3 papers
cs.LG2025
GD-VAEs: Geometric Dynamic Variational Autoencoders for Learning Nonlinear Dynamics and Dimension Reductions
Ryan Lopez, Paul J. Atzberger
We develop data-driven methods incorporating geometric and topological information to learn parsimonious representations of nonlinear dynamics from observations. The approaches lea…
cond-mat.soft2024
Simulation of Stochastic Non-Equilibrium Thermal Effects of Particle Inclusions within Fluid Interfaces and Membranes
Dev Jasuja, Paul J. Atzberger
We formulate theoretical modeling approaches and develop practical computational simulation methods for investigating the non-equilibrium statistical mechanics of fluid interfaces…
cs.LG2024
Geometric Neural Operators (GNPs) for Data-Driven Deep Learning of Non-Euclidean Operators
Blaine Quackenbush, Paul J. Atzberger
We introduce Geometric Neural Operators (GNPs) for accounting for geometric contributions in data-driven deep learning of operators. We show how GNPs can be used (i) to estimate ge…