Authors: Louis Sharrock, Nikolas Kantas
A new paper has been published in the SIAM Journal by MPE Reading Student, Louis Sharrock.
The paper can be viewed online here: Joint Online Parameter Estimation and Optimal Sensor Placement for the Partially Observed Stochastic Advection-Diffusion Equation | SIAM/ASA Journal on Uncertainty Quantification | Vol. 10, No. 1 | Society for Industrial and Applied Mathematics
In this paper, we consider the problem of jointly performing online parameter estimation and optimal sensor placement for a partially observed infinite-dimensional linear diffusion process. We present a novel solution to this problem in the form of a continuous-time, two-timescale stochastic gradient descent algorithm, which recursively seeks to maximize the asymptotic log-likelihood of the observations with respect to the unknown model parameters and to minimize the expected mean squared error of the hidden state estimate with respect to the sensor locations. We also provide extensive numerical results illustrating the performance of the proposed approach in the case that the hidden signal is governed by the two-dimensional stochastic advection-diffusion equation.© 2022, Society for Industrial and Applied Mathematics Permalink: https://doi.org/10.1137/20M1375073