167 citations · 1.3k across the 78 of their papers we have counts for
11 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…
Nonlinear Reconstruction for Operator Learning of PDEs with Discontinuities
Samuel Lanthaler, Roberto Molinaro, Patrik Hadorn +1
A large class of hyperbolic and advection-dominated PDEs can have solutions with discontinuities. This paper investigates, both theoretically and empirically, the operator learning…
Gradient Gating for Deep Multi-Rate Learning on Graphs
T. Konstantin Rusch, Benjamin P. Chamberlain, Michael W. Mahoney +2
We present Gradient Gating (G), a novel framework for improving the performance of Graph Neural Networks (GNNs). Our framework is based on gating the output of GNN layers with…
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…
Agnostic Physics-Driven Deep Learning
Benjamin Scellier, Siddhartha Mishra, Yoshua Bengio +1
This work establishes that a physical system can perform statistical learning without gradient computations, via an Agnostic Equilibrium Propagation (Aeqprop) procedure that combin…