Generative Machine Learning Approaches for Data-Driven Modeling and Reductions of Non-Linear Dynamics

Explore generative machine learning approaches for data-driven modeling and reductions of non-linear dynamics in scientific simulations in this 46-minute lecture by Paul Atzberger. Delve into Geometric Variational Autoencoders (GD-VAEs) for obtaining representations that incorporate topological information, smoothness, and adherence to physical principles. Discover how GD-VAEs can be applied to high-dimensional dynamical systems and non-linear PDEs. Learn about Stochastic Dynamic Generative Adversarial Networks (SDYN-GANs) for data-driven learning of probabilistic models from stochastic system observations. Understand how SDYN-GANs can be used to learn parameters of drift and diffusive contributions in inertial stochastic systems, as well as unknown non-linear force-laws from trajectory observations. Gain insights into strategies for developing robust and interpretable machine learning methods for scientific simulations, particularly in the context of soft materials, complex fluids, and biophysical systems.