most citedError analysis for deep neural network approximations of parametric hyperbolic conservation laws

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math.NA2022★ 5 cited

wPINNs: Weak Physics informed neural networks for approximating entropy solutions of hyperbolic conservation laws

Tim De Ryck, Siddhartha Mishra, Roberto Molinaro

Physics informed neural networks (PINNs) require regularity of solutions of the underlying PDE to guarantee accurate approximation. Consequently, they may fail at approximating dis…

math.NA2022★ 7 cited

Error analysis for deep neural network approximations of parametric hyperbolic conservation laws

Tim De Ryck, Siddhartha Mishra

We derive rigorous bounds on the error resulting from the approximation of the solution of parametric hyperbolic scalar conservation laws with ReLU neural networks. We show that th…