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math.NA2026
Improving the accuracy of physics-informed neural networks via last-layer retraining
Saad Qadeer, Panos Stinis
Physics-informed neural networks (PINNs) are a versatile tool in the burgeoning field of scientific machine learning for solving partial differential equations (PDEs). However, det…
math.NA2025
Stabilizing PDE--ML coupled systems
Saad Qadeer, Panos Stinis, Hui. Wan
A long-standing obstacle in the use of machine-learnt surrogates with larger PDE systems is the onset of instabilities when solved numerically. Efforts towards ameliorating these h…
math.NA2021
Machine-learning custom-made basis functions for partial differential equations
Brek Meuris, Saad Qadeer, Panos Stinis
Spectral methods are an important part of scientific computing's arsenal for solving partial differential equations (PDEs). However, their applicability and effectiveness depend cr…