Research Highlight
Kernel learning-based backward SDE filter for data assimilation
Achievement
we developed a kernel learning backward SDE filter method to estimate the state of a stochastic dynamical system based on its partial noisy observations. A system of forward backward stochastic differential equations is used to propagate the state of the target dynamical model, and Bayesian inference is applied to incorporate the observational information.
The novel methodology that we introduced in this work is to treat the approximated filtering density values obtained by the backward SDE filter at discrete spatial sample points as "simulated training data samples" and then derive a continuous approximation for the filtering density by using machine learning methods. In this way, the information of filtering density at scattered spatial samples is effectively combined as a smooth distribution for the target state in the entire state space.
Figure 1: the convergence of the kernel method by using more spatial sample points to describe the filtering density
Figure 2: comparison performance between our kernel learning Backward SDE method and two other state-of-the-art methods in solving a 20-dimensional Lorenz 96 tracking problem.
Publication
Richard Archibald, Feng Bao, Kernel learning backward SDE filter for data assimilation, Journal of Computational Physics, Vol. 455, pp. 111009, 2022.