167 citations · 1.3k across the 78 of their papers we have counts for
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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…
On the discrete equation model for compressible multiphase fluid flows
Marco Petrella, Remi Abgrall, Siddhartha Mishra
The modeling of multi-phase flow is very challenging, given the range of scales as well as the diversity of flow regimes that one encounters in this context. We revisit the discret…
Error estimates for physics informed neural networks approximating the Navier-Stokes equations
Tim De Ryck, Ameya D. Jagtap, Siddhartha Mishra
We prove rigorous bounds on the errors resulting from the approximation of the incompressible Navier-Stokes equations with (extended) physics informed neural networks. We show that…