Title: Exterior Calculus in Machine-Learned Models

Abstract: For many applications, scientific machine learning techniques provide few guarantees on structure preservation, particularly when learning surrogate models. Towards this limitation, we present a unified perspective of various ways to incorporate exterior calculus techniques into scientific machine learning frameworks, showing how different assumptions on model structure (and on the availability of data) result in different structure-preserving formulations. All of these methods extract reduced models from data while exactly preserving the underlying geometry. Finally, we show results for a selection of these exterior calculus techniques, with a focus on H(div) problems in two dimensions.

 

 

Meeting ID: 980 1596 6959

Passcode: 560286