for quantum systems
Andre Erpenbeck, Yuanran Zhu, Yang Yu, Lei Zhang, Richard Gerum, Olga Goulko, Chao Yang, Guy Cohen, Emanuel Gull
https://arxiv.org/abs/2506.13760

Compact representation and long-time extrapolation of real-time data for quantum systems
Representing real-time data as a sum of complex exponentials provides a compact form that enables both denoising and extrapolation. As a fully data-driven method, the Estimation of Signal Parameters via Rotational Invariance Techniques (ESPRIT) algorithm is agnostic to the underlying physical equations, making it broadly applicable to various observables and experimental or numerical setups. In this work, we consider applications of the ESPRIT algorithm primarily to extend real-time dynamical d…

This https://arxiv.org/abs/2310.01147 has been replaced.
link: https://scholar.google.com/scholar?q=a

Optimizing Symbol Visibility through Displacement
In information visualization, the position of symbols often encodes associated data values. When visualizing data elements with both a numerical and a categorical dimension, positioning in the categorical axis admits some flexibility. This flexibility can be exploited to reduce symbol overlap, and thereby increase legibility. In this paper, we initialize the algorithmic study of optimizing symbol legibility via a limited displacement of the symbols. Specifically, we consider closed unit square …

Effects of lower floating-point precision on scale-resolving numerical simulations of turbulence
Martin Karp, Ronith Stanly, Timofey Mukha, Luca Galimberti, Siavash Toosi, Hang Song, Lissandro Dalcin, Saleh Rezaeiravesh, Niclas Jansson, Stefano Markidis, Matteo Parsani, Sanjeeb Bose, Sanjiva Lele, Philipp Schlatter
https://arxiv…

Effects of lower floating-point precision on scale-resolving numerical simulations of turbulence
Modern computing clusters offer specialized hardware for reduced-precision arithmetic that can speed up the time to solution significantly. This is possible due to a decrease in data movement, as well as the ability to perform arithmetic operations at a faster rate. However, for high-fidelity simulations of turbulence, such as direct and large-eddy simulation, the impact of reduced precision on the computed solution and the resulting uncertainty across flow solvers and different flow cases have…

Measuring the Unmeasurable? Systematic Evidence on Scale Transformations in Subjective Survey Data
Caspar Kaiser, Anthony Lepinteur
https://arxiv.org/abs/2507.16440 https://

Measuring the Unmeasurable? Systematic Evidence on Scale Transformations in Subjective Survey Data
Economists routinely use survey measures of, for example, risk preferences, trust, political attitudes, or wellbeing. The literature generally treats numerical response categories as if they represent equal psychological intervals. We provide the first systematic test of this assumption, developing a general framework to quantify how easily results can be overturned when this linearity assumption is relaxed. Using original experimental data, we show that respondents interpret survey scales in w…

Radio signatures of AGN-wind-driven shocks in elliptical galaxies: From simulations to observations
Haojie Xia, Feng Yuan, Zhiyuan Li, Bocheng Zhu
https://arxiv.org/abs/2507.19716

Radio signatures of AGN-wind-driven shocks in elliptical galaxies: From simulations to observations
We investigate the synchrotron emission signatures of shocks driven by active galactic nucleus (AGN) wind in elliptical galaxies based on our two-dimensional axisymmetric hydrodynamic $\textit{MACER}$ numerical simulations. Using these simulation data, we calculate the synchrotron radiation produced by nonthermal electrons accelerated at shocks, adopting reasonable assumptions for the magnetic field and relativistic electron distribution (derived from diffusive shock acceleration theory), and p…

Numerical analysis of quasiperiodic oscillations in the Hartle-Thorne spacetime
K. Boshkayev, T. Konysbayev, Ye. Kurmanov, M. Muccino, H. Quevedo
https://arxiv.org/abs/2506.11581 …

Numerical analysis of quasiperiodic oscillations in the Hartle-Thorne spacetime
We numerically analyze quasiperiodic oscillations (QPOs) using a well-established spacetime model with neutron star sources. Within the framework of general relativity, we present expressions for the fundamental frequencies of test particles in the gravitational field of a slowly rotating and slightly deformed compact object defined by the Hartle-Thorne (HT) metric. Using the Relativistic Precession Model (RPM) formulated by Stella and Morinsk, we examine quasiperiodic oscillation data from eig…

Deep Learning Weather Models for Subregional Ocean Forecasting: A Case Study on the Canary Current Upwelling System
Giovanny C-Londo\~no, Javier S\'anchez, \'Angel Rodr\'iguez-Santana
https://arxiv.org/abs/2505.24429

Deep Learning Weather Models for Subregional Ocean Forecasting: A Case Study on the Canary Current Upwelling System
Oceanographic forecasting impacts various sectors of society by supporting environmental conservation and economic activities. Based on global circulation models, traditional forecasting methods are computationally expensive and slow, limiting their ability to provide rapid forecasts. Recent advances in deep learning offer faster and more accurate predictions, although these data-driven models are often trained with global data from numerical simulations, which may not reflect reality. The emer…

Multi-Machine Scaling Laws for Fuel and Impurity Puffing Rates Sufficient for Detachment Access: a Systematic Review of Magnetic Confinement Fusion Devices
M. Moscheni, A. Herrmann, R. Kembleton, M. Kryjak, S. Lazerson, F. Levi, M. Siccinio, P. Staniec, T. Giegerich, C. Tantos, the Gauss Fusion GmbH Team
https://arxiv.org/abs/2507.20523

Multi-Machine Scaling Laws for Fuel and Impurity Puffing Rates Sufficient for Detachment Access: a Systematic Review of Magnetic Confinement Fusion Devices
From a database of 457 experimental and numerical data from 32 machines among solid-walled tokamaks, stellarators and linear plasma devices, we derive physics-informed multi-machine scaling laws predictive of fuel and impurity puffing rates sufficient to access plasma detachment -- leading candidate for a reactor-relevant solution to the open issue of plasma-wall interaction. Validation of our laws in up to 40 plasmas in low- and high-confinement mode also featuring advanced configurations demo…

Mechanical enhancement of quantum oscillations
Maximilian Daschner, Ivan Kokanovi\'c, F. Malte Grosche
https://arxiv.org/abs/2507.02612 https://…

Mechanical enhancement of quantum oscillations
We investigate quantum oscillation measurements in the Dirac nodal-line semimetal TaNiTe$_5$ which exhibit a strongly enhanced amplitude in the magnetoresistance. We show that mechanical properties of the measurement setup in combination with de Haas - van Alphen oscillations in the magnetic torque can cause this enhancement in the measured resistance, without involvement of any topological properties in this material. To support the empirical data, a numerical model is provided, showing good a…

This https://arxiv.org/abs/2407.11746 has been replaced.
initial toot: https://mastoxiv.page/@ar…

Sparse data assimilation for under-resolved large-eddy simulations
The need for accurate and fast scale-resolving simulations of fluid flows, where turbulent dispersion is a crucial physical feature, is evident. Large-eddy simulations (LES) are computationally more affordable than direct numerical simulations, but their accuracy depends on sub-grid scale models and the quality of the computational mesh. In order to compensate related errors, a data assimilation approach for LES is devised in this work. The presented method is based on variational assimilatio…

Narrate2Nav: Real-Time Visual Navigation with Implicit Language Reasoning in Human-Centric Environments
Amirreza Payandeh, Anuj Pokhrel, Daeun Song, Marcos Zampieri, Xuesu Xiao
https://arxiv.org/abs/2506.14233

Narrate2Nav: Real-Time Visual Navigation with Implicit Language Reasoning in Human-Centric Environments
Large Vision-Language Models (VLMs) have demonstrated potential in enhancing mobile robot navigation in human-centric environments by understanding contextual cues, human intentions, and social dynamics while exhibiting reasoning capabilities. However, their computational complexity and limited sensitivity to continuous numerical data impede real-time performance and precise motion control. To this end, we propose Narrate2Nav, a novel real-time vision-action model that leverages a novel self-su…

This https://arxiv.org/abs/2112.09041 has been replaced.
link: https://scholar.google.com/scholar?q=a

Ahlfors-regular conformal dimension and energies of graph maps
For a hyperbolic rational map $f$ with connected Julia set, we give upper and lower bounds on the Ahlfors-regular conformal dimension of its Julia set $J_f$ from a family of energies of associated graph maps. Concretely, the dynamics of $f$ is faithfully encoded by a pair of maps $π, ϕ: G_1 \to G_0$ between finite graphs that satisfies a natural expanding condition. Associated to this combinatorial data, for each $q \geq 1$, is a numerical invariant $\overline{E}^q[π,ϕ]$, its asymptotic $q$…

This https://arxiv.org/abs/2409.03686 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Numerical spectral analysis of Cauchy-type inverse problems: A probabilistic approach
We investigate the inverse Cauchy and data completion problems for elliptic partial differential equations in a bounded domain $D \subset \mathbb{R}^d$, $d \ge 2$, with a special emphasis on the steady-state heat conduction in anisotropic media. More precisely, boundary conditions are prescribed on an accessible part of the boundary $\varnothing \neq Γ_0 \subsetneqq \partial{D}$ and/or internal conditions are available inside the domain $D$ and the aim is to reconstruct the solution to these i…

Integral fractional viscoelastic models in SPH: LAOS simulations versus experimental data
Luca Santelli, Adolfo V\'azquez-Quesada, Aizzati Burgoa, Aitor Arriaga, Ritardo Hernandez, Marco Ellero
https://arxiv.org/abs/2507.14149

Integral fractional viscoelastic models in SPH: LAOS simulations versus experimental data
The rheological behaviour of a polymer was investigated by performing numerical simulations in complex flow and comparing them to experiments. For our simulations, we employed a Smoothed Particle Hydrodynamics scheme, utilizing an integral fractional model based on the K-BKZ framework. The results are compared with experiments performed on melt-state isotactic polypropylene under medium and large amplitude oscillatory shear. The numerical results are in good agreement with the experimental da…

PICore: Physics-Informed Unsupervised Coreset Selection for Data Efficient Neural Operator Training
Anirudh Satheesh, Anant Khandelwal, Mucong Ding, Radu Balan
https://arxiv.org/abs/2507.17151

PICore: Physics-Informed Unsupervised Coreset Selection for Data Efficient Neural Operator Training
Neural operators offer a powerful paradigm for solving partial differential equations (PDEs) that cannot be solved analytically by learning mappings between function spaces. However, there are two main bottlenecks in training neural operators: they require a significant amount of training data to learn these mappings, and this data needs to be labeled, which can only be accessed via expensive simulations with numerical solvers. To alleviate both of these issues simultaneously, we propose PICore…

Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations
Difeng Cai, Paulina Sep\'ulveda
https://arxiv.org/abs/2506.23344

Data-Driven Self-Supervised Learning for the Discovery of Solution Singularity for Partial Differential Equations
The appearance of singularities in the function of interest constitutes a fundamental challenge in scientific computing. It can significantly undermine the effectiveness of numerical schemes for function approximation, numerical integration, and the solution of partial differential equations (PDEs), etc. The problem becomes more sophisticated if the location of the singularity is unknown, which is often encountered in solving PDEs. Detecting the singularity is therefore critical for developing …

Study of $\tau\rightarrow e M^ M^-$ decays in the N-B-LSSM
Rong-Zhi Sun, Shu-Min Zhao, Shuang Di, Xing-Xing Dong
https://arxiv.org/abs/2507.01276 https://…

Study of $τ\rightarrow e M^+ M^-$ decays in the N-B-LSSM
Within the framework of the next to the minimal supersymmetric (SUSY) extension of the Standard Model (SM) with a local B-L gauge symmetry (N-B-LSSM), we study lepton flavor violating (LFV) $τ\rightarrow e M^+ M^-$ decays: $τ\rightarrow e π^+π^-$,~$τ\rightarrow e π^+K^-$,~$τ\rightarrow e K^+K^-$. According to the latest experimental data, the influence of different sensitive parameters on the branching ratios is considered. It can be seen from the numerical analysis that the main sensiti…

Tails from the Bulk: Gravitational Decay in AdS$_5$
John R. V. Crump, Jorge E. Santos
https://arxiv.org/abs/2506.18991 https://arxiv.…

Tails from the Bulk: Gravitational Decay in AdS$_5$
We study gravitational perturbations of Schwarzschild-AdS black holes in $d = 5$ and identify a regime of late-time power-law decay for smooth initial data. Based on an analysis of the quasinormal mode spectrum, we predict and characterise this decay behaviour. We perform fully nonlinear numerical evolutions with long integration times that support the prediction and exhibit no signs of instability. Remarkably, the decay is modulated by a universal oscillatory pattern, consistent with subleadin…

HPC-AI Coupling Methodology for Scientific Applications
Yutong Lu, Dan Huang, Pin Chen
https://arxiv.org/abs/2507.01025 https://arxiv…

HPC-AI Coupling Methodology for Scientific Applications
Artificial intelligence (AI) technologies have fundamentally transformed numerical-based high-performance computing (HPC) applications with data-driven approaches and endeavored to address existing challenges, e.g. high computational intensity, in various scientific domains. In this study, we explore the scenarios of coupling HPC and AI (HPC-AI) in the context of emerging scientific applications, presenting a novel methodology that incorporates three patterns of coupling: surrogate, directive, …

Convex computation of regions of attraction from data using Sums-of-Squares programming
Oumayma Khattabi, Matteo Tacchi-B\'enard, Sorin Olaru
https://arxiv.org/abs/2507.14073 …

Convex computation of regions of attraction from data using Sums-of-Squares programming
The paper concentrates on the analysis of the region of attraction (ROA) for unknown autonomous dynamical systems. The aim is to explore a data-driven approach based on moment-sum-of-squares (SoS) hierarchy, which enables novel RoA outer approximations despite the reduced information on the structure of the dynamics. The main contribution of this work is bypassing the system model and, consequently, the recurring constraint on its polynomial structure. Numerical experimentation showcases the in…

A Data-Driven Approach for Predicting Hydrodynamic Forces on Spherical Particles Using Volume Fraction Representations
Alexander Metelkin, Sam Jacob Jacob, Bernhard Vowinckel
https://arxiv.org/abs/2507.20767

A Data-Driven Approach for Predicting Hydrodynamic Forces on Spherical Particles Using Volume Fraction Representations
Particle-laden flows are simulated at various scales using numerical techniques that range from particle-resolved Direct Numerical Simulations (pr-DNS) for small-scale systems to Lagrange point-particle methods for laboratory-scale problems, and Euler-Euler approaches for larger-scale applications. Recent research has been particularly focused on the development of both physics-based and data-driven closures to enhance the accuracy of the Lagrangian point-particle approach by leveraging highly …

Computing and compressing local vertex functions in imaginary and real frequencies from the multipoint numerical renormalization group using quantics tensor cross interpolation
Markus Frankenbach, Marc Ritter, Mathias Pelz, Nepomuk Ritz, Jan von Delft, Anxiang Ge
https://arxiv.org/abs/2506.13359

Computing and compressing local vertex functions in imaginary and real frequencies from the multipoint numerical renormalization group using quantics tensor cross interpolation
The multipoint numerical renormalization group (mpNRG) is a powerful impurity solver that provides accurate spectral data useful for computing local, dynamic correlation functions in imaginary or real frequencies non-perturbatively across a wide range of interactions and temperatures. It gives access to a local, non-perturbative four-point vertex in imaginary and real frequencies, which can be used as input for subsequent computations such as diagrammatic extensions of dynamical mean--field the…

Numerical evaluation of deliberative discussions of the UK food system: stimuli, demographics, and opinion reversion
John Buckell, Thomas Hancock
https://arxiv.org/abs/2506.14102 …

Numerical evaluation of deliberative discussions of the UK food system: stimuli, demographics, and opinion reversion
There is increasing acknowledgement - including from the UK government - of the benefit of employing deliberative processes (deliberative fora, citizens' juries, etc.). Evidence suggests that the qualitative reporting of deliberative fora are often unclear or imprecise. If this is the case, their value to policymakers could be diminished. In this study we develop numerical methods of deliberative processes to document people's preferences, as a complement to qualitative analysis. Data are taken…

Summary Statistics of Large-scale Model Outputs for Observation-corrected Outputs
Atlanta Chakraborty, Julie Bessac
https://arxiv.org/abs/2506.15845 https:…

Summary Statistics of Large-scale Model Outputs for Observation-corrected Outputs
Physics-based models capture broad spatial and temporal dynamics, but often suffer from biases and numerical approximations, while observations capture localized variability but are sparse. Integrating these complementary data modalities is important to improving the accuracy and reliability of model outputs. Meanwhile, physics-based models typically generate large outputs that are challenging to manipulate. In this paper, we propose Sig-PCA, a space-time framework that integrates summary stati…

Replaced article(s) found for math.NA. https://arxiv.org/list/math.NA/new
[1/1]:
- A Model-Consistent Data-Driven Computational Strategy for PDE Joint Inversion Problems
Kui Ren, Lu Zhang

Numerical Modeling of n-Hexane Pyrolysis with an Optimized Kinetic Mechanism in a Hydrogen Plasma Reactor
Subin Choi, Chanmi Jung, Dae Hoon Lee, Jeongan Choi, Jaekwang Kim
https://arxiv.org/abs/2506.13789

Numerical Modeling of n-Hexane Pyrolysis with an Optimized Kinetic Mechanism in a Hydrogen Plasma Reactor
The physicochemical mechanisms underlying the pyrolysis of n-hexane in a high temperature Ar-H2 environment were investigated for plasma pyrolysis process. An optimal chemical kinetics model was developed using the Reaction Mechanism Generator (RMG), an automated tool for constructing reaction mechanisms. This model was validated through 0-D analyses, where simulation result were compared with existing kinetic models (LLNL,JetSurf) and experimental data from conventional n-hexane pyrolysis. Sub…

Identifying Solution Constraints for ODE Systems
Nicolae Tarfulea
https://arxiv.org/abs/2507.15805 https://arxiv.org/pdf/2507.15805…

Identifying Solution Constraints for ODE Systems
This work develops a framework to discover relations between the components of the solution to a given initial-value problem for a first-order system of ordinary differential equations. This is done by using sparse identification techniques on the data represented by the numerical solution of the initial-value problem at hand. The only assumption is that there are only a few terms that connects the components, so that the mathematical relations to be discovered are sparse in the set of possible…

A comparison of stretched-grid and limited-area modelling for data-driven regional weather forecasting
Jasper S. Wijnands, Michiel Van Ginderachter, Bastien Fran\c{c}ois, Sophie Buurman, Piet Termonia, Dieter Van den Bleeken
https://arxiv.org/abs/2507.18378

A comparison of stretched-grid and limited-area modelling for data-driven regional weather forecasting
Regional machine learning weather prediction (MLWP) models based on graph neural networks have recently demonstrated remarkable predictive accuracy, outperforming numerical weather prediction models at lower computational costs. In particular, limited-area model (LAM) and stretched-grid model (SGM) approaches have emerged for generating high-resolution regional forecasts, based on initial conditions from a regional (re)analysis. While LAM uses lateral boundaries from an external global model, S…

Physics-Informed Neural Networks with Dynamical Boundary Constraints
Andr\'es Mart\'inez-Esteban, Pablo Calvo-Barl\'es, Luis Mart\'in-Moreno, Sergio G Rodrigo
https://arxiv.org/abs/2507.21800

Physics-Informed Neural Networks with Dynamical Boundary Constraints
Physics-informed neural networks (PINNs) are numerical solvers that embed all the physical information of a system into the loss function of a neural network. In this way the learned solution accounts for data (if available), the governing differential equations, or any other constraint known of the physical problem. However, they face serious issues, notably their tendency to converge on trivial or misleading solutions. The latter occurs when, although the loss function reaches low values the …

Bridging Equilibrium and Kinetics Prediction with a Data-Weighted Neural Network Model of Methane Steam Reforming
Zofia Pizo\'n, Shinji Kimijima, Grzegorz Brus
https://arxiv.org/abs/2506.17224

Bridging Equilibrium and Kinetics Prediction with a Data-Weighted Neural Network Model of Methane Steam Reforming
Hydrogen's role is growing as an energy carrier, increasing the need for efficient production, with methane steam reforming being the most widely used technique. This process is crucial for applications like fuel cells, where hydrogen is converted into electricity, pushing for reactor miniaturization and optimized process control through numerical simulations. Existing models typically address either kinetic or equilibrium regimes, limiting their applicability. Here we show a surrogate model ca…

Numerical analysis of scattered point measurement-based regularization for backward problems for fractional wave equations
Dakang Cen, Zhiyuan Li, Wenlong Zhang
https://arxiv.org/abs/2506.18948

Numerical analysis of scattered point measurement-based regularization for backward problems for fractional wave equations
In this work, our aim is to reconstruct the unknown initial value from terminal data. We develop a numerical framework on nonuniform time grids for fractional wave equations under the lower regularity assumptions. Then, we introduce a regularization method that effectively handles scattered point measurements contaminated with stochastic noise. The optimal error estimates of stochastic convergence not only balance discretization errors, the noise, and the number of observation points, but also …

Numerical Artifacts in Learning Dynamical Systems
Bing-Ze Lu, Richard Tsai
https://arxiv.org/abs/2507.14491 https://arxiv.org/pdf/250…

Numerical Artifacts in Learning Dynamical Systems
In many applications, one needs to learn a dynamical system from its solutions sampled at a finite number of time points. The learning problem is often formulated as an optimization problem over a chosen function class. However, in the optimization procedure, it is necessary to employ a numerical scheme to integrate candidate dynamical systems and assess how their solutions fit the data. This paper reveals potentially serious effects of a chosen numerical scheme on the learning outcome. In …

Three-dimensional numerical study on hydrogen bubble growth at electrode
Wei Qin, Tian Long, Jacob Maarek, St\'ephane Zaleski
https://arxiv.org/abs/2507.15582 https://

Three-dimensional numerical study on hydrogen bubble growth at electrode
3D direct numerical simulation of electrolysis is applied to investigate the growth and detachment of bubbles at electrodes. The moving gas-liquid interface is modeled employing the VOF-based method. To ensure the accuracy of the simulations, a mesh-independence study has been performed. The simulations include the growth phase of the bubbles followed by their detachment from the electrode surface and the results are validated with analytical models and experimental data. The bubble g…

Exponential Runge-Kutta Galerkin finite element method for a reaction-diffusion system with nonsmooth initial data
Runjie Zhang, Jinwei Fang, Shuo Yang
https://arxiv.org/abs/2507.15345

Exponential Runge-Kutta Galerkin finite element method for a reaction-diffusion system with nonsmooth initial data
This study presents a numerical analysis of the Field-Noyes reaction-diffusion model with nonsmooth initial data, employing a linear Galerkin finite element method for spatial discretization and a second-order exponential Runge-Kutta scheme for temporal integration. The initial data are assumed to reside in the fractional Sobolev space H^gamma with 0 < gamma < 2, where classical regularity conditions are violated, necessitating specialized error analysis. By integrating semigroup techniques and…

mLaSDI: Multi-stage latent space dynamics identification
William Anderson, Kevin Chung, Youngsoo Choi
https://arxiv.org/abs/2506.09207 https://

mLaSDI: Multi-stage latent space dynamics identification
Determining accurate numerical solutions of partial differential equations (PDEs) is an important task in many scientific disciplines. However, solvers can be computationally expensive, leading to the development of reduced-order models (ROMs). Recently, Latent Space Dynamics Identification (LaSDI) was proposed as a data-driven, non-intrusive ROM framework. LaSDI compresses the training data using an autoencoder and learns a system of user-chosen ordinary differential equations (ODEs), which go…

Higher-order transmissibility and its linear approximation for in-service crack identification in train wheelset axles
Ehsan Naghizadeh, Paolo Tiso, Eleni Chatzi
https://arxiv.org/abs/2507.18636

Higher-order transmissibility and its linear approximation for in-service crack identification in train wheelset axles
In-service structural health monitoring is a so far rarely exploited, yet potent option for early-stage crack detection and identification in train wheelset axles. This procedure is non-trivial to enforce on the basis of a purely data-driven approach and typically requires the adoption of numerical, e.g. finite element-based, simulation schemes of the dynamic behavior of these axles. Damage in this particular case can be formulated as a breathing crack problem, which further complicates simulat…

This https://arxiv.org/abs/2408.08129 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Efficient and scalable atmospheric dynamics simulations using non-conforming meshes
We present the massively parallel performance of a $h$-adaptive solver for atmosphere dynamics that allows for non-conforming mesh refinement. The numerical method is based on a Discontinuous Galerkin (DG) spatial discretization, highly scalable thanks to its data locality properties, and on a second order Implicit-Explicit Runge-Kutta (IMEX-RK) method for time discretization, particularly well suited for low Mach number flows. Simulations with non-conforming meshes for flows over orography can…

An integrated theoretical, experimental, and numerical study of small-amplitude water waves
Lennon \'O N\'araigh, Nicolas Farault, Nicola Young
https://arxiv.org/abs/2507.18403

An integrated theoretical, experimental, and numerical study of small-amplitude water waves
We introduce an inexpensive experimental setup for analyzing free-surface water waves: a $1\,\mathrm{m}$-long tabletop flume made from perspex, driven by a variable-frequency piston wavemaker built from Lego. Using mobile-phone video capture, we collect experimental data and compare it with predictions from linear gravity-capillary wave theory and with multiphase simulations performed in OpenFOAM. We find excellent quantitative agreement across all three approaches. Our setup may be valuable fo…

Numerical approximation of a PDE-constrained Optimization problem that appears in Data-Driven Computational Mechanics
Pedro B. Bazon, Cristian G. Gebhardt, Gustavo C. Buscaglia, Roberto F. Ausas
https://arxiv.org/abs/2506.10894

Numerical approximation of a PDE-constrained Optimization problem that appears in Data-Driven Computational Mechanics
We investigate an optimization problem that arises when working within the paradigm of Data-Driven Computational Mechanics. In the context of the diffusion-reaction problem, such an optimization problem seeks for the continuous primal fields (gradient and flux) that are closest to some predefined discrete fields taken from a material data set. The optimization is performed over primal fields that satisfy the physical conservation law and the geometrical compatibility. We consider a reaction ter…

Dynamics of a data-driven low-dimensional model of Rayleigh-Benard convection
Qiwei Chen, Andres Castillo-Castellanos, C. Ricardo Constante-Amores
https://arxiv.org/abs/2507.11858

Dynamics of a data-driven low-dimensional model of Rayleigh-Benard convection
We present a multiscale, data-driven reduced-order framework for two-dimensional Rayleigh Benard convection in a square cell at high Rayleigh number, where the flow exhibits intermittent large-scale circulation reversals. Starting from direct numerical simulations using Nek5000, we extract a set of energy-ranked POD modes from the combined velocity and temperature fields. A Gaussian filter decomposes the temporal coefficients into low-frequency (slow) and high-frequency (fast) components, enabl…

Neural-operator element method: Efficient and scalable finite element method enabled by reusable neural operators
Weihang Ouyang, Yeonjong Shin, Si-Wei Liu, Lu Lu
https://arxiv.org/abs/2506.18427

Neural-operator element method: Efficient and scalable finite element method enabled by reusable neural operators
The finite element method (FEM) is a well-established numerical method for solving partial differential equations (PDEs). However, its mesh-based nature gives rise to substantial computational costs, especially for complex multiscale simulations. Emerging machine learning-based methods (e.g., neural operators) provide data-driven solutions to PDEs, yet they present challenges, including high training cost and low model reusability. Here, we propose the neural-operator element method (NOEM) by s…

Is memory all you need? Data-driven Mori-Zwanzig modeling of Lagrangian particle dynamics in turbulent flows
Xander de Wit, Alessandro Gabbana, Michael Woodward, Yen Ting Lin, Federico Toschi, Daniel Livescu
https://arxiv.org/abs/2507.16058

Is memory all you need? Data-driven Mori-Zwanzig modeling of Lagrangian particle dynamics in turbulent flows
The dynamics of Lagrangian particles in turbulence play a crucial role in mixing, transport, and dispersion processes in complex flows. Their trajectories exhibit highly non-trivial statistical behavior, motivating the development of surrogate models that can reproduce these trajectories without incurring the high computational cost of direct numerical simulations of the full Eulerian field. This task is particularly challenging because reduced-order models typically lack access to the full set…

Towards Real-time Structural Dynamics Simulation with Graph-based Digital Twin Modelling
Jun Zhang, Tong Zhang, Ying Wang
https://arxiv.org/abs/2506.18724 …

Towards Real-time Structural Dynamics Simulation with Graph-based Digital Twin Modelling
Precise and timely simulation of a structure's dynamic behavior is crucial for evaluating its performance and assessing its health status. Traditional numerical methods are often limited by high computational costs and low efficiency, while deep learning approaches offer a promising alternative. However, these data-driven methods still face challenges, such as limited physical interpretability and difficulty in adapting to diverse structural configurations. To address these issues, this study p…

TURB-Smoke. A database of Lagrangian pollutants emitted from point-sources and dispersed in turbulent flows
Luca Biferale, Fabio Bonaccorso, Niccol\`o Cocciaglia, Robin A. Heinonen, Lorenzo Piro
https://arxiv.org/abs/2507.22749

TURB-Smoke. A database of Lagrangian pollutants emitted from point-sources and dispersed in turbulent flows
Identifying the location and characteristics of pollution sources in turbulent flows is challenging, especially for environmental monitoring and emergency response, due to sparse, stochastic, and infrequent cue detection. Even in idealized settings, accurately modeling these phenomena remains highly complex, with realistic representations typically achievable only through experimental or simulation-based data. We introduce TURB-Smoke, a cutting-edge numerical dataset designed for investigating …

An Introduction to Solving the Least-Squares Problem in Variational Data Assimilation
I. Dau\v{z}ickait\.e, M. A. Freitag, S. G\"urol, A. S. Lawless, A. Ramage, J. A. Scott, J. M. Tabeart
https://arxiv.org/abs/2506.09211

An Introduction to Solving the Least-Squares Problem in Variational Data Assimilation
Variational data assimilation is a technique for combining measured data with dynamical models. It is a key component of Earth system state estimation and is commonly used in weather and ocean forecasting. The approach involves a large-scale generalized nonlinear least-squares problem. Solving the resulting sequence of sparse linear subproblems requires the use of sophisticated numerical linear algebra methods. In practical applications, the computational demands severely limit the number of it…

State-based approach to the numerical solution of Dirichlet boundary optimal control problems for the Laplace equation
Ulrich Langer, Richard L\"oscher, Olaf Steinbach, Huidong Yang
https://arxiv.org/abs/2507.11646

State-based approach to the numerical solution of Dirichlet boundary optimal control problems for the Laplace equation
We investigate the Dirichlet boundary control of the Laplace equation, considering the control in $H^{1/2}(\partial Ω)$, which is the natural space for Dirichlet data when the state belongs to $H^1(Ω)$. The cost of the control is measured in the $H^{1/2}(\partial Ω)$ norm that also plays the role of the regularization term. We discuss regularization and finite element error estimates enabling us to derive an optimal relation between the finite element mesh size $h$ and the regularization par…

Robust PDE discovery under sparse and highly noisy conditions via attention neural networks
Shilin Zhang, Yunqing Huang, Nianyu Yi, shihan Zhang
https://arxiv.org/abs/2506.17908

Robust PDE discovery under sparse and highly noisy conditions via attention neural networks
The discovery of partial differential equations (PDEs) from experimental data holds great promise for uncovering predictive models of complex physical systems. In this study, we introduce an efficient automatic model discovery framework, ANN-PYSR, which integrates attention neural networks with the state-of-the-art PySR symbolic regression library. Our approach successfully identifies the governing PDE in six benchmark examples. Compared to the DLGA framework, numerical experiments demonstrate …

Replaced article(s) found for math.NA. https://arxiv.org/list/math.NA/new
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- Detecting null patterns in tensor data
Peter A. Brooksbank, Martin D. Kassabov, James B. Wilson