Stochastic fluids with transport noise: Approximating diffusion from data using SVD and ensemble forecast back-propagation

TL;DR

This paper develops and tests two novel methods for calibrating diffusion terms in stochastic fluid models, using SVD-based analysis and ensemble forecast back-propagation to improve model accuracy and data fitting.

Contribution

It introduces two innovative approaches for estimating diffusion parameters in SPDEs for fluids, combining SVD techniques and ensemble forecast back-propagation.

Findings

Methods accurately calibrate diffusion in idealized fluid models

Approaches improve forecast verification metrics like CRPS

Techniques are validated with known reference data

Abstract

We introduce and test methods for the calibration of the diffusion term in Stochastic Partial Differential Equations (SPDEs) describing fluids. We take two approaches, one uses ideas from the singular value decomposition and the Biot-Savart law. The other backpropagates through an ensemble forecast, with respect to diffusion parameters, to minimise a probabilistic ensemble forecasting metric. We describe the approaches in the specific context of solutions to SPDEs describing the evolution of fluid particles, sometimes called inviscid vortex methods. The methods are tested in an idealised setting in which the reference data is a known realisation of the parameterised SPDE, and also using a forecast verification metric known as the Continuous Rank Probability Score (CRPS).