Reduced Order Modeling for Tsunami Forecasting with Bayesian Hierarchical Pooling

TL;DR

This paper introduces randPROM, a novel reduced order modeling approach using neural Galerkin-Projections and hierarchical pooling, enabling efficient, statistically interpretable tsunami forecasts with fewer simulations.

Contribution

It develops a new physics-informed ROM framework that generalizes to multiple initial conditions using Bayesian hierarchical pooling, applied to tsunami modeling.

Findings

randPROM accurately predicts tsunami wave arrival times and heights.

The method reduces computational effort by decreasing the number of required simulations.

It provides statistically interpretable and physically justified tsunami forecasts.

Abstract

Reduced order models (ROM) can represent spatiotemporal processes in significantly fewer dimensions and can be solved many orders faster than their governing partial differential equations (PDEs). For example, using a proper orthogonal decomposition produces a ROM that is a small linear combination of fixed features and weights, but that is constrained to the given process it models. In this work, we explore a new type of ROM that is not constrained to fixed weights, based on neural Galerkin-Projections, which is an initial value problem that encodes the physics of the governing PDEs, calibrated via neural networks to accurately model the trajectory of these weights. Then using a statistical hierarchical pooling technique to learn a distribution on the initial values of the temporal weights, we can create new, statistically interpretable and physically justified weights that are generalized to many similar problems. When recombined with the spatial features, we form a complete physics surrogate, called a randPROM, for generating simulations that are consistent in distribution to a neighborhood of initial conditions close to those used to construct the ROM. We apply the randPROM technique to the study of tsunamis, which are unpredictable, catastrophic, and highly-detailed non-linear problems, modeling both a synthetic case of tsunamis near Fiji and the real-world Tohoku 2011 disaster. We demonstrate that randPROMs may enable us to significantly reduce the number of simulations needed to generate a statistically calibrated and physically defensible prediction model for arrival time and height of tsunami waves.