Tootfinder

Conditionally adaptive augmented Lagrangian method for physics-informed learning of forward and inverse problems using artificial neural networks
Qifeng Hu, Shamsulhaq Basir, Inanc Senocak
https://arxiv.org/abs/2508.15695

Conditionally adaptive augmented Lagrangian method for physics-informed learning of forward and inverse problems using artificial neural networks
We present several advances to the physics and equality constrained artificial neural networks (PECANN) framework that substantially improve its capability to learn solutions of canonical partial differential equations (PDEs). First, we generalize the augmented Lagrangian method (ALM) to support multiple independent penalty parameters, enabling simultaneous enforcement of heterogeneous constraints. Second, we reformulate pointwise constraint enforcement and Lagrange multipliers as expectations …

Rigorous dense graph limit of a model for biological transportation networks
Nuno J. Alves, Jan Haskovec
https://arxiv.org/abs/2507.15829 https://

Rigorous dense graph limit of a model for biological transportation networks
We rigorously derive the dense graph limit of a discrete model describing the formation of biological transportation networks. The discrete model, defined on undirected graphs with pressure-driven flows, incorporates a convex energy functional combining pumping and metabolic costs. It is constrained by a Kirchhoff law reflecting the local mass conservation. We first rescale and reformulate the discrete energy functional as an integral `semi-discrete' functional, where the Kirchhoff law transfor…

A comprehensive approach to the physics of mesons
Angel. S. Miramontes, Jose M. Morgado Chavez, Joannis Papavassiliou, Jan M. Pawlowski
https://arxiv.org/abs/2507.15646

A comprehensive approach to the physics of mesons
We develop a novel approach for the self-consistent solution of coupled sets of Bethe-Salpeter and Schwinger-Dyson equations in QCD. This framework allows us to maintain the axial Ward-Takahashi identities of the theory within advanced approximation schemes, such as the skeleton or three-particle irreducible expansions. For this purpose we reformulate the Schwinger-Dyson equation of the axial-vector vertex such that the bulk of its quantum corrections is expressed in terms of a novel vertex. Cr…

Option pricing under non-Markovian stochastic volatility models: A deep signature approach
Jingtang Ma, Xianglin Wu, Wenyuan Li
https://arxiv.org/abs/2508.15237 https://

Option pricing under non-Markovian stochastic volatility models: A deep signature approach
This paper studies the pricing problem in which the underlying asset follows a non-Markovian stochastic volatility model. Classical partial differential equation methods face significant challenges in this context, as the option prices depend not only on the current state, but also on the entire historical path of the process. To overcome these difficulties, we reformulate the asset dynamics as a rough stochastic differential equation and then represent the rough paths via linear or non-linear …

Surface Stokes Without Inf-Sup Condition
Ricardo H. Nochetto, Mansur Shakipov
https://arxiv.org/abs/2508.13342 https://arxiv.org/pdf/2508.13342

Surface Stokes Without Inf-Sup Condition
For a $d$-dimensional hypersurface of class $C^3$ without boundary, we reformulate the surface Stokes equations as a nonsymmetric indefinite elliptic problem governed by two Laplacians. We then use this elliptic reformulation as a basis for a numerical method based on lifted parametric FEM. Assuming no geometric error for simplicity, we prove its well-posedness, quasi-best approximation in a robust mesh-dependent $H^1$-norm for any polynomial degree, as well as an optimal $L^2$ error estimate f…

Leveraging Geometric Insights in Hyperbolic Triplet Loss for Improved Recommendations
Viacheslav Yusupov, Maxim Rakhuba, Evgeny Frolov
https://arxiv.org/abs/2508.11978 https://

Leveraging Geometric Insights in Hyperbolic Triplet Loss for Improved Recommendations
Recent studies have demonstrated the potential of hyperbolic geometry for capturing complex patterns from interaction data in recommender systems. In this work, we introduce a novel hyperbolic recommendation model that uses geometrical insights to improve representation learning and increase computational stability at the same time. We reformulate the notion of hyperbolic distances to unlock additional representation capacity over conventional Euclidean space and learn more expressive user and …

Efficient GPU-Centered Singular Value Decomposition Using the Divide-and-Conquer Method
Shifang Liu, Huiyuan Li, Hongjiao Sheng, Haoyuan Gui, Xiaoyu Zhang
https://arxiv.org/abs/2508.11467

Efficient GPU-Centered Singular Value Decomposition Using the Divide-and-Conquer Method
Singular Value Decomposition (SVD) is a fundamental matrix factorization technique in linear algebra, widely applied in numerous matrix-related problems. However, traditional SVD approaches are hindered by slow panel factorization and frequent CPU-GPU data transfers in heterogeneous systems, despite advancements in GPU computational capabilities. In this paper, we introduce a GPU-centered SVD algorithm, incorporating a novel GPU-based bidiagonal divide-and-conquer (BDC) method. We reformulate t…

Intermediate time scale in the first product formation time distribution of Michaelis-Menten kinetics with inhibitors
Arthur M. S. Carvalho, Gerson C. Duarte-Filho, Fernando A. N. Santos
https://arxiv.org/abs/2508.11645

Intermediate time scale in the first product formation time distribution of Michaelis-Menten kinetics with inhibitors
Michaelis-Menten kinetics is one of the most recognized models in enzyme kinetics, crucial for the understanding of biochemical reactions in several metabolic processes. In this study, we perform a stochastic analysis of the Michaelis-Menten kinetics with the introduction of inhibitory mechanisms, which significantly diversifies the study of the reaction. We apply the Fock space formalism to reformulate the master equation, transforming it into a Schrödinger-type equation. We investigate rever…

Ideal Fermi gas in the Dunkl formalism
Djamel Eddine Zenkhri, Abdelhakim Benkrane
https://arxiv.org/abs/2508.11806 https://arxiv.org/pdf/2508.11806

Ideal Fermi gas in the Dunkl formalism
This paper investigates the thermodynamic properties of an ideal Fermi gas within the framework of the Dunkl formalism, which incorporates deformation effects through reflection symmetric differential operators. The formalism is applied to reformulate the creation and annihilation operators, leading to modified expressions for the fundamental thermodynamic quantities while preserving the underlying Fermi Dirac statistics. We derived modified expressions for the main thermodynamic quantities. In…

RAGs to Riches: RAG-like Few-shot Learning for Large Language Model Role-playing
Timothy Rupprecht, Enfu Nan, Arash Akbari, Arman Akbari, Lei Lu, Priyanka Maan, Sean Duffy, Pu Zhao, Yumei He, David Kaeli, Yanzhi Wang
https://arxiv.org/abs/2509.12168

RAGs to Riches: RAG-like Few-shot Learning for Large Language Model Role-playing
Role-playing Large language models (LLMs) are increasingly deployed in high-stakes domains such as healthcare, education, and governance, where failures can directly impact user trust and well-being. A cost effective paradigm for LLM role-playing is few-shot learning, but existing approaches often cause models to break character in unexpected and potentially harmful ways, especially when interacting with hostile users. Inspired by Retrieval-Augmented Generation (RAG), we reformulate LLM role-pl…

Non-Hermitian Chiral Superfluids with a Complex Interaction
Jia-Hang Ji, Wenxing Nie
https://arxiv.org/abs/2508.12360 https://arxiv.org/pdf/2508.12360

Non-Hermitian Chiral Superfluids with a Complex Interaction
Recently, the influence of dissipation on a quantum system has attracted much attention, particularly on how the non-Hermitian terms modify the energy spectrum, band topology, and phase transition point. Motivated by the recent investigation of non-Hermitian $s$-wave superfluidity, we study the non-Hermitian chiral $p+ip$ superfluid (SF) with a complex-valued interaction, originating from inelastic scattering between fermions. We reformulate the non-Hermitian mean-field theory for chiral SFs an…

Efficient Optimization of Low-Rank Antisymmetric Product of Geminals Wavefunction Using the Direct Givens Rotation Method
Airi Kawasaki, Rei Oshima, Naoki Nakatani, Hiromi Nakai
https://arxiv.org/abs/2508.11822

Efficient Optimization of Low-Rank Antisymmetric Product of Geminals Wavefunction Using the Direct Givens Rotation Method
In our previous study, we proposed the low-rank antisymmetric product of geminals (APG) method, which reconstructs the wavefunction by extracting only the important eigenvalues from the APG wave function. However, its practical application was limited by the high computational cost from an orbital optimization process, making higher-rank calculations difficult. In this work, we reformulate the orbital part of the wavefunction using Givens rotation matrices, enabling an analytical treatment of t…

On the Monotonicity of relative entropy: A Comparative Study of Petz's and Uhlmann's Approaches
Santiago Matheus, Francesco Bottacin, Edoardo Provenzi
https://arxiv.org/abs/2509.11221

On the Monotonicity of relative entropy: A Comparative Study of Petz's and Uhlmann's Approaches
We revisit the monotonicity of relative entropy under the action of quantum channels, a foundational result in quantum information theory. Among the several available proofs, we focus on those by Petz and Uhlmann, which we reformulate within a unified, finite-dimensional operator-theoretic framework. In the first part, we examine Petz's strategy, identify a subtle flaw in his original use of Jensen's contractive operator inequality, and point out how it was corrected to restore the validity of …

A Markovian Framing of WaveFunctionCollapse for Procedurally Generating Aesthetically Complex Environments
Franklin Yiu, Mohan Lu, Nina Li, Kevin Joseph, Tianxu Zhang, Julian Togelius, Timothy Merino, Sam Earle
https://arxiv.org/abs/2509.09919

A Markovian Framing of WaveFunctionCollapse for Procedurally Generating Aesthetically Complex Environments
Procedural content generation often requires satisfying both designer-specified objectives and adjacency constraints implicitly imposed by the underlying tile set. To address the challenges of jointly optimizing both constraints and objectives, we reformulate WaveFunctionCollapse (WFC) as a Markov Decision Process (MDP), enabling external optimization algorithms to focus exclusively on objective maximization while leveraging WFC's propagation mechanism to enforce constraint satisfaction. We emp…

Quantum Dynamics of a Scalar Particle in Schwarzschild Spacetime using the Generalized Feshbach Villars Transformation
Sarra Garah, Abdelmalek Boumali
https://arxiv.org/abs/2509.12506

Quantum Dynamics of a Scalar Particle in Schwarzschild Spacetime using the Generalized Feshbach Villars Transformation
In this work, we apply the generalised Feshbach Villars transformation (GFVT) to spin-0 scalar fields in a Schwarzschild gravitational background. Starting from the covariant Klein Gordon equation, we reformulate the dynamics in the FV two-component representation, which enables a natural separation of positive- and negative-energy branches. In the far-field approximation, the system exhibits a hydrogen like bound spectrum, confirming the ability of GFVT to provide a consistent probabilistic in…

Quantum Prime Factorization: A Novel Approach Based on Fermat Method
Julien Mellaerts
https://arxiv.org/abs/2508.10041 https://arxiv.org/pdf/2508.10041

Quantum Prime Factorization: A Novel Approach Based on Fermat Method
In this paper, we introduce a novel quantum algorithm for the factorization of composite odd numbers. This work makes two significant contributions. First, we present a new improvement to the classical Fermat method, fourfold reducing the computational complexity of factoring. Second, we reformulate Fermat factorization method as an optimization problem suitable for Quantum Annealers which allowed us to factorize 8,689,739, the biggest number ever factorized using a quantum device to our knowle…

Novel discretization method to calculate g-functions of vertical geothermal boreholes with improved accuracy and efficiency
Yue Yang, Xiaodong Yang, Chenhui Lin, Luo Xu, Qi Wang, Shuwei Xu, Wenchuan Wu
https://arxiv.org/abs/2508.11154

Novel discretization method to calculate g-functions of vertical geothermal boreholes with improved accuracy and efficiency
The calculation of g-functions is essential for the design and simulation of geothermal boreholes. However, existing methods, such as the stacked finite line source (SFLS) model, face challenges regarding computational efficiency and accuracy, particularly with fine-grained discretization. This paper introduces a novel discretization method to address these limitations. We reformulate the g-function calculation under the uniform borehole wall temperature boundary condition as the solution to sp…

Pomeron evolution, entanglement entropy and Abramovskii-Gribov-Kancheli cutting rules
Mustapha Ouchen, Alex Prygarin
https://arxiv.org/abs/2508.12102 https://

Pomeron evolution, entanglement entropy and Abramovskii-Gribov-Kancheli cutting rules
We use Pomeron evolution equation in zero transverse dimension based on the Abramovskii-Gribov-Kancheli~(AGK) cutting rules to calculate the von Neumann entropy and $q$-moments that used as an experimental test for the Koba-Nielsen-Olesen~(KNO) scaling. In order to avoid the negative probabilities that emerge from the negative AGK weights in the Minkowski space, we reformulate the Pomeron evolution in the Euclidean space. The resulting positive definite probabilities for cut and uncut Pomeron…

Learning Constraint Surrogate Model for Two-stage Stochastic Unit Commitment
Amir Bahador Javadi, Amin Kargarian, Mort Naraghi-Pour
https://arxiv.org/abs/2509.10246 https://

Learning Constraint Surrogate Model for Two-stage Stochastic Unit Commitment
The increasing penetration of renewable energy sources introduces significant uncertainty in power system operations, making traditional deterministic unit commitment approaches computationally expensive. This paper presents a machine learning surrogate modeling approach designed to reformulate the feasible design space of the two-stage stochastic unit commitment (TSUC) problem, reducing its computational complexity. The proposed method uses a support vector machine (SVM) to construct a surroga…

E3-Rewrite: Learning to Rewrite SQL for Executability, Equivalence,and Efficiency
Dongjie Xu, Yue Cui, Weijie Shi, Qingzhi Ma, Hanghui Guo, Jiaming Li, Yao Zhao, Ruiyuan Zhang, Shimin Di, Jia Zhu, Kai Zheng, Jiajie Xu
https://arxiv.org/abs/2508.09023

E3-Rewrite: Learning to Rewrite SQL for Executability, Equivalence,and Efficiency
SQL query rewriting aims to reformulate a query into a more efficient form while preserving equivalence. Most existing methods rely on predefined rewrite rules. However, such rule-based approaches face fundamental limitations: (1) fixed rule sets generalize poorly to novel query patterns and struggle with complex queries; (2) a wide range of effective rewriting strategies cannot be fully captured by declarative rules. To overcome these issues, we propose using large language models (LLMs) to ge…

Symmetry and Thermodynamic Bounds on Cross-Coupling Transport in Chiral Liquid Crystals
Shunsuke Takano, Takuya Nakanishi, Kenta Nakagawa, Toru Asahi
https://arxiv.org/abs/2507.08225

Symmetry and Thermodynamic Bounds on Cross-Coupling Transport in Chiral Liquid Crystals
We reformulate the Leslie effects that describe the dynamic cross-couplings in chiral liquid crystals driven by the transport of heat, electric charge, and mass. The Ericksen--Leslie model is extended in the linear response framework by representing nematic order with the Q-tensor. Subsequently, the thermodynamic uncertainty relation is applied to identify the upper bounds of the Leslie cross-coupling coefficients. We reveal that the cross-coupling coefficients are dependent on the scalar order…

Linearization-Based Feedback Stabilization of McKean-Vlasov PDEs
Dante Kalise, Lucas M. Moschen, Grigorios A. Pavliotis
https://arxiv.org/abs/2507.12411 ht…

Linearization-Based Feedback Stabilization of McKean-Vlasov PDEs
We study the feedback stabilization of the McKean-Vlasov PDE on the torus. Our goal is to steer the dynamics toward a prescribed stationary distribution or accelerate convergence to it using a time-dependent control potential. We reformulate the controlled PDE in a weighted-projected space and apply the ground-state transform to obtain a Schrodinger-type operator. The resulting operator framework enables spectral analysis, verification of the infinite-dimensional Hautus test, and the constructi…

LL3M: Large Language 3D Modelers
Sining Lu, Guan Chen, Nam Anh Dinh, Itai Lang, Ari Holtzman, Rana Hanocka
https://arxiv.org/abs/2508.08228 https://arxiv.o…

LL3M: Large Language 3D Modelers
We present LL3M, a multi-agent system that leverages pretrained large language models (LLMs) to generate 3D assets by writing interpretable Python code in Blender. We break away from the typical generative approach that learns from a collection of 3D data. Instead, we reformulate shape generation as a code-writing task, enabling greater modularity, editability, and integration with artist workflows. Given a text prompt, LL3M coordinates a team of specialized LLM agents to plan, retrieve, write,…

Fast and Provable Hankel Tensor Completion for Multi-measurement Spectral Compressed Sensing
Jinsheng Li, Xu Zhang, Shuang Wu, Wei Cui
https://arxiv.org/abs/2507.04847

Fast and Provable Hankel Tensor Completion for Multi-measurement Spectral Compressed Sensing
In this paper, we introduce a novel low-rank Hankel tensor completion approach to address the problem of multi-measurement spectral compressed sensing. By lifting the multiple signals to a Hankel tensor, we reformulate this problem into a low-rank Hankel tensor completion task, exploiting the spectral sparsity via the low multilinear rankness of the tensor. Furthermore, we design a scaled gradient descent algorithm for Hankel tensor completion (ScalHT), which integrates the low-rank Tucker deco…

A Differential Evolution Algorithm with Neighbor-hood Mutation for DOA Estimation
Bo Zhou, Kaijie Xu, Yinghui Quan, Mengdao Xing
https://arxiv.org/abs/2507.06020

A Differential Evolution Algorithm with Neighbor-hood Mutation for DOA Estimation
Two-dimensional (2D) Multiple Signal Classification algorithm is a powerful technique for high-resolution direction-of-arrival (DOA) estimation in array signal processing. However, the exhaustive search over the 2D an-gular domain leads to high computa-tional cost, limiting its applicability in real-time scenarios. In this work, we reformulate the peak-finding process as a multimodal optimization prob-lem, and propose a Differential Evolu-tion algorithm with Neighborhood Mutation (DE-NM) to eff…

Efficient Multi-Agent Coordination via Dynamic Joint-State Graph Construction
Yanlin Zhou, Manshi Limbu, Xuesu Xiao
https://arxiv.org/abs/2509.07234 https://

Efficient Multi-Agent Coordination via Dynamic Joint-State Graph Construction
Multi-agent pathfinding (MAPF) traditionally focuses on collision avoidance, but many real-world applications require active coordination between agents to improve team performance. This paper introduces Team Coordination on Graphs with Risky Edges (TCGRE), where agents collaborate to reduce traversal costs on high-risk edges via support from teammates. We reformulate TCGRE as a 3D matching problem-mapping robot pairs, support pairs, and time steps-and rigorously prove its NP-hardness via reduc…

SSNCVX: A primal-dual semismooth Newton method for convex composite optimization problem
Zhanwang Deng, Tao Wei, Jirui Ma, Zaiwen Wen
https://arxiv.org/abs/2509.11995 https://…

SSNCVX: A primal-dual semismooth Newton method for convex composite optimization problem
In this paper, we propose a uniform semismooth Newton-based algorithmic framework called SSNCVX for solving a broad class of convex composite optimization problems. By exploiting the augmented Lagrangian duality, we reformulate the original problem into a saddle point problem and characterize the optimality conditions via a semismooth system of nonlinear equations. The nonsmooth structure is handled internally without requiring problem specific transformation or introducing auxiliary variable…

Minimum-norm interpolation for unknown surface reconstruction
Alex Shiu Lun Chu, Leevan Ling, Ka Chun Cheung
https://arxiv.org/abs/2507.08632 https://

Minimum-norm interpolation for unknown surface reconstruction
We study algorithms to estimate geometric properties of raw point cloud data through implicit surface representations. Given that any level-set function with a constant level set corresponding to the surface can be used for such estimations, numerical methods need not specify a unique target function for the domain-type interpolation problems. In this paper, we focus on kernel-based interpolation by radial basis functions (RBF) and reformulate the uniquely solvable interpolation problem into a …

Physics-Informed Neural Networks with Hard Nonlinear Equality and Inequality Constraints
Ashfaq Iftakher, Rahul Golder, M. M. Faruque Hasan
https://arxiv.org/abs/2507.08124 https://arxiv.org/pdf/2507.08124 https://arxiv.org/html/2507.08124
arXiv:2507.08124v1 Announce Type: new
Abstract: Traditional physics-informed neural networks (PINNs) do not guarantee strict constraint satisfaction. This is problematic in engineering systems where minor violations of governing laws can significantly degrade the reliability and consistency of model predictions. In this work, we develop KKT-Hardnet, a PINN architecture that enforces both linear and nonlinear equality and inequality constraints up to machine precision. It leverages a projection onto the feasible region through solving Karush-Kuhn-Tucker (KKT) conditions of a distance minimization problem. Furthermore, we reformulate the nonlinear KKT conditions using log-exponential transformation to construct a general sparse system with only linear and exponential terms, thereby making the projection differentiable. We apply KKT-Hardnet on both test problems and a real-world chemical process simulation. Compared to multilayer perceptrons and PINNs, KKT-Hardnet achieves higher accuracy and strict constraint satisfaction. This approach allows the integration of domain knowledge into machine learning towards reliable hybrid modeling of complex systems.
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Revisiting the Fermion Sign Problem from the Structure of Lee-Yang Zeros. I. The Form of Partition Function for Indistinguishable Particles and Its Zeros at 0~K
Ran-Chen He, Jia-Xi Zeng, Shu Yang, Cong Wang, Qi-Jun Ye, Xin-Zheng Li
https://arxiv.org/abs/2507.22779

Revisiting the Fermion Sign Problem from the Structure of Lee-Yang Zeros. I. The Form of Partition Function for Indistinguishable Particles and Its Zeros at 0~K
To simulate indistinguishable particles, recent studies of path-integral molecular dynamics formulated their partition function $Z$ as a recurrence relation involving a variable $ξ$, with $ξ=1$(-1) for bosons (fermions). Inspired by Lee-Yang phase transition theory, we extend $ξ$ into the complex plane and reformulate $Z$ as a polynomial in $ξ$. By analyzing the distribution of the partition function zeros, we gain insights into the analytical properties of indistinguishable particles, part…

An operator approach to the Madelung-Bohm continuity equation
M. A. Garc\'ia-M\'arquez, H. M. Moya-Cessa, I. Ramos-Prieto, F. Soto-Eguibar
https://arxiv.org/abs/2509.01913

An operator approach to the Madelung-Bohm continuity equation
We solve the probability continuity equation within the Madelung-Bohm framework, assuming a separable phase expressed as $S(x,t) = Q(x)\dotν(t) + μ(t)$. Using operator methods, we reformulate the wave function's amplitude into a form that is more practical for application to any given initial condition. This results in the function $F(x,t)$, which characterizes the wavefunction's amplitude, with $F$ being the transformation of the position operator via a squeeze-like operator. To demonstrate …

Power-Constrained and Quantized MIMO-RSMA Systems with Imperfect CSIT: Joint Precoding, Antenna Selection, and Power Control
Jiwon Sung, Seokjun Park, Jinseok Choi
https://arxiv.org/abs/2508.05080

Power-Constrained and Quantized MIMO-RSMA Systems with Imperfect CSIT: Joint Precoding, Antenna Selection, and Power Control
To utilize the full potential of the available power at a base station (BS), we propose a joint precoding, antenna selection, and transmit power control algorithm for a total power budget at the BS. We formulate a sum spectral efficiency (SE) maximization problem for downlink multi-user multiple-input multiple-output (MIMO) rate-splitting multiple access (RSMA) systems with arbitrary-resolution digital-to-analog converters (DACs). We reformulate the problem by defining the ergodic sum SE using …

A preconditioned boundary value method for advection-diffusion equations with half Laplacian via spectrum doubling
Pu Yuan, Paul Zegeling, Xian-Ming Gu
https://arxiv.org/abs/2507.07717

A preconditioned boundary value method for advection-diffusion equations with half Laplacian via spectrum doubling
In this paper, we study an advection-diffusion equation that involves a half-Laplacian operator derived from the Riesz fractional Laplacian, combined with a differential operator \(\mathcal{L}\). By applying the half-Laplacian operator $(-Δ)^{\frac{1}{2}}$ on both sides of the equation and using the relationship between the Hilbert transform and $(-Δ)^{\frac{1}{2}}$, we reformulate the problem as a second-order damped Cauchy problem and then convert it into an equivalent first-order system. T…

Incorporating Fixed Pole Information in the Data-Driven Least Squares Realization Problem
Christof Vermeersch, Sibren Lagauw, Bart De Moor
https://arxiv.org/abs/2509.09394 https…

Incorporating Fixed Pole Information in the Data-Driven Least Squares Realization Problem
In practical least squares realization problems, partial information about the poles of the dynamical model may be known a priori. Existing techniques for incorporating prior knowledge, such as prefiltering the given data, are typically heuristic and lack theoretical guarantees. We extend our previously developed globally optimal approach for the least squares realization problem to accommodate fixed poles. In particular, we reformulate the problem as a (rectangular) multiparameter eigenvalue p…

A novel non-metricity extension of scalar-tensor gravity in spatially curved spacetime
Ghulam Murtaza, Avik De, Andronikos Paliathanasis
https://arxiv.org/abs/2509.00569 https:/…

A novel non-metricity extension of scalar-tensor gravity in spatially curved spacetime
We investigate a non-minimally coupled scalar field theory within the framework of scalar-tensor gravity formulated in non-metricity geometry, focusing on spatially curved FLRW spacetimes. Employing the dynamical systems approach with Hubble-normalized variables, we reformulate the field equations into an autonomous system and analyze the resulting critical points. Four distinct cases, determined by the scalar coupling and potential functions, are studied in detail. For each case, we identify t…

Deep learning for the semi-classical limit of the Schr\"odinger equation
Jizu Huang, Rukang You, Tao Zhou
https://arxiv.org/abs/2509.04453 https://arx…

Deep learning for the semi-classical limit of the Schrödinger equation
In this paper, we integrate neural networks and Gaussian wave packets to numerically solve the Schrödinger equation with a smooth potential near the semi-classical limit. Our focus is not only on accurately obtaining solutions when the non-dimensional Planck's constant, $\varepsilon$, is small, but also on constructing an operator that maps initial values to solutions for the Schrödinger equation with multiscale properties. Using Gaussian wave packets framework, we first reformulate the SchrÃ…

Data-Driven Density Steering via the Gromov-Wasserstein Optimal Transport Distance
Haruto Nakashima, Siddhartha Ganguly, Kenji Kashima
https://arxiv.org/abs/2508.06052 https://

Data-Driven Density Steering via the Gromov-Wasserstein Optimal Transport Distance
We tackle the data-driven chance-constrained density steering problem using the Gromov-Wasserstein metric. The underlying dynamical system is an unknown linear controlled recursion, with the assumption that sufficiently rich input-output data from pre-operational experiments are available. The initial state is modeled as a Gaussian mixture, while the terminal state is required to match a specified Gaussian distribution. We reformulate the resulting optimal control problem as a difference-of-con…

The spectrum of the Steklov-Helmholtz operator
Nilima Nigam, Kshitij Patil, Weiran Sun
https://arxiv.org/abs/2509.07249 https://arxiv.org/pdf/2509.07249

The spectrum of the Steklov-Helmholtz operator
We present a wavenumber-robust strategy for computing Steklov eigenpairs of the Helmholtz operator $-Δ-μ^2$. As the wavenumber $μ\rightarrow μ_D$ from below (where $μ_D^2 $ is a Dirichlet- Laplace eigenvalue of multiplicity $\ell$), the lowest $\ell$ Steklov-Helmholtz eigenvalues diverge to $-\infty$. Computationally, the Steklov-Helmholtz eigenvalue problem becomes severely ill-conditioned when $μ\approx μ_D$. We first reformulate the problem in terms of a suitably-defined Dirichlet-t…

Reinforcement Learning-based Control via Y-wise Affine Neural Networks (YANNs)
Austin Braniff, Yuhe Tian
https://arxiv.org/abs/2508.16474 https://arxiv.org…

Reinforcement Learning-based Control via Y-wise Affine Neural Networks (YANNs)
This work presents a novel reinforcement learning (RL) algorithm based on Y-wise Affine Neural Networks (YANNs). YANNs provide an interpretable neural network which can exactly represent known piecewise affine functions of arbitrary input and output dimensions defined on any amount of polytopic subdomains. One representative application of YANNs is to reformulate explicit solutions of multi-parametric linear model predictive control. Built on this, we propose the use of YANNs to initialize RL a…

Morse: Dual-Sampling for Lossless Acceleration of Diffusion Models
Chao Li, Jiawei Fan, Anbang Yao
https://arxiv.org/abs/2506.18251 https://

Morse: Dual-Sampling for Lossless Acceleration of Diffusion Models
In this paper, we present Morse, a simple dual-sampling framework for accelerating diffusion models losslessly. The key insight of Morse is to reformulate the iterative generation (from noise to data) process via taking advantage of fast jump sampling and adaptive residual feedback strategies. Specifically, Morse involves two models called Dash and Dot that interact with each other. The Dash model is just the pre-trained diffusion model of any type, but operates in a jump sampling regime, creat…

A Parallel Solver with Multiphysics Finite Element Method for Poroelasticity Coupled with Elasticity Model
Zhihao Ge, Chengxin Wang
https://arxiv.org/abs/2509.06673 https://

A Parallel Solver with Multiphysics Finite Element Method for Poroelasticity Coupled with Elasticity Model
In this paper, we propose a parallel solver for solving the quasi-static linear poroelasticity coupled with linear elasticity model in the Lagrange multiplier framework. Firstly, we reformulate the model into a coupling of the nearly incompressible elasticity and an unsteady affection-diffusion equations by setting new variable ``elastic pressure" and ``volumetric fluid content". And we introduce a Lagrange multiplier to guarantee the normal stress continuity on the interface. Then, we give the…

Adversarial Training: Enhancing Out-of-Distribution Generalization for Learning Wireless Resource Allocation
Shengjie Liu, Chenyang Yang
https://arxiv.org/abs/2506.21208

Adversarial Training: Enhancing Out-of-Distribution Generalization for Learning Wireless Resource Allocation
Deep neural networks (DNNs) have widespread applications for optimizing resource allocation. Yet, their performance is vulnerable to distribution shifts between training and test data, say channels. In this letter, we resort to adversarial training (AT) for enhancing out-of-distribution (OOD) generalizability of DNNs trained in unsupervised manner. We reformulate AT to capture the OOD degradation, and propose a one-step gradient ascent method for AT. The proposed method is validated by optimizi…

Anisotropic Spacetimes in $f(G)$-gravity: Bianchi I, Bianchi III and Kantowski-Sachs Cosmologies
R. Bogadi, A. Giacomini, M. Govender, C. Hansraj, G. Leon, A. Paliathanasis
https://arxiv.org/abs/2508.18055

Anisotropic Spacetimes in $f(G)$-gravity: Bianchi I, Bianchi III and Kantowski-Sachs Cosmologies
We investigate the evolution of cosmological anisotropies within the framework of $f\left(G\right)$-gravity. Specifically, we consider a locally rotationally symmetric geometry in four-dimensional spacetime that describes the Bianchi I, Bianchi III, and the Kantowski-Sachs spacetimes. Within this context, we introduce a Lagrange multiplier which allows us to reformulate the geometric degrees of freedom in terms of a scalar field. The resulting theory is dynamically equivalent to an Einstein-Gau…

Discretizing linearized Einstein-Bianchi system by symmetric and traceless tensors
Yuyang Guo, Jun Hu, Ting Lin
https://arxiv.org/abs/2508.04560 https://ar…

Discretizing linearized Einstein-Bianchi system by symmetric and traceless tensors
The Einstein-Bianchi system uses symmetric and traceless tensors to reformulate Einstein's original field equations. However, preserving these algebraic constraints simultaneously remains a challenge for numerical methods. This paper proposes a new formulation that treats the linearized Einstein-Bianchi system (near the trivial Minkowski metric) as the Hodge wave equation associated with the conformal Hessian complex. To discretize this equation, a conforming finite element conformal Hessian co…

A Frank-Wolfe-based primal heuristic for quadratic mixed-integer optimization
Gioni Mexi, Deborah Hendrych, S\'ebastien Designolle, Mathieu Besan\c{c}on, Sebastian Pokutta
https://arxiv.org/abs/2508.01299

A Frank-Wolfe-based primal heuristic for quadratic mixed-integer optimization
We propose a primal heuristic for quadratic mixed-integer problems. Our method extends the Boscia framework -- originally a mixed-integer convex solver leveraging a Frank-Wolfe-based branch-and-bound approach -- to address nonconvex quadratic objective and constraints. We reformulate nonlinear constraints, introduce preprocessing steps, and a suite of heuristics including rounding strategies, gradient-guided selection, and large neighborhood search techniques that exploit integer-feasible verti…

Sharp-Peak Functions for Exactly Penalizing Binary Integer Programming
Shenglong Zhou, Shuai Li, Hui Zhang, Ziyan Luo
https://arxiv.org/abs/2509.00895 https://

Sharp-Peak Functions for Exactly Penalizing Binary Integer Programming
Unconstrained binary integer programming (UBIP) is a challenging optimization problem due to the presence of binary variables. To address the challenge, we introduce a novel class of functions named sharp-peak functions (SPFs), which equivalently reformulate the binary constraints as equality constraints, giving rise to an SPF-constrained optimization. Rather than solving this constrained reformulation directly, we focus on its associated penalty model. The established exact penalty theory show…

A Passivity Analysis for Nonlinear Consensus on Digraphs
Feng-Yu Yue, Daniel Zelazo
https://arxiv.org/abs/2508.21428 https://arxiv.org/pdf/2508.21428

A Passivity Analysis for Nonlinear Consensus on Digraphs
This work presents a passivity-based analysis for the nonlinear output agreement problem in network systems over directed graphs. We reformulate the problem as a convergence analysis on the agreement submanifold. First, we establish how passivity properties of individual agents and controllers determine the passivity of their associated system relations. Building on this, we introduce the concept of submanifold-constrained passivity and develop a novel compensation theorem that ensures output c…

Fourth-Order Compact FDMs for Steady and Time-Dependent Nonlinear Convection-Diffusion Equations
Qiwei Feng, Catalin Trenchea
https://arxiv.org/abs/2507.18799 https://

Sparse Polynomial Regression under Anomalous Data
Roozbeh Abolpour, Mohammad Reza Hesamzadeh, Maryam Dehghani
https://arxiv.org/abs/2508.18199 https://arxi…

Sparse Polynomial Regression under Anomalous Data
This paper starts with the general form of the polynomial regression model. We reformulate the Sparse Polynomial Regression Model (SPRM) with anomalous data filtering as Mixed-Integer Linear Program (MILP). This MILP is then converted to a non-convex Quadratically Constrained Quadratic Program (QCQP). Through a proposed mapping, the derived QCQP is reformulated as a Fractional Program (FP). We theoretically show that the reformulated FP has better computational properties than the original QCQP…

Momentum Equation-Based Regularization and Image Registration for Two-Dimensional Ultrasound Elasticity Imaging
Olalekan A. Babaniyi, Rebecca Rodrigues, Michael S. Richards
https://arxiv.org/abs/2508.19086

Momentum Equation-Based Regularization and Image Registration for Two-Dimensional Ultrasound Elasticity Imaging
Objective: Evaluate and compare multiple mechanics-based and traditional regularization strategies within a variational image registration framework for quasi-static ultrasound elastography. Methods:We reformulate a previously proposed momentum-equation-based post-processing method (SPREME) as a regularization term directly integrated into an image registration energy functional. Four regularization types are implemented and compared: a strain magnitude ($\R_ε$), a strain magnitude with incomp…

A Zeroth-Order Extra-Gradient Method For Black-Box Constrained Optimization
Yuke Zhou, Ruiyang Jin, Siyang Gao, Jianxiao Wang, Jie Song
https://arxiv.org/abs/2506.20546

A Zeroth-Order Extra-Gradient Method For Black-Box Constrained Optimization
Non-analytical objectives and constraints often arise in control systems, particularly in problems with complex dynamics, which are challenging yet lack efficient solution methods. In this work, we consider general constrained optimization problems involving black-box objectives and constraints. To solve it, we reformulate it as a min-max problem and propose a zeroth-order extra gradient (ZOEG) algorithm that combines the extra gradient method with a feedback-based stochastic zeroth-order gradi…

A Variable-Separation-based Domain Decomposition Method for Parametric Dynamical Systems
Yuming Ba, Liang Chen, Yaru Chen, Qiuqi Li
https://arxiv.org/abs/2508.17276 https://

A Variable-Separation-based Domain Decomposition Method for Parametric Dynamical Systems
This paper proposes a model order reduction method for a class of parametric dynamical systems. Using a temporal Fourier integral transform, we reformulate these systems into complex-valued elliptic equations in the frequency domain, containing both the frequency variables and the parameters inherited from the original model. To reduce the computational cost of the frequency-variable elliptic equations, we extend the variable-separation-based domain decomposition method to the complex-valued co…

KKT-based optimality conditions for neural network approximation
Vinesha Peiris, Nadezda Sukhorukova, Julien Ugon
https://arxiv.org/abs/2506.17305 https://…

KKT-based optimality conditions for neural network approximation
In this paper, we obtain necessary optimality conditions for neural network approximation. We consider neural networks in Manhattan ($l_1$ norm) and Chebyshev ($\max$ norm). The optimality conditions are based on neural networks with at most one hidden layer. We reformulate nonsmooth unconstrained optimisation problems as larger dimension constrained problems with smooth objective functions and constraints. Then we use KKT conditions to develop the necessary conditions and present the optimalit…

Krylov and core transformation algorithms for an inverse eigenvalue problem to compute recurrences of multiple orthogonal polynomials
Amin Faghih, Michele Rinelli, Marc Van Barel, Raf Vandebril, Robbe Vermeiren
https://arxiv.org/abs/2506.19796

Krylov and core transformation algorithms for an inverse eigenvalue problem to compute recurrences of multiple orthogonal polynomials
In this paper, we develop algorithms for computing the recurrence coefficients corresponding to multiple orthogonal polynomials on the step-line. We reformulate the problem as an inverse eigenvalue problem, which can be solved using numerical linear algebra techniques. We consider two approaches: the first is based on the link with block Krylov subspaces and results in a biorthogonal Lanczos process with multiple starting vectors; the second consists of applying a sequence of Gaussian eliminati…