Bayesian Inference for Fluid Dynamics: A Case Study for the Stochastic Rotating Shallow Water Model

TL;DR

This paper demonstrates the use of a tempering-based adaptive particle filter to perform Bayesian inference on a high-dimensional stochastic fluid dynamics model, validating its effectiveness through tests on simpler models and discussing its efficiency.

Contribution

It introduces a novel application of tempering and sample regeneration techniques to high-dimensional stochastic fluid models derived from SALT, advancing Bayesian inference methods in this domain.

Findings

Validated the particle filter approach on Lorenz '63 model

Demonstrated applicability to high-dimensional SALT-SRSW model

Discussed efficiency and potential improvements

Abstract

In this work, we use a tempering-based adaptive particle filter to infer from a partially observed stochastic rotating shallow water (SRSW) model which has been derived using the Stochastic Advection by Lie Transport (SALT) approach. The methodology we present here validates the applicability of tempering and sample regeneration via a Metropolis-Hastings algorithm to high-dimensional models used in stochastic fluid dynamics. The methodology is first tested on the Lorenz '63 model with both full and partial observations. Then we discuss the efficiency of the particle filter the SALT-SRSW model.