Presented by: Dr. Nat Trask
University of Pennsylvania
Hosted by:
Mathematics in Computation Talk Series
Abstract:
Within the last year, the artificial intellI community has turned a renewed focus toward engineering and physical sciences, both within the U.S. Department of Energy (DOE) and industry. Many of these efforts hinge upon an assumption that scale alone will be able to achieve predictive scientific models. To date, however, works show that neural physics models rapidly degrade as they are used at the periphery of their training data distribution; this presents a major risk to applying them to design or discovery tasks which, by definition, aim to operate specifically at this frontier. This talk will present recent work in which topological structure in both the representation of geometry and of physics can be used to construct models that are able to extrapolate: both in the sense of predicting physics on geometries or forecasting to future times unseen during training. This structure can be accessed by developing hybrid neural architectures which wrap state-of-the-art transformers in a “topological scaffold” provided by mixed finite element machinery. By exposing variational structure, provable properties are established regarding stability and accuracy for learned models which is intractable for contemporary “black-box” architectures. Several examples from both community benchmarks and DOE digital twinning efforts are provided where these architectures are able to achieve state of the art performance, often with orders of magnitude smaller models.
Speaker’s Bio:
Dr. Trask is an associate professor in the Mechanical Engineering and Applied Mechanics department at the University of Pennsylvania. He maintains a joint appointment with Sandia National Laboratories, and is co-director of Scalable, Efficient and Accelerated Causal Reasoning Operators, Graphs and Spikes for Earth and Embedded Systems, a DOE Mathematical Multifaceted Integrated Capability Center developing next generation scientific machine learning architectures. He has worked on a number of application areas spanning multi-scale/multi-physics in fluids, solids, electromagnetism, materials, and solid-state physics.
Host:
Viktor Reshniak, [email protected], 865-341-4394