PINNs error estimates for nonlinear equations in ℝ-smooth Banach spaces
Not on the map. Why?
Abstract (arXiv)
In the paper, we describe in operator form classes of PDEs that admit PINN's error estimation. Also, for Lp spaces, we obtain a Bramble-Hilbert type lemma that is a tool for PINN's residuals bounding.
Key facts. Cited by 2 papers in the map (data through 7 Oct 2026). Builds on 13 of its 40 references that are in the map. First posted on arXiv 18 May 2023.
Builds on
13 of 40 references.
References · 13
- 2017Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equationscited by 362
- 2017Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equationscited by 188
- 2017Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equationscited by 158
- 2020Estimates on the generalization error of Physics Informed Neural Networks (PINNs) for approximating PDEscited by 115
- 2021Parallel Physics-Informed Neural Networks via Domain Decompositioncited by 112
- 2021On the approximation of functions by tanh neural networkscited by 81
- 2022Physics-informed neural networks for inverse problems in supersonic flowscited by 75
- 2019A Theoretical Analysis of Deep Neural Networks and Parametric PDEscited by 74
- 2022Error estimates for physics informed neural networks approximating the Navier-Stokes equationscited by 63
- 2021When Do Extended Physics-Informed Neural Networks (XPINNs) Improve Generalization?cited by 57
- 2019Deep learning observables in computational fluid dynamicscited by 38
- 2022wPINNs: Weak Physics informed neural networks for approximating entropy solutions of hyperbolic conservation lawscited by 29
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Citing papers per year: 2024: 1; 2025: 1.
2 papers.