Speaker: Rudy Geelen (Department of Aerospace Engineering, Texas A&M)

Title: Learning from data using nonlinear manifolds: a model reduction perspective

Abstract: Despite the remarkable rise of available computer resources and computing technologies, the need for model order reduction to cope with computer simulations of complex physical, chemical, and other processes is an ever-present reality. Reduced-order models are imperative in making computationally tractable outer-loop applications that require simulating systems for many scenarios with different parameters and under varying inputs. They require that one numerically solves the differential equations describing the physical system of interest in low-dimensional, reduced spaces. However, traditional model reduction techniques often fail to identify a low-dimensional linear subspace for approximating the solution to many physics-based simulations. In this talk I will present a novel framework for learning, from data, projection-based reduced-order models of physics-based dynamical systems using nonlinear manifolds. Numerical experiments on a number of nonlinear problems demonstrate the generalizability of the methodology and the increase in accuracy that can be obtained over standard POD-based methods.

Speaker: Romit Moulik (Department of Information Science and Technology, Pennsylvania State University)

Title: Weather and Climate Emulation with physics-informed machine learning

Abstract: Recently, advances in machine learning, hardware (e.g. GPUs/TPUs), and availability of high-quality data have set the stage for machine learning (ML) to tackle problems for weather and climate. This has led to a paradigm shift in operational weather forecasting, most evidently seen by the vast amount of resources being invested into AI models at the leading operational centers including NOAA, ECMWF, and others. This has been motivated by the influx of deep learning-based models in the last three years for weather forecasting which have been demonstrated to have forecasting skill approaching or even exceeding the best available numerical weather prediction (NWP) models. In this seminar, we explore the rise of ML-based modeling for weather and climate prediction, specifically, by looking at (1) a vision transformer-based model for medium-range weather forecasting called Stormer and, (2) one of the first systematic evaluations of machine learning-based emulators for climate research. We conclude by discussing some exciting new directions that are a consequence of our developed models.

Speaker: Tan Bui-Thanh (Oden Institute for Computational Engineering and Sciences, University of Texas at Austin)

Title: Towards Real-Time Probabilistic SciML algorithms for Digital Twins

Abstract: Digital twins/models (DTs) are designed to be replicas of systems and processes. At the core of a digital twin (DT) is a physical/mathematical model that captures the behavior of the real system across temporal and spatial scales. One of the key roles of DMs is enabling “what if” scenario testing of hypothetical simulations to understand the implications at any point throughout the life cycle of the process, to monitor the process, to calibrate parameters to match the actual process and to quantify the uncertainties. In this talk, we will present various (faster than) real-time Scientific Deep Learning (SciDL) approaches for forward, inverse, and UQ problems. Both theoretical and numerical results for various problems including transport, heat, Burgers, (transonic and supersonic) Euler, and Navier-Stokes equations will be presented.