3 papers
cs.LG2026
Variational Neural Networks for Observable Thermodynamics (V-NOTS)
Christopher Eldred, François Gay-Balmaz, Vakhtang Putkaradze
Much attention has recently been devoted to data-based computing of evolution of physical systems. In such approaches, information about data points from past trajectories in phase…
math.DS2024
Geometric, Variational, and Bracket Descriptions of Fluid Motion with Open Boundaries
Christopher Eldred, François Gay-Balmaz, Meng Wu
We develop a Lie group geometric framework for the motion of fluids with permeable boundaries that extends Arnold's geometric description of fluid in closed domains. Our setting is…
cs.LG2024
CLPNets: Coupled Lie-Poisson Neural Networks for Multi-Part Hamiltonian Systems with Symmetries
Christopher Eldred, François Gay-Balmaz, Vakhtang Putkaradze
To accurately compute data-based prediction of Hamiltonian systems, especially the long-term evolution of such systems, it is essential to utilize methods that preserve the structu…