From Data Geometry to Scien0fic Discovery: Uncertainty Quan0fica0on and Scien0fic Machine Learning on Manifolds for Reliable Data-driven Modeling and Simula0on in Science and Engineering

Abstract

:We are integra0ng modern tools from data science and scien0fic machine learning with uncertainty quan0fica0on to accelerate and op0mize simula0on and analysis for scien0fic discovery and datainformed design, op0miza0on, and decision making in science and engineering. In mathema0cal modeling of complex systems, one typically progresses from observa0ons of the world first to equa0ons for a model, and then to the analysis of the model to make predic0ons. However, several major challenges arise in this process since the complex high-dimensional physical systems of interest oSen involve mul0ple physics, mul0ple length- and 0me-scales, as well as nonlinear and history dependent behaviors. To further complicate maUers, physics-based models must contend with a myriad of uncertain0es such as inherent stochas0city in the physics (aleatory uncertainty) and uncertain0es in model-form (epistemic uncertain0es). Advances in data science, machine learning, and ar0ficial intelligence has enabled the crea0on of “useful” reduced-order/surrogate models. Yet, for very large, complex mul0scale, highdimensional, nonlinear, and expensive to evaluate systems, direct applica0on of these techniques alone is not enough: their effec0veness relies heavily on access to training data which, in the context of highdimensional complex systems, is oSen limited due to the high costs associated with simula0on and experimenta0on. In this talk we show that these challenges can be addressed by developing surrogate models on manifolds that can be used for uncertainty quan0fica0on. This is achieved by introducing another widely-used machine learning task referred to as manifold learning, a linear or nonlinear transforma0on that operates directly on high-dimensional observa0ons -data- to iden0fy/discover a lowdimensional manifold or latent space that encodes the salient informa0on from the observa0on while dras0cally reducing its size.

Short Bio:

Dimitris Giovanis is an Assistant Research Professor in the Dept. of Civil & Systems Engineering at Johns Hopkins University. Dr. Giovanis develops data-driven computa0onal tools and algorithms -- he is the lead developer of the opensource soSware UQpy-- that combine scien0fic machine learning with modeling on low-dimensional manifolds and uncertainty quan0fica0on to push the envelope of both tradi0onal modeling and physics-informed scien0fic machine learning to very high-dimensional and complex physical systems in which computa0onal efficiency is cri0cal and their behavior is highly unpredictable. His work spans applica0ons in materials in extreme environments, natural hazards, biomechanics, aerospace, and epidemics. His Ph.D. was focused on stochas0c finite element methods, he has a master’s degree in computa0onal mechanics and holds a five-year diploma in Civil Engineering, all at the Na0onal Technical University of Athens. He joined the Department of Civil and Systems Engineering at Johns Hopkins as a postdoc in 2016 and joined the faculty in 2020. He is affiliated with the Center on Ar0ficial Intelligence for Materials in Extreme Environments (CAIMEE), the Hopkins Extreme Materials Ins0tute (HEMI), the Mathema0cal Ins0tute for Data Science (MINDS), the Ins0tute for Data Intensive Engineering and Science (IDIES), and the NHERI’s SimCenter. He is a member of the ASCE/EMI Probabilis0c Methods CommiUee, the ASCE/EMI Machine Learning Group, and member of the SIAM/UQ group. He is also an Assistant Coach for the JHU men’s Water Polo team