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Weak physics informed neural networks for approximating entropy solutions of hyperbolic conservation laws
(2022)SAM Research ReportPhysics informed neural networks (PINNs) require regularity of solutions of the underlying PDE to guarantee accurate approximation. Consequently, they may fail at approximating discontinuous solutions of PDEs such as nonlinear hyperbolic equations. To ameliorate this, we propose a novel variant of PINNs, termed as weak PINNs (wPINNs) for accurate approximation of entropy solutions of scalar conservation laws. wPINNs are based on approximating ...Report -
Convolutional Neural Operators for robust and accurate learning of PDEs
(2023)SAM Research ReportAlthough very successfully used in conventional machine learning, convolution based neural network architectures -- believed to be inconsistent in function space -- have been largely ignored in the context of learning solution operators of PDEs. Here, we present novel adaptations for convolutional neural networks to demonstrate that they are indeed able to process functions as inputs and outputs. The resulting architecture, termed as ...Report