Goal-Oriented Real-Time Bayesian Inference for Linear Autonomous Dynamical Systems With Application to Digital Twins for Tsunami Early Warning

TL;DR

This paper introduces a real-time Bayesian framework for digital twins of autonomous dynamical systems, enabling efficient data assimilation and prediction for tsunami early warning using high-dimensional PDE models.

Contribution

It proposes a novel goal-oriented Bayesian inference method exploiting model structure to perform real-time inverse problems with high-dimensional parameters.

Findings

Successfully infers seafloor motion from pressure data

Predicts tsunami propagation in real time

Handles models with up to 10^8 parameters

Abstract

We present a goal-oriented framework for constructing digital twins with the following properties: (1) they employ discretizations of high-fidelity PDE models governed by autonomous dynamical systems, leading to large-scale forward problems; (2) they solve a linear inverse problem to assimilate observational data to infer uncertain model components followed by a forward prediction of the evolving dynamics; and (3) the entire end-to-end, data-to-inference-to-prediction computation is carried out without approximation and in real time through a Bayesian framework that rigorously accounts for uncertainties. Several challenges must be overcome to realize this framework, including the large scale of the forward problem, the high dimensionality of the parameter space, and for a class of problems including those we target, the slow decay of the singular values of the parameter-to-observable map. Here we introduce a methodology to overcome these challenges by exploiting the autonomous structure of the forward model to decompose the solution of the inverse problem into an offline phase in which the PDE model is solved a limited number of times, and an online phase that computes the parameter inference and prediction of quantities of interest in real time, given observational data. Our goal is to apply this framework to construct digital twins for subduction zones to provide early warning for tsunamis. To this end, we show how our methodology can be used to employ seafloor pressure observations, along with the coupled acoustic-gravity wave equations, to infer the earthquake-induced seafloor motion (discretized with 10^9 parameters) and forecast the tsunami propagation. We present results of an end-to-end inference, prediction, and uncertainty quantification for a representative test problem with 10^8 inversion parameters for which goal-oriented Bayesian inference is accomplished in real time.