Abstract

We employ a Bayesian framework to solve an inverse problem that aims to identify the initial condition distribution of wave propagation, given a limited set of observable data. To optimize sampling efficiency, we introduce a multi-fidelity No-U-Turn Sampler (MF-NUTS) with an adaptive mass matrix. Maximizing sampling efficiency is crucial, as our ultimate goal is to extend this methodology to a large-scale inverse problem to identify the source parameters of historical tsunami-generating earthquakes. The forward model for tsunami propagation (GeoClaw) requires over 20 minutes of supercomputer time on 24 cores to evaluate each sample for a triple-fault rupture, necessitating a strategy that prioritizes high-probability samples. In this study, we focus on identifying the defining parameter distribution of a simple two-dimensional wave propagation problem. The data consists of maximum wave heights recorded at a small number of observation points, along with the corresponding arrival times of the maximal waves, resembling the type of data available in historical tsunami accounts. Although MF-NUTS is applied to wave propagation here, its approach is widely applicable across various domains in the sciences, providing a powerful tool for efficiently solving statistical inverse problems.

Degree

College and Department

Computational, Mathematical, and Physical Sciences; Mathematics

Rights

https://lib.byu.edu/about/copyright/