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

Jiexing Gao, Yurii Zakharian

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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