A Data-Driven Finite Element Exterior Calculus

Explore a seminar on "A Data Driven Finite Element Exterior Calculus" presented by Nat Trask from the University of Pennsylvania as part of the FEM@LLNL Seminar Series. Delve into the development of reduced-order models for multiphysics systems using machine learning techniques that maintain the verification and validation guarantees of modern finite element methods. Discover how deep learning architectures can construct trainable partitions of unity, providing control volumes with associated boundary operators. Examine the creation of a discrete de Rham complex with corresponding Hodge theory, and learn about its connections to graph neural networks. Investigate the application of this framework to digital twins, supporting real-time data assimilation and optimal control. Understand how Bayesian optimization can be used to learn unknown physics on chain complex adjacency matrices, resulting in models with intrinsic representations of epistemic uncertainty. Gain insights into the MFEM project and its community through this comprehensive presentation on innovative finite element research and applications.