Error analysis for physics-informed neural networks (PINNs) approximating Kolmogorov PDEs

DOI10.1007/s10444-022-09985-9zbMath1502.65170arXiv2106.14473OpenAlexW3186608048MaRDI QIDQ2095545

Tim De Ryck, Siddhartha Mishra

Publication date: 17 November 2022

Published in: Advances in Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2106.14473

zbMATH Keywords

Kolmogorov equationsdeep learningphysics-informed neural networks

Mathematics Subject Classification ID

Artificial neural networks and deep learning (68T07) Nonlinear parabolic equations (35K55) KdV equations (Korteweg-de Vries equations) (35Q53) Heat equation (35K05) Derivative securities (option pricing, hedging, etc.) (91G20) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65M99)

Related Items (9)

Physics-informed neural networks for approximating dynamic (hyperbolic) PDEs of second order in time: error analysis and algorithms ⋮ Reliable extrapolation of deep neural operators informed by physics or sparse observations ⋮ A New Certified Hierarchical and Adaptive RB-ML-ROM Surrogate Model for Parametrized PDEs ⋮ Higher-order error estimates for physics-informed neural networks approximating the primitive equations ⋮ A theoretical case study of the generalization of machine-learned potentials ⋮ Boundary-safe PINNs extension: application to non-linear parabolic PDEs in counterparty credit risk ⋮ Meshless methods for American option pricing through physics-informed neural networks ⋮ Mobility Estimation for Langevin Dynamics Using Control Variates ⋮ Greedy training algorithms for neural networks and applications to PDEs

Uses Software

• DeepXDE
• FPINNs
• XPINNs
• DeepONet

Cites Work

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