4 papers
Complex Diffusion Maps with -Parameterized Kernels Revealing Inherent Harmonic Representations
Tongzhen Dang, Weiyang Ding, Michael K. Ng
In this paper, we propose Complex Diffusion Maps (CDM), a novel diffusion mapping framework that aims to reveal the dominant complex harmonics of high-dimensional data. Inspired by…
A Layer Separation Optimization Framework for Cross-Entropy Training in Deep Learning
Yaru Liu, Michael K. Ng, Yiqi Gu
This paper investigates the deep learning optimization problem with softmax cross-entropy loss. We propose a layer separation strategy to alleviate the strong nonconvexity encounte…
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…
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…