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math.NA2023★ 96 cited
Multilevel domain decomposition-based architectures for physics-informed neural networks
Victorita Dolean, Alexander Heinlein, Siddhartha Mishra +1
Physics-informed neural networks (PINNs) are a powerful approach for solving problems involving differential equations, yet they often struggle to solve problems with high frequenc…
math.NA2023
A Monte-Carlo ab-initio algorithm for the multiscale simulation of compressible multiphase flows
Marco Petrella, Remi Abgrall, Siddhartha Mishra
We propose a novel Monte-Carlo based ab-initio algorithm for directly computing the statistics for quantities of interest in an immiscible two-phase compressible flow. Our algorith…