3 papers
math.NA2025
Structure-Preserving Neural Ordinary Differential Equations for Stiff Systems
Allen Alvarez Loya, Daniel A. Serino, J. W. Burby +1
Neural ordinary differential equations (NODEs) are an effective approach for data-driven modeling of dynamical systems arising from simulations and experiments. One of the major sh…
math.DS2025
Fast-Slow Neural Networks for Learning Singularly Perturbed Dynamical Systems
Daniel A. Serino, Allen Alvarez Loya, Joshua W. Burby +2
Singularly perturbed dynamical systems play a crucial role in climate dynamics and plasma physics. A powerful and well-known tool to address these systems is the Fenichel normal fo…
math.NA2024
High Order Accurate Hermite Schemes on Curvilinear Grids with Compatibility Boundary Conditions
Allen Alvarez Loya, Daniel Appelö, William D. Henshaw
High order accurate Hermite methods for the wave equation on curvilinear domains are presented. Boundaries are treated using centered compatibility conditions rather than more stan…