7 citations · 23 across the 5 of their papers we have counts for
3 papers · 1 filter
Finite basis physics-informed neural networks as a Schwarz domain decomposition method
Victorita Dolean, Alexander Heinlein, Siddhartha Mishra +1
Physics-informed neural networks (PINNs) [4, 10] are an approach for solving boundary value problems based on differential equations (PDEs). The key idea of PINNs is to use a neura…
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…
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…