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 a high fidelity forward model given by 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 boundary forcing to forward propagate the tsunamis toward populated areas along coastlines and issue wave height forecasts with quantified uncertainties for early warning.
However, solution of a single forward problem alone entails severe computational costs stemming from the need to resolve ocean acoustic waves with wavelengths of order 1.5 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 roofline-optimal multi-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 enabling early warning with high fidelity models.
This work is joint with Sreeram Venkat, Stefan Hennekinig, and Milinda Fernando.