Conditional neural Whitney forms for structure-preserving digital twins

Nathaniel Trask
University of Pennsylvania
Mechanical Engineering and Applied Mechanics

In this talk we will present a framework exploiting connections between graph neural networks and the finite element exterior calculus to build data-driven models which preserve notions of structure from governing physics, including conservation structure, gauge symmetries, bracket structure, and detailed balance while supporting uncertainty quantification. We will focus on recent work developing notions of conditioning, whereby one can sample from finite element models conditioned upon measurements which support real-time data-assimilation.