Abstract
In this paper, we introduce an adaptive kernel method for solving the optimal filtering problem. The computational framework that we adopt is the Bayesian filter, in which we recursively generate an optimal estimate for the state of a target stochastic dynamical system based on partial noisy observational data. The mathematical model that we use to formulate the propagation of the state dynamics is the Fokker–Planck equation, and we introduce an operator decomposition method to efficiently solve the Fokker–Planck equation. An adaptive kernel method is introduced to adaptively construct Gaussian kernels to approximate the probability distribution of the target state. Bayesian inference is applied to incorporate the observational data into the state model simulation. Numerical experiments have been carried out to validate the performance of our kernel method.
| Original language | English |
|---|---|
| Pages (from-to) | 37-59 |
| Number of pages | 23 |
| Journal | Journal of Machine Learning for Modeling and Computing |
| Volume | 3 |
| Issue number | 3 |
| DOIs | |
| State | Published - 2022 |
Funding
This work is partially supported by the U.S. Department of Energy through FASTMath Institute and Office of Science, Advanced Scientific Computing Research program under the Grant No. DE-SC0022297. The third author (F.B.) would also like to acknowledge the support from the U.S. National Science Foundation through Project No. DMS-2142672.
Keywords
- Bayesian inference
- kernel approximation
- optimal filtering problem
- partial differential equation