Tootfinder

Well-balanced high-order method for non-conservative hyperbolic PDEs with source terms: application to one-dimensional blood flow equations with gravity
Chiara Colombo, Caterina Dalmaso, Lucas O. M\"uller, Annunziato Siviglia
https://arxiv.org/abs/2509.22190

Well-balanced high-order method for non-conservative hyperbolic PDEs with source terms: application to one-dimensional blood flow equations with gravity
The present work proposes a well-balanced finite volume-type numerical method for the solution of non-conservative hyperbolic partial differential equations (PDEs) with source terms. The method is characterized, first, by the use of a recently introduced high-order spatial reconstruction, based on generalized Riemann problem information from the previous time level. Such reconstruction is well-balanced up to order three, compact, efficient and easy to implement. Second, the method incorporates …

Automated Runge-Kutta-Nystr\"om time stepping for finite element methods in Irksome
Robert C. Kirby, Scott P. MacLachlan, Pablo D. Brubeck
https://arxiv.org/abs/2508.20255 …

Automated Runge-Kutta-Nyström time stepping for finite element methods in Irksome
Irksome is a library based on the Unified Form Language (UFL) that automates the application of Runge-Kutta time-stepping methods for finite element spatial discretizations of partial differential equations (PDEs). This paper describes recent updates to Irksome that allow users to express semidiscrete forms of PDEs that contain second-order temporal derivatives, whence it generates stage-coupled variational problems to be solved at each time step for Runge-Kutta-Nyström methods. Firedrake then…

VPPE: Application of Scaled Vecchia Approximations to Parallel Partial Emulation
Josh Seidman, Elaine T. Spiller
https://arxiv.org/abs/2508.19144 https://a…

VPPE: Application of Scaled Vecchia Approximations to Parallel Partial Emulation
Computer models or simulators are widely used across scientific fields, but are computationally expensive limiting their use to explore possible scenarios/outcomes. Gaussian process emulators are statistical surrogates that can rapidly approximate the outputs of computer models at untested inputs and enable uncertainty quantification studies. The parallel partial emulation (PPE) was developed to model simulators with vector-valued outputs. While the PPE is adept at fitting simulator data with m…

Strichartz estimates for higher order Schr\"odinger equations with Partial regular initial data
Vishvesh Kumar, Shyam Swarup Mondal, Iswarya Sitiraju, Manli Song
https://arxiv.org/abs/2508.15670

Strichartz estimates for higher order Schrödinger equations with Partial regular initial data
In this paper, we establish refined Strichartz estimates for higher-order Schrödinger equations with initial data exhibiting partial regularity. By partial regularity, we mean that the initial data are not required to have full Sobolev regularity but only regularity with respect to a subset of the spatial variables. As an application of these estimates, we investigate the well-posedness of nonlinear Schrödinger equations with power-type nonlinearities. In addition, we extend our analysis to t…

Hilbert geometry of the symmetric positive-definite bicone: Application to the geometry of the extended Gaussian family
Jacek Karwowski, Frank Nielsen
https://arxiv.org/abs/2508.14369

Hilbert geometry of the symmetric positive-definite bicone: Application to the geometry of the extended Gaussian family
The extended Gaussian family is the closure of the Gaussian family obtained by completing the Gaussian family with the counterpart elements induced by degenerate covariance or degenerate precision matrices, or a mix of both degeneracies. The parameter space of the extended Gaussian family forms a symmetric positive semi-definite matrix bicone, i.e. two partial symmetric positive semi-definite matrix cones joined at their bases. In this paper, we study the Hilbert geometry of such an open bounde…

Rankin-Selberg integrals for $\mathrm{GSpin}$ groups with application to the global Gan-Gross-Prasad conjecture
Pan Yan
https://arxiv.org/abs/2508.09066 https://

Rankin-Selberg integrals for $\mathrm{GSpin}$ groups with application to the global Gan-Gross-Prasad conjecture
We construct Rankin-Selberg integrals using Bessel models for a product of tensor product partial $L$-functions \begin{equation*} L^S(s,π\timesτ_1) L^S(s,π\timesτ_2)\cdots L^S(s,π\timesτ_r) \end{equation*} where $π$ is an irreducible cuspidal automorphic representation of a quasi-split $\mathrm{GSpin}$ group, and $τ_1, \cdots, τ_r$ are irreducible unitary cuspidal automorphic representations of $\mathrm{GL}_{k_1}, \cdots, \mathrm{GL}_{k_r}$ respectively. As an application, we prove one…

A New Partial State-Feedback IDA-PBC for Two-Dimensional Nonlinear Systems: Application to Power Converters with Experimental Results
Rafael Cisneros, Leyan Fang, Wei He, Romeo Ortega
https://arxiv.org/abs/2510.01425

A New Partial State-Feedback IDA-PBC for Two-Dimensional Nonlinear Systems: Application to Power Converters with Experimental Results
In this paper we propose a variation of the widely popular Interconnection-and-Damping-Assigment Passivity-Based Control (IDA-PBC) based on Poincare's Lemma to design output feedback globally stabilizing controllers for two dimensional systems. The procedure is constructive and, in comparison with the classical IDA-PBC, whose application is often stymied by the need to solve the (infamous) matching partial differential equation (PDE), in this new method the PDE is replaced by an ordinary differ…

A Dual Ensemble Kalman Filter Approach to Robust Control of Nonlinear Systems: An Application to Partial Differential Equations
Anant A. Joshi, Saviz Mowlavi, Mouhacine Benosman
https://arxiv.org/abs/2508.21684

A Dual Ensemble Kalman Filter Approach to Robust Control of Nonlinear Systems: An Application to Partial Differential Equations
This paper considers the problem of data-driven robust control design for nonlinear systems, for instance, obtained when discretizing nonlinear partial differential equations (PDEs). A robust learning control approach is developed for nonlinear affine in control systems based on Lyapunov redesign technique. The robust control is developed as a sum of an optimal learning control which stabilizes the system in absence of disturbances, and an additive Lyapunov-based robustification term which hand…

Bilevel optimization for learning hyperparameters: Application to solving PDEs and inverse problems with Gaussian processes
Nicholas H. Nelsen, Houman Owhadi, Andrew M. Stuart, Xianjin Yang, Zongren Zou
https://arxiv.org/abs/2510.05568

Bilevel optimization for learning hyperparameters: Application to solving PDEs and inverse problems with Gaussian processes
Methods for solving scientific computing and inference problems, such as kernel- and neural network-based approaches for partial differential equations (PDEs), inverse problems, and supervised learning tasks, depend crucially on the choice of hyperparameters. Specifically, the efficacy of such methods, and in particular their accuracy, stability, and generalization properties, strongly depends on the choice of hyperparameters. While bilevel optimization offers a principled framework for hyperpa…

A New Approach to Partial Conjunction Analysis in Neuroimaging
Monitirtha Dey, Anna Vesely, Thorsten Dickhaus
https://arxiv.org/abs/2508.03675 https://arxi…

A New Approach to Partial Conjunction Analysis in Neuroimaging
The problem of identifying the brain regions activated through a particular cognitive task is pivotal in neuroimaging. This problem becomes even more complex if we have several cognitive tasks or several subjects. In this paper, we view this problem as a partial conjunction (PC) hypotheses testing problem, i.e., we are testing whether a specific brain region is activated in at least $γ$ (for some pre-fixed $γ$) subjects. We propose the application of a recent advance in the simultaneous stati…

Estimating Peer Effects Using Partial Network Data
Vincent Boucher, Aristide Houndetoungan
https://arxiv.org/abs/2509.08145 https://arxiv.org/pdf/2509.0814…

Estimating Peer Effects Using Partial Network Data
We study the estimation of peer effects through social networks when researchers do not observe the entire network structure. Special cases include sampled networks, censored networks, and misclassified links. We assume that researchers can obtain a consistent estimator of the distribution of the network. We show that this assumption is sufficient for estimating peer effects using a linear-in-means model. We provide an empirical application to the study of peer effects on students' academic ach…

Forward-Forward Autoencoder Architectures for Energy-Efficient Wireless Communications
Daniel Seifert, Onur G\"unl\"u, Rafael F. Schaefer
https://arxiv.org/abs/2510.11418

Forward-Forward Autoencoder Architectures for Energy-Efficient Wireless Communications
The application of deep learning to the area of communications systems has been a growing field of interest in recent years. Forward-forward (FF) learning is an efficient alternative to the backpropagation (BP) algorithm, which is the typically used training procedure for neural networks. Among its several advantages, FF learning does not require the communication channel to be differentiable and does not rely on the global availability of partial derivatives, allowing for an energy-efficient i…

Go with Your Gut: Scaling Confidence for Autoregressive Image Generation
Harold Haodong Chen, Xianfeng Wu, Wen-Jie Shu, Rongjin Guo, Disen Lan, Harry Yang, Ying-Cong Chen
https://arxiv.org/abs/2509.26376

Go with Your Gut: Scaling Confidence for Autoregressive Image Generation
Test-time scaling (TTS) has demonstrated remarkable success in enhancing large language models, yet its application to next-token prediction (NTP) autoregressive (AR) image generation remains largely uncharted. Existing TTS approaches for visual AR (VAR), which rely on frequent partial decoding and external reward models, are ill-suited for NTP-based image generation due to the inherent incompleteness of intermediate decoding results. To bridge this gap, we introduce ScalingAR, the first TTS fr…

Proving symmetry of localized solutions and application to dihedral patterns in the planar Swift-Hohenberg PDE
Dominic Blanco, Matthieu Cadiot
https://arxiv.org/abs/2509.10375 h…

Proving symmetry of localized solutions and application to dihedral patterns in the planar Swift-Hohenberg PDE
In this article, we extend the framework developed previously to allow for rigorous proofs of existence of smooth, localized solutions in semi-linear partial differential equations possessing both space and non-space group symmetries. We demonstrate our approach on the Swift-Hohenberg model. In particular, for a given symmetry group $\mathcal{G}$, we construct a natural Hilbert space $H^l_{\mathcal{G}}$ containing only functions with $\mathcal{G}$-symmetry. In this space, products and different…

Efficient and Explicit Block Encoding of Finite Difference Discretizations of the Laplacian
Andreas Sturm, Niclas Schillo
https://arxiv.org/abs/2509.02429 https://

Efficient and Explicit Block Encoding of Finite Difference Discretizations of the Laplacian
The data input model is a fundamental component of every quantum algorithm, as its efficiency is crucial for achieving potential speed-ups over classical methods. For quantum linear algebra tasks that utilize quantum eigenvalue or singular value transformations, block encoding is the established technique for accessing matrix data. A key application of this is solving partial differential equations, where the Laplacian operator and its finite difference discretization serve as foundational exam…

Minimal Trails in Restricted DAGs
Alexis Derumigny, Niels Horsman, Dorota Kurowicka
https://arxiv.org/abs/2510.02113 https://arxiv.org/pdf/2510.02113

Minimal Trails in Restricted DAGs
In this paper, the properties of minimal trails in a directed acyclic graph that is restricted not to contain an active cycle are studied. We are motivated by an application of the results in the copula-based Bayesian Network model developed recently. We propose a partial order on the set of trails activated by a certain subset of nodes, and show that every minimal trail, according to such an order, has a simple structure.

Computable Bounds for Strong Approximations with Applications
Haoyu Ye, Morgane Austern
https://arxiv.org/abs/2508.03833 https://arxiv.org/pdf/2508.03833…

Computable Bounds for Strong Approximations with Applications
The Komlós$\unicode{x2013}$Major$\unicode{x2013}$Tusnády (KMT) inequality for partial sums is one of the most celebrated results in probability theory. Yet its practical application is hindered by its dependence on unknown constants. This paper addresses this limitation for bounded i.i.d. random variables. At the cost of an additional logarithmic factor, we propose a computable version of the KMT inequality that depends only on the variables' range and standard deviation. We also derive an em…

DD-DeepONet: Domain decomposition and DeepONet for solving partial differential equations in three application scenarios
Bo Yang, Xingquan Li, Jie Zhao, Ying Jiang
https://arxiv.org/abs/2508.02717

DD-DeepONet: Domain decomposition and DeepONet for solving partial differential equations in three application scenarios
In certain practical engineering applications, there is an urgent need to perform repetitive solving of partial differential equations (PDEs) in a short period. This paper primarily considers three scenarios requiring extensive repetitive simulations. These three scenarios are categorized based on whether the geometry, boundary conditions(BCs), or parameters vary. We introduce the DD-DeepONet, a framework with strong scalability, whose core concept involves decomposing complex geometries into s…

Spatial Gaussian fields for complex areas with application to marine megafauna conservation
Martina Le-Bert Heyl, Janet van Niekerk, Haavard Rue
https://arxiv.org/abs/2510.00611

Spatial Gaussian fields for complex areas with application to marine megafauna conservation
Spatial Gaussian fields (SGFs) are widely employed in modeling the distributions of marine megafauna, yet they traditionally rely on assumptions of isotropy and stationarity, conditions that often prove unrealistic in complex ecological environments featuring coastlines, islands, and depth gradients acting as partial movement barriers. Existing spatial models typically treat these barriers as either fully impermeable, completely blocking species movement and dispersal, or entirely absent, which…

Structural Extrapolation in Regression Discontinuity Designs with an Application to School Expenditure Referenda
Austin Feng, Francesco Ruggieri
https://arxiv.org/abs/2508.02658

Structural Extrapolation in Regression Discontinuity Designs with an Application to School Expenditure Referenda
We propose a structural approach to extrapolate average partial effects away from the cutoff in regression discontinuity designs (RDDs). Our focus is on applications that exploit closely contested school district referenda to estimate the effects of changes in education spending on local economic outcomes. We embed these outcomes in a spatial equilibrium model of local jurisdictions in which fiscal policy is determined by majority rule voting. This integration provides a microfoundation for the…

Crosslisted article(s) found for q-bio.PE. https://arxiv.org/list/q-bio.PE/new
[1/1]:
- Weak Form Learning for Mean-Field Partial Differential Equations: an Application to Insect Movement
Seth Minor, Bret D. Elderd, Benjamin Van Allen, David M. Bortz, Vanja Dukic

Bryne: sustainable prototyping of finite element models
Benjamin Terschanski, Robert Kl\"ofkorn, Andreas Dedner, Julia Kowalski
https://arxiv.org/abs/2509.02378 https://

Bryne: sustainable prototyping of finite element models
Open-source simulation frameworks are evolving rapidly to provide accessible tools for the numerical solution of partial differential equations. Modern finite element (FEM) software such as FEniCS, Firedrake, or dune-fem alleviates the need for modelers to recode the discretization and linear solver backend for each application and enables rapid prototyping of solvers. However, while it has become easier to build prototype FEM models, creating a solver reusable beyond its specific initial simul…

Prediction error certification for PINNs: Theory, computation, and application to Stokes flow
Birgit Hillebrecht, Benjamin Unger
https://arxiv.org/abs/2508.07994 https://…

Prediction error certification for PINNs: Theory, computation, and application to Stokes flow
Rigorous error estimation is a fundamental topic in numerical analysis. With the increasing use of physics-informed neural networks (PINNs) for solving partial differential equations, several approaches have been developed to quantify the associated prediction error. In this work, we build upon a semigroup-based framework previously introduced by the authors for estimating the PINN error. While this estimator has so far been limited to academic examples - due to the need to compute quantities r…

Physics-informed low-rank neural operators with application to parametric elliptic PDEs
Sebastian Schaffer, Lukas Exl
https://arxiv.org/abs/2509.07687 https://

Physics-informed low-rank neural operators with application to parametric elliptic PDEs
We present the Physics-Informed Low-Rank Neural Operator (PILNO), a neural operator framework for efficiently approximating solution operators of partial differential equations (PDEs) on point cloud data. PILNO combines low-rank kernel approximations with an encoder--decoder architecture, enabling fast, continuous one-shot predictions while remaining independent of specific discretizations. The model is trained using a physics-informed penalty framework, ensuring that PDE constraints and bounda…

A generalization of Savin's small perturbation theorem for fully nonlinear elliptic equations and applications
Zhenyu Fan
https://arxiv.org/abs/2509.01138 https://

A generalization of Savin's small perturbation theorem for fully nonlinear elliptic equations and applications
In this note, we generalize Savin's small perturbation theorem to nonhomogeneous fully nonlinear equations $F(D^2u, Du, u,x)=f$ provided the coefficients and the right-hand side terms are Hölder small perturbations. As an application, we establish a partial regularity result for the sigma-$k$ Hessian equation $σ_{k}(D^2u)=f$.

Quasi-Monte Carlo methods for uncertainty quantification of tumor growth modeled by a parametric semi-linear parabolic reaction-diffusion equation
Alexander D. Gilbert, Frances Y. Kuo, Dirk Nuyens, Graham Pash, Ian H. Sloan, Karen E. Willcox
https://arxiv.org/abs/2509.25753

Quasi-Monte Carlo methods for uncertainty quantification of tumor growth modeled by a parametric semi-linear parabolic reaction-diffusion equation
We study the application of a quasi-Monte Carlo (QMC) method to a class of semi-linear parabolic reaction-diffusion partial differential equations used to model tumor growth. Mathematical models of tumor growth are largely phenomenological in nature, capturing infiltration of the tumor into surrounding healthy tissue, proliferation of the existing tumor, and patient response to therapies, such as chemotherapy and radiotherapy. Considerable inter-patient variability, inherent heterogeneity of th…