Cover Image

Error analysis for empirical risk minimization over clipped ReLU networks in solving linear Kolmogorov partial differential equations

Fuente: arXiv

Saved in:

Bibliographic Details
Main Authors:	Xiao, Jichang, Wang, Xiaoqun
Format:	Preprint
Published:	2023
Subjects:	Numerical Analysis 60H30, 65C30, 62M45, 68T07
Online Access:	Acceder al recurso
Tags:	Add Tag No Tags, Be the first to tag this record!

Similar Items

Deep Learning Based on Randomized Quasi-Monte Carlo Method for Solving Linear Kolmogorov Partial Differential Equation
by: Xiao, Jichang, et al.
Published: (2023)

Discontinuous hybrid neural networks for the one-dimensional partial differential equations
by: Wang, Xiaoyu, et al.
Published: (2025)

Error analysis for learning fractional stochastic differential equations with applications in neural approximations
by: Dehshiri, Mahdi, et al.
Published: (2026)

A discontinuous Galerkin plane wave neural network method for Helmholtz equation and Maxwell's equations
by: Yuan, Long, et al.
Published: (2025)

Neural network solvers for parametrized elasticity problems that conserve linear and angular momentum
by: Boon, Wietse M., et al.
Published: (2024)

A framework of discontinuous Galerkin neural networks for iteratively approximating residuals
by: Yuan, Long, et al.
Published: (2025)

Deep neural networks with ReLU, leaky ReLU, and softplus activation provably overcome the curse of dimensionality for Kolmogorov partial differential equations with Lipschitz nonlinearities in the $L^p$-sense
by: Ackermann, Julia, et al.
Published: (2023)

A Parameter-Driven Physics-Informed Neural Network Framework for Solving Two-Parameter Singular Perturbation Problems Involving Boundary Layers
by: Boro, Pradanya, et al.
Published: (2025)

A forward differential deep learning-based algorithm for solving high-dimensional nonlinear backward stochastic differential equations
by: Kapllani, Lorenc, et al.
Published: (2024)

A backward differential deep learning-based algorithm for solving high-dimensional nonlinear backward stochastic differential equations
by: Kapllani, Lorenc, et al.
Published: (2024)

A C^s-smooth mixed degree and regularity isogeometric spline space over planar multi-patch domains
by: Kapl, Mario, et al.
Published: (2024)

Deep neural networks with ReLU, leaky ReLU, and softplus activation provably overcome the curse of dimensionality for space-time solutions of semilinear partial differential equations
by: Ackermann, Julia, et al.
Published: (2024)

The Neural Approximated Virtual Element Method for Elasticity Problems
by: Berrone, Stefano, et al.
Published: (2025)

On the algorithmic construction of deep ReLU networks
by: Huybrechs, Daan
Published: (2025)

Deep Adaptive Dimension Reduction for Bayesian Inference in Inverse Problems
by: Wang, Yueyang, et al.
Published: (2026)

A Complete Symmetry Classification of Shallow ReLU Networks
by: Ramakrishnan, Pranavkrishnan
Published: (2026)

Computational homogenization for aerogel-like polydisperse open-porous materials using neural network--based surrogate models on the microscale
by: Klawonn, Axel, et al.
Published: (2024)

Approximation Rates for Shallow ReLU$^k$ Neural Networks on Sobolev Spaces via the Radon Transform
by: Mao, Tong, et al.
Published: (2024)

A Tractography Analysis Framework Using Diffusion Maps to Study Thalamic Connectivity in Traumatic Brain Injury
by: Sharma, Akul, et al.
Published: (2025)

An energy-based deep splitting method for the nonlinear filtering problem
by: Bågmark, Kasper, et al.
Published: (2022)

The minimal width of universal $p$-adic ReLU neural networks
by: Kiss, Sándor Z., et al.
Published: (2026)

Data-Free Asymptotics-Informed Operator Networks for Singularly Perturbed PDEs
by: Lee, Jinsil, et al.
Published: (2025)

Self-adaptive physics-informed neural network for forward and inverse problems in heterogeneous porous flow
by: Aziz, Md. Abdul, et al.
Published: (2025)

A convergent scheme for the Bayesian filtering problem based on the Fokker--Planck equation and deep splitting
by: Bågmark, Kasper, et al.
Published: (2024)

How many samples to label for an application given a foundation model? Chest X-ray classification study
by: Nechaev, Nikolay, et al.
Published: (2025)

Challenges in automatic differentiation and numerical integration in physics-informed neural networks modelling
by: Daněk, Josef, et al.
Published: (2024)

Discontinuous Galerkin finite element operator network for solving non-smooth PDEs
by: Chawla, Kapil, et al.
Published: (2026)

Certified and accurate computation of function space norms of deep neural networks
by: Gründler, Johannes, et al.
Published: (2026)

Residual Multi-Fidelity Neural Network Computing
by: Davis, Owen, et al.
Published: (2023)

High-dimensional Bayesian filtering through deep density approximation
by: Bågmark, Kasper, et al.
Published: (2025)

Nonlinear filtering based on density approximation and deep BSDE prediction
by: Bågmark, Kasper, et al.
Published: (2025)

Equidistribution-based training of Free Knot Splines and ReLU Neural Networks
by: Appella, Simone, et al.
Published: (2024)

Computing k-means in mixed precision
by: Carson, Erin, et al.
Published: (2024)

Greedy construction of quadratic manifolds for nonlinear dimensionality reduction and nonlinear model reduction
by: Schwerdtner, Paul, et al.
Published: (2024)

Online learning of quadratic manifolds from streaming data for nonlinear dimensionality reduction and nonlinear model reduction
by: Schwerdtner, Paul, et al.
Published: (2024)

Enhanced uncertainty quantification variational autoencoders for the solution of Bayesian inverse problems
by: Tonini, Andrea, et al.
Published: (2025)

Density estimation for elliptic PDE with random input by preintegration and quasi-Monte Carlo methods
by: Gilbert, Alexander D., et al.
Published: (2024)

Data Completion for Electrical Impedance Tomography by Conditional Diffusion Models
by: Chen, Ke, et al.
Published: (2026)

Learning to Integrate
by: Ernst, Oliver G., et al.
Published: (2025)

A deep shotgun method for solving high-dimensional parabolic partial differential equations
by: Xu, Wenjun, et al.
Published: (2025)