AI x Science Seminar: Nat Trask

In scientific machine learning, researchers construct simulators of physical systems which are either computationally expensive or intractable to model with conventional simulation tools. Despite impressive steps in the last couple years, these techniques generally fail to meet the requirements to reliably deploy in realistic engineering settings: methods fail to treat complex engineering geometries, physical principles related to conservation hold at best in a weak sense, emergent physics in multiscale systems do not provide correct non-equilibrium statistical response, and predictions lack the theoretical and uncertainty quantification guarantees which allow engineers to design high-consequence systems. To address these issues, we will introduce several notions of \textit{physical structure preservation} which support the mathematical guarantees which underpin the conventional predictive modeling. While the community is often artificially divided between physics-agnostic transformers and conventional numerical discretizations, we demonstrate several hybrid techniques that realize the benefits of both while naturally imposing notions of structure preservation. We demonstrate: construction of real-time digital twins built upon a data-driven finite element exterior calculus; construction of auto-regressive integrators with guaranteed long term stability independent of rollout length; and construction of data-driven particle models built upon metriplectic bracket theory which preserve emergent statistical mechanics.

Seminar: 12:00 – 1:00 pm
Speaker Lunch: 1:00 – 2:00 pm

Presented by: Penn AI, Innovation in Data Engineering and Science (IDEAS), and the Data Driven Discovery Initiative (DDDI).