Real-time Bayesian Inversion, Forecasting, and OED for Tsunami Early Warning

Prof. Omar Ghattas, University of Texas at Austin

Wednesday, October 28, 2026, 2:00-2:40 pm UTC (30 min talk + 10 min questions)
7 am PDT / 9 am CDT / 10 am EDT / 2 pm UTC / 3 pm CET / 11 pm JST

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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 acoustic 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 and linearity of the parameter-to-observable and parameter-to-prediction maps, which permits FFT block-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 online, after a modest number of offline adjoint wave propagations equal to the number of sensors.

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. If time permits, we will discuss data-driven prior construction, goal-oriented dimension reduction, and construction of fast surrogates for tsunami forecasting using the nonlinear shallow water equations, which are required 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.

Bio:

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 and Director of the OPTIMUS (OPTimization, Inverse problems, Machine learning, and Uncertainty for complex Systems) Center in the Oden Institute for Computational Engineering & Sciences, and a member of the faculty in the Computational Science, Engineering, and Mathematics graduate program. He holds courtesy appointments in Earth & Planetary Sciences and Biomedical Engineering. Before moving to UT Austin in 2005, he spent 16 years on the faculty of Carnegie Mellon University. His current research focuses on theory and algorithms for large-scale Bayesian inversion, stochastic optimal control/design, and digital twins for complex engineered and natural systems. He is a three-time winner of the ACM Gordon Bell Prize, a recipient of the SIAM Geosciences Career Prize and the SIAM Babuska Prize, and a Fellow of SIAM and USACM. He holds BSE, MS, and PhD degrees from Duke University.