Machine Learned Reduced-Order Models for Advective Partial Differential Equations




RE 032


 Romit Maulik

Margaret Butler Postdoctoral Fellow, 

Argonne Leadership Computing Facility, 

Argonne National Laboratory



Nonlinear partial differential equations suffer from large compute costs in the presence of multi-scale behavior due to the requirement of very fine grids in space and time. Reduced-order models promise the alleviation of these costs by utilizing 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 some recent developments related to the integration of data science tools within computational engineering workflows that allow for in-situ generation and deployment of model-order reduction. Following the lessons learned from these studies, perspectives will be provided for the generation of parametric surrogates for real-world datasets across different applications.


Stochastic & Multiscale Modeling and Computation



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