PINNs error estimates for nonlinear equations in $\mathbb{R}$-smooth Banach spaces

Jiexing Gao; Yurii Zakharian

PINNs error estimates for nonlinear equations in $\mathbb{R}$-smooth Banach spaces

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arxiv 2305.11915 v3 pith:XWISMDN5 submitted 2023-05-18 math.FA cs.LGcs.NAmath.NA

Jiexing Gao , Yurii Zakharian This is my paper · ORCID

classification math.FAcs.LGcs.NAmath.NA

keywords errorpinnspacesadmitbanachboundingbramble-hilbertclasses

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abstract

In the paper, we describe in operator form classes of PDEs that admit PINN's error estimation. Also, for $L^p$ spaces, we obtain a Bramble-Hilbert type lemma that is a tool for PINN's residuals bounding.

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Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Prediction error certification for PINNs: Theory, computation, and application to Stokes flow
math.NA 2025-08 conditional novelty 6.0 of 10

A modified semigroup-based error bound makes PINN error certification applicable to Stokes flow, but the practical certification is not fully rigorous.

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