Optimal Estimation of Dynamically Evolving Diffusivities

TL;DR

This paper introduces an augmented, iterated Kalman smoother method for estimating time-dependent parameters in evolutionary differential equations, with applications in fluid dynamics and plasma physics.

Contribution

It presents a novel approach that incorporates unknown, evolving coefficients into the state vector with stochastic modeling, improving system identification in inverse problems.

Findings

Effective estimation of anomalous diffusion coefficients in turbulent fluids

Accurate plasma rotation velocity estimation in plasma tomography

Demonstrated convergence of the iterative Kalman smoother approach

Abstract

The augmented, iterated Kalman smoother is applied to system identification for inverse problems in evolutionary differential equations. In the augmented smoother, the unknown, time-dependent coefficients are included in the state vector, and have a stochastic component. At each step in the iteration, the estimate of the time evolution of the coefficients is linear. We update the slowly varying mean temperature and conductivity by averaging the estimates of the Kalman smoother. Applications include the estimation of anomalous diffusion coefficients in turbulent fluids and the plasma rotation velocity in plasma tomography.