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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
A DeepLagrangian method for learning and generating aggregation patterns in multi-dimensional Keller-Segel chemotaxis systems
Yani Feng, Michael K. Ng, Zhiwen Zhang
The Keller-Segel (KS) chemotaxis system is used to describe the overall behavior of a collection of cells under the influence of chemotaxis. However, solving the KS chemotaxis syst…
math.NA2025
Functional tensor train neural network for solving high-dimensional PDEs
Yani Feng, Michael K. Ng, Kejun Tang +1
Discrete tensor train decomposition is widely employed to mitigate the curse of dimensionality in solving high-dimensional PDEs through traditional methods. However, the direct app…