Upcoming Event: NSF-Simons CosmicAI Hybrid Seminar Series

Real time Bayesian inversion, prediction, and OED for tsunami early warning

Omar Ghattas, Professor, Walker Department of Mechanical Engineering and Oden Institute, University of Texas at Austin

Abstract

We address real-time Bayesian inverse problems governed by time-shift-invariant wave equations, with particular focus on tsunami inference and optimal experimental design. Efforts are underway to instrument subduction zones with ocean bottom acoustic pressure sensors to provide tsunami early warning. Our goal is to create a physics-based early-warning system that employs this pressure data, along with the 3D coupled acoustic–gravity wave equations, to infer the earthquake-induced spatiotemporal seafloor motion in real time. The Bayesian solution of this inverse problem then provides the seafloor forcing to forward propagate the tsunamis toward populated areas along coastlines and issue forecasts with quantified uncertainties.   In the context of the Cascadia Subduction Zone, a single forward wave propagation requires ~1 hour on a supercomputer. The Bayesian inverse problem, with a billion uncertain parameters, formally requires hundreds of thousands of adjoint wave propagations; thus real time inference appears to be intractable. 

We propose a novel approach to enable exact solution of the inverse and prediction problems in real time. The key is to exploit the time-shift-invariance of the parameter-to-observable map, which permits FFT diagonalization and fast GPU implementation. We demonstrate that tsunami inverse problems with a billion parameters can be solved exactly in a fraction of a second.   This fast Bayesian inversion capability is then exploited to solve the optimal experimental design problem of placement of seafloor pressure sensors to maximize expected information gain in predictive quantities of interest. Time permitting, we discuss data-driven prior construction, goal-oriented dimension reduction, and construction of fast surrogates for nonlinear shallow water equation-based tsunami predictions, which are more accurate in shallower waters. This work is joint with Stefan Henneking, Sreeram Venkat, Bowen Shi, and Yuhang Li at UT Austin, and Alice Gabriel at UCSD.

Biography

Dr. Omar Ghattas is Professor of Mechanical Engineering at The University of Texas at Austin and holds the Cockrell Chair in Engineering. He is also Principal Faculty in the Oden Institute for Computational Engineering & Sciences and Director of the OPTIMUS (OPTimization, Inverse problems, Machine learning, and Uncertainty for complex Systems) Center. Before moving to UT Austin in 2005, he spent 16 years on the faculty of Carnegie Mellon University. He holds BSE (civil and environmental engineering) and MS and PhD (computational mechanics) degrees from Duke University. He is a three-time recipient of the ACM Gordon Bell Prize (2003, 2015, 2025). He received the 2019 SIAM Computational Science & Engineering Best Paper Prize, the 2019 SIAM Geosciences Career Prize, and the 2025 SIAM Ivo and Renata Babŭska Prize. He is a Fellow of the Society for Industrial and Applied Mathematics (SIAM) and of the U.S. Association for Computational Mechanics (USACM).   Research in the OPTIMUS Center focuses on advanced mathematical, computational, and statistical theory and algorithms for large-scale inverse and optimal design/control problems governed by models of complex engineered and natural systems. 

He and his group are developing algorithms to overcome the challenges of Bayesian inverse problems and data assimilation, Bayesian optimal experimental design, and optimal control & design under uncertainty, for large-scale complex systems. These include structure-exploiting methods for dimension reduction, surrogates, and neural network approximation, along with high performance computing algorithms. These components are integrated and coupled together to form frameworks for digital twins. Driving applications include those in geophysics and earth systems (earthquakes, ice sheet dynamics, subsurface poroelasticity, seismology, tsunamis) and advanced materials and manufacturing processes (metamaterials, nanomaterials, additive manufacturing, nondestructive evaluation).