BIMSA > Seminar on Control Theory and Nonlinear Filtering A Dynamical Neural Galerkin Scheme for Filtering Problems
A Dynamical Neural Galerkin Scheme for Filtering Problems
Organizer
Shing Toung Yau
Speaker
Zeju Sun
Time
Wednesday, April 17, 2024 4:00 PM - 4:30 PM
Venue
Online
Abstract
In this talk, we will review a paper entitled ‘A Dynamical Neural Galerkin Scheme for Filtering Problems’ by J. Aghili et, al. The abstract of this paper is as follows. ‘This paper considers the filtering problem which consists in reconstructing the state of a dynamical system with partial observations coming from sensor measurements, and the knowledge that the dynamics are governed by a physical PDE model with unknown parameters. We present a filtering algorithm where the reconstruction of the dynamics is done with neural network approximations whose weights are dynamically updated using observational data. In addition to the estimate of the state, we also obtain time-dependent parameter estimations of the PDE parameters governing the observed evolution. We illustrate the behavior of the method in a one-dimensional KdV equation involving the transport of solutions with local support. Our numerical investigation reveals the importance of the location and number of the observations. In particular, it suggests to consider dynamical sensor placement.