34 citations · 59 across the 23 of their papers we have counts for
6 papers · 1 filter
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…
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…
SMS: Spiking Marching Scheme for Efficient Long Time Integration of Differential Equations
Qian Zhang, Adar Kahana, George Em Karniadakis +1
We propose a Spiking Neural Network (SNN)-based explicit numerical scheme for long time integration of time-dependent Ordinary and Partial Differential Equations (ODEs, PDEs). The…
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…
Time-dependent stochastic basis adaptation for uncertainty quantification
Ramakrishna Tipireddy, Panos Stinis, Alexandre M. Tartakovsky
We extend stochastic basis adaptation and spatial domain decomposition methods to solve time varying stochastic partial differential equations (SPDEs) with a large number of input…
Improving solution accuracy and convergence for stochastic physics parameterizations with colored noise
Panos Stinis, Huan Lei, Jing Li +1
Stochastic parameterizations are used in numerical weather prediction and climate modeling to help capture the uncertainty in the simulations and improve their statistical properti…