Abstract: Nonlinear partial differential equations suffer from large compute costs in the presence of multiscale behavior due to the requirement of very fine grids in space and time. Reduced-order models promise to alleviate these costs by using strategies ranging from the projection of the governing equations to a convenient subspace to full surrogacy with the use of non-intrusive machine learning.
This talk will outline our research in the development of such models with highlights such as the use of convolutional auto-encoders for nonlinear embedding identification, the use of neural ordinary differential equations, and recurrent neural networks for temporal dynamics evolution. Moreover, we will present preliminary results from the use of probabilistic modeling methods for quantifying uncertainty in the presence of imperfect data. Following the lessons learned from these studies, perspectives will be provided for the generation of parametric surrogates for real-world datasets across different applications.