Cover Image

Generalization Error Analysis of Deep Backward Dynamic Programming for Solving Nonlinear PDEs

Fuente: arXiv

Saved in:

Bibliographic Details
Main Authors:	Ouyang, Du, Xiao, Jichang, Wang, Xiaoqun
Format:	Preprint
Published:	2024
Subjects:	Numerical Analysis
Online Access:	Acceder al recurso
Tags:	Add Tag No Tags, Be the first to tag this record!

Similar Items

Error analysis for empirical risk minimization over clipped ReLU networks in solving linear Kolmogorov partial differential equations
by: Xiao, Jichang, et al.
Published: (2023)

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

Quasi-Monte Carlo for unbounded integrands with importance sampling
by: Ouyang, Du, et al.
Published: (2023)

ALM-PINNs Algorithms for Solving Nonlinear PDEs and Parameter Inversion Problems
by: Tian, Yimeng, et al.
Published: (2024)

Deep Picard Iteration for High-Dimensional Nonlinear PDEs
by: Han, Jiequn, et al.
Published: (2024)

Solving Nonlinear PDEs with Sparse Radial Basis Function Networks
by: Shao, Zihan, et al.
Published: (2025)

RBF-Generated Finite Difference Method Coupled with Quadratic Programming for Solving PDEs on Surfaces with Derivative Boundary Conditions
by: Chen, Peng, et al.
Published: (2026)

Solving PDEs With Deep Neural Nets under General Boundary Conditions
by: Zhang, Chenggong
Published: (2025)

Explicit $θ$-Schemes for Solving Anticipated Backward Stochastic Differential Equations
by: Hu, Mingshang, et al.
Published: (2019)

Solving Roughly Forced Nonlinear PDEs via Misspecified Kernel Methods and Neural Networks
by: Baptista, Ricardo, et al.
Published: (2025)

Generalized Moving Least-Squares Methods for Solving Vector-valued PDEs on Unknown Manifolds
by: Li, Rongji, et al.
Published: (2024)

Enhanced convergence rates of Adaptive Importance Sampling with recycling schemes via quasi-Monte Carlo methods
by: Chen, Jianlong, et al.
Published: (2025)

A New Adaptive Deep Learning based Reduced Order Model for Hybrid-Type Parabolic PDEs: Rigorous Error Analysis and Applications
by: Kotowski, Dawid, et al.
Published: (2026)

Nested Multilevel Monte Carlo with Preintegration for Efficient Risk Estimation
by: Xu, Yu, et al.
Published: (2026)

Importance sampling and active subspace in quasi-Monte Carlo
by: Yu, Jiaxin, et al.
Published: (2026)

Approximation Theory and Applications of Randomized Neural Networks for Solving High-Dimensional PDEs
by: De Ryck, T., et al.
Published: (2025)

Bean: A Language for Backward Error Analysis
by: Kellison, Ariel E., et al.
Published: (2025)

Stochastic Quadrature Rules for Solving PDEs using Neural Networks
by: Taylor, Jamie M., et al.
Published: (2025)

Solving High-Dimensional PDEs Using Linearized Neural Networks
by: Mao, Tong, et al.
Published: (2026)

Incorporating Local Hölder Regularity into PINNs for Solving Elliptic PDEs
by: Zhou, Qirui, et al.
Published: (2025)

Optimal Error Estimates of a Linearized Backward Euler Localized Orthogonal Decomposition for the Landau-Lifshitz Equation
by: Ma, Zetao, et al.
Published: (2026)

Latent Neural Operator Pretraining for Solving Time-Dependent PDEs
by: Wang, Tian, et al.
Published: (2024)

Enhanced BPINN Training Convergence in Solving General and Multi-scale Elliptic PDEs with Noise
by: Hou, Yilong, et al.
Published: (2024)

Randomized Quasi-Monte Carlo and Importance Sampling for Super-Fast Growing Functions with Applications to Finance
by: Chen, Jianlong, et al.
Published: (2025)

Solving PDEs on Unknown Manifolds with Machine Learning
by: Liang, Senwei, et al.
Published: (2021)

A Quantum Spectral Framework for Solving PDEs
by: Huang, Chih-Kang, et al.
Published: (2026)

Subspace Diffusion Posterior Sampling for Travel-Time Tomography
by: Cao, Xiang, et al.
Published: (2024)

A Nonlinear Generalization of the Bauer-Fike Theorem and Novel Iterative Methods for Solving Nonlinear Eigenvalue Problems
by: Katende, Ronald
Published: (2024)

Numerical Reconstruction and Analysis of Backward Semilinear Subdiffusion Problems
by: Wu, Xu, et al.
Published: (2025)

A Meshfree RBF-FD Constant along Normal Method for Solving PDEs on Surfaces
by: Bayona, Víctor, et al.
Published: (2024)

Neural Evolutionary Kernel Method: A Knowledge-Guided Framework for Solving Evolutionary PDEs
by: Ling, Shuo, et al.
Published: (2026)

What Can One Expect When Solving PDEs Using Shallow Neural Networks?
by: He, Roy Y., et al.
Published: (2025)

Deep Forward-Backward Dynamic Programming Schemes for High-Dimensional Semilinear Nonlocal PDEs and FBSDE with Jumps
by: Wang, Wansheng, et al.
Published: (2025)

Spline-Based Stochastic Collocation Methods for Uncertainty Quantification in Nonlinear Hyperbolic PDEs
by: Chertock, Alina, et al.
Published: (2024)

New High-Order Numerical Methods for Hyperbolic Systems of Nonlinear PDEs with Uncertainties
by: Chertock, Alina, et al.
Published: (2023)

Finite Element Eigenfunction Network (FEENet): A Hybrid Framework for Solving PDEs on Complex Geometries
by: Li, Shiyuan, et al.
Published: (2026)

Structured Backward Error for the WKB method
by: Corless, Robert M., et al.
Published: (2024)

Generalization Error Estimates of Machine Learning Methods for Solving High Dimensional Schrödinger Eigenvalue Problems
by: Yu, Hao, et al.
Published: (2024)

Numerical Solution and Errors Analysis of Iterative Method for a Nonlinear Plate Bending Problem
by: Wilfried, Akakpo A., et al.
Published: (2025)

Adaptive-Growth Randomized Neural Networks for PDEs: Algorithms and Numerical Analysis
by: Dang, Haoning, et al.
Published: (2024)