Optimal Estimation of Dynamically Evolving Diffusivities

by   Kurt S. Riedel, et al.

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.



page 1

page 2

page 3

page 4


Continuous time limit of the stochastic ensemble Kalman inversion: Strong convergence analysis

The Ensemble Kalman inversion (EKI) method is a method for the estimatio...

Subdiffusion with Time-Dependent Coefficients: Improved Regularity and Second-Order Time Stepping

This article concerns second-order time discretization of subdiffusion e...

Reconstruction of a Space-Time Dependent Source in Subdiffusion Models via a Perturbation Approach

In this article we study inverse problems of recovering a space-time dep...

Reduced order modeling with time-dependent bases for PDEs with stochastic boundary conditions

Low-rank approximation using time-dependent bases (TDBs) has proven effe...

Iterate Averaging and Filtering Algorithms for Linear Inverse Problems

It has been proposed that classical filtering methods, like the Kalman f...

Statistical Analysis of Some Evolution Equations Driven by Space-only Noise

We study the statistical properties of stochastic evolution equations dr...

L2 convergence of smooth approximations of Stochastic Differential Equations with unbounded coefficients

The aim of this paper is to obtain convergence in mean in the uniform to...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.