313 citations · 704 across the 32 of their papers we have counts for
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cs.CE2026
Feature tracking in physics-informed neural networks via joint optimization of nonlinear deformation manifolds: application to shocks
Akshay Thakur, Matthew Zahr
Physics-informed neural networks (PINNs) often converge to inaccurate solutions for conservation laws with shocks, because uniformly distributed collocation points undersample loca…
cs.CE2021★ 313 cited
Physics-informed graph neural Galerkin networks: A unified framework for solving PDE-governed forward and inverse problems
Han Gao, Matthew J. Zahr, Jian-Xun Wang
Despite the great promise of the physics-informed neural networks (PINNs) in solving forward and inverse problems, several technical challenges are present as roadblocks for more c…
cs.CE2020★ 13 cited
Preserving general physical properties in model reduction of dynamical systems via constrained-optimization projection
A. Schein, K. T. Carlberg, M. J. Zahr
Model-reduction techniques aim to reduce the computational complexity of simulating dynamical systems by applying a (Petrov-)Galerkin projection process that enforces the dynamics…