MAE Colloquium: Nat Trask (UPenn)

Geometry and structure preservation in scientific AI: building models that generalize beyond training data

In science and engineering contexts, the majority of current AI methods are \textit{interpolatory}, relying on supervised examples of input/output fields to predict physical systems. These tools, by definition, cannot extrapolate to evaluate the performance of new geometries or physics not observed in training data. This precludes their use in design and discovery, areas where AI is presumed to have massive potential impact. In this talk, we introduce frameworks for representing both physics and geometry in a coordinate free manner, allowing us to construct data-driven models that predict physics in extrapolatory regimes. We then introduce a metriplectic framework which can be used to learn stochastic physics in a "top-down" manner direct from data in mesoscopic regimes, where the interplay between fluctuations and dissipative processes must be carefully treated to obtain thermodynamically valid models of non-equilibrium processes. Examples will be provided in fluid mechanics, plasma physics, fracture mechanics and suspension flows.
 

Bio: Nat Trask is an associate professor in the Department of Mechanical Engineering and Applied Mechanics at the University of Pennsylvania. His research focuses on the integration of physical and mathematical structure into machine learning architectures, providing mathematically rigorous paths toward developing AI-driven tools. The techniques lie primarily in concepts related to exterior calculus and geometric/variational mechanics and provide a means of extracting models that can be used in extreme physics settings when the derivation of solution of first-principles model is intractable. He has a particular interest in the relationship between graph neural networks and traditional finite element discretizations of continuum models. Trask uses these techniques to construct probabilistic digital twins and perform autonomous scientific discovery and have worked in a number of multiscale/multiphysics application areas including combustion, energy storage, climate simulation, fusion power, multiphase flows, fracture, and soft matter.

Trask earned his Ph.D. in applied mathematics from Brown University in 2016 and his B.Eng./M.Sc. in mechanical engineering and applied mathematics from the University of Massachusetts, Amherst in 2010.