Error analysis for physics-informed neural networks (PINNs) approximating Kolmogorov PDEs (Q2095545)

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

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instance of

scholarly article

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title

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

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Advances in Computational Mathematics

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publication date

17 November 2022

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full work available at URL

https://arxiv.org/abs/2106.14473

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zbMATH Keywords

physics-informed neural networks

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deep learning

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Kolmogorov equations

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describes a project that uses

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MaRDI publication profile

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cites work

Physics Informed Neural Networks (PINNs) For Approximating Nonlinear Dispersive PDEs

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Analysis of the Generalization Error: Empirical Risk Minimization over Deep Artificial Neural Networks Overcomes the Curse of Dimensionality in the Numerical Approximation of Black--Scholes Partial Differential Equations

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On the approximation of functions by tanh neural networks

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Neural‐network‐based approximations for solving partial differential equations

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Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations

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Error bounds for approximations with deep ReLU neural networks in Ws,p norms

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Approximation rates for neural networks with encodable weights in smoothness spaces

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Extended Physics-Informed Neural Networks (XPINNs): A Generalized Space-Time Domain Decomposition Based Deep Learning Framework for Nonlinear Partial Differential Equations

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Conservative physics-informed neural networks on discrete domains for conservation laws: applications to forward and inverse problems

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Q3091370

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Error estimates for DeepONets: a deep learning framework in infinite dimensions

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Q5829356

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DeepXDE: A Deep Learning Library for Solving Differential Equations

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Deep learning observables in computational fluid dynamics

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Iterative surrogate model optimization (ISMO): an active learning algorithm for PDE constrained optimization with deep neural networks

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Physics-informed neural networks for high-speed flows

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Estimates on the generalization error of physics-informed neural networks for approximating a class of inverse problems for PDEs

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Stochastic differential equations. An introduction with applications.

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fPINNs: Fractional Physics-Informed Neural Networks

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Hidden physics models: machine learning of nonlinear partial differential equations

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Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

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Deep learning in high dimension: Neural network expression rates for generalized polynomial chaos expansions in UQ

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B-PINNs: Bayesian physics-informed neural networks for forward and inverse PDE problems with noisy data

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Identifiers

zbMATH Open document ID

1502.65170

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DOI

10.1007/s10444-022-09985-9

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Mathematics Subject Classification ID

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Mathematics(1 entry)

mardi Publication:2095545