Events

Abstract

Tsunamis generated from megathrust earthquakes are capable of massive destruction. Efforts are underway to instrument subduction zones with seafloor acoustic pressure sensors to provide tsunami early warning. Our goal is to create a digital twin framework that employs this pressure data, along with the 3D coupled acoustic–gravity wave equation forward model, to infer the earthquake-induced spatiotemporal seafloor motion in real time.  The Bayesian solution of this inverse problem then provides the boundary forcing to forward propagate the tsunamis toward populated areas along coastlines and issue forecasts with quantified uncertainties.

Solution of a single forward problem alone entails severe computational costs stemming from the need to resolve ocean acoustic waves with wavelengths of order 0.15 km in a subduction zone of length ~1000 km and width ~200 km. This can require ~1 hour on a large

supercomputer.  The Bayesian inverse problem, with billions of uncertain parameters, formally requires hundreds of thousands of such forward and adjoint wave propagations; thus our goal of real time inference appears to be intractable. We propose a novel approach to enable accurate solution of the inverse and prediction problems in a few seconds on a GPU cluster. The key is to exploit the structure of the parameter-to-observable map, namely that it is a shift-invariant operator and its discretization can be recast as a block Toeplitz matrix, permitting FFT diagonalization and fast GPU implementation. We discuss the Bayesian formulation of the inverse problem and real time GPU solution, and demonstrate that tsunami inverse problems with 10^8 parameters can be solved exactly (up to discretization error) in a fraction of a second. Thus, early warning can be provided with accurate high-fidelity models.

This work is joint with Sreeram Venkat, Stefan Hennekinig, and Milinda Fernando.

About the Speaker

Omar Ghattas is Professor of Mechanical Engineering at The University of Texas at Austin and holds the Cockrell Chair in Engineering. He is also Director of the OPTIMUS (OPTimization, Inverse problems, Machine learning, and Uncertainty for complex Systems) Center in the Oden Institute. He holds courtesy appointments in Earth & Planetary Sciences, Computer Science, and Biomedical Engineering. Before moving to UT Austin in 2005, he spent 16 years on the faculty of Carnegie Mellon University. His research focuses on theory and algorithms for large-scale inverse and optimization problems governed by models of complex engineered and natural systems, with focus on Bayesian inverse problems, Bayesian optimal experimental design, and stochastic optimal control & design. He is a two-time winner of the ACM Gordon Bell Prize, a recipient of the SIAM Geosciences Career Prize, and a Fellow of the Society for Industrial and Applied Mathematics (SIAM).