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math.NA2026
Tensor train methods for high-dimensional nonlinear filtering problems with correlated noise
Yuhua Meng, Stephen S. -T. Yau, Zhiwen Zhang
Nonlinear filtering with correlated noise leads to a Duncan-Mortensen-Zakai (DMZ) equation in the form of a stochastic partial differential equation (SPDE). Unlike the independent…
math.NA2025
Regularity estimate and sparse approximation of pathwise robust Duncan-Mortensen-Zakai equation
Yuhua Meng, Zhongjian Wang, Stephen S. T. Yau +1
In this paper, we establish an \textit{a priori} estimate for arbitrary-order derivatives of the solution to the pathwise robust Duncan-Mortensen-Zakai (DMZ) equation within the fr…
math.NA2024
Sparse discovery of differential equations based on multi-fidelity Gaussian process
Yuhuang Meng, Yue Qiu
Sparse identification of differential equations aims to compute the analytic expressions from the observed data explicitly. However, there exist two primary challenges. Firstly, it…