Kernel learning backward SDE filter for data assimilation

Richard Archibald; Feng Bao

doi:10.1016/j.jcp.2022.111009

Kernel learning backward SDE filter for data assimilation

Richard Archibald, Feng Bao

Data Analysis and Machine Learning

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

In this paper, we develop 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. To characterize the dynamical model in the entire state space, we introduce a kernel learning method to learn a continuous global approximation for the conditional probability density function of the target state by using discrete approximated density values as training data. Numerical experiments demonstrate that the kernel learning backward SDE is highly effective.

Original language	English
Article number	111009
Journal	Journal of Computational Physics
Volume	455
DOIs	https://doi.org/10.1016/j.jcp.2022.111009
State	Published - Apr 15 2022

Funding

This work is partially supported by U.S. Department of Energy through FASTMath Institute and Office of Science, Advanced Scientific Computing Research program under the grant DE-SC0022297 . The second author (FB) would also like to acknowledge the support from U.S. National Science Foundation through project DMS-2142672 .

Funders	Funder number
FASTMath Institute
National Science Foundation	DMS-2142672
U.S. Department of Energy
Office of Science
Advanced Scientific Computing Research	DE-SC0022297

Keywords

Backward stochastic differential equations
Kernel learning
Nonlinear filtering problem
Stochastic optimization

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10.1016/j.jcp.2022.111009

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AB - In this paper, we develop 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. To characterize the dynamical model in the entire state space, we introduce a kernel learning method to learn a continuous global approximation for the conditional probability density function of the target state by using discrete approximated density values as training data. Numerical experiments demonstrate that the kernel learning backward SDE is highly effective.

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Kernel learning backward SDE filter for data assimilation

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