72 citations · 247 across the 52 of their papers we have counts for
6 papers · 1 filter
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…
Structure-preserving Sparse Identification of Nonlinear Dynamics for Data-driven Modeling
Kookjin Lee, Nathaniel Trask, Panos Stinis
Discovery of dynamical systems from data forms the foundation for data-driven modeling and recently, structure-preserving geometric perspectives have been shown to provide improved…
Machine learning structure preserving brackets for forecasting irreversible processes
Kookjin Lee, Nathaniel A. Trask, Panos Stinis
Forecasting of time-series data requires imposition of inductive biases to obtain predictive extrapolation, and recent works have imposed Hamiltonian/Lagrangian form to preserve st…
Physics-constrained deep neural network method for estimating parameters in a redox flow battery
QiZhi He, Panos Stinis, Alexandre Tartakovsky
In this paper, we present a physics-constrained deep neural network (PCDNN) method for parameter estimation in the zero-dimensional (0D) model of the vanadium redox flow battery (V…
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…
Optimal renormalization of multi-scale systems
Jacob Price, Brek Meuris, Madelyn Shapiro +1
While model order reduction is a promising approach in dealing with multi-scale time-dependent systems that are too large or too expensive to simulate for long times, the resulting…