Kernel learning backward SDE filter for data assimilation

In this paper, we develop a kernel learning backward SDE filter method to estimate the state of stochastic dynamical system based on its partial noisy observations. A forward differential equations is used propagate target model, and Bayesian inference applied incorporate observational information. To characterize model in entire space, introduce learn continuous global approximation for conditional probability density function by using discrete approximated values as training data. Numerical experiments demonstrate that highly effective.