7 papers
Weak adversarial tensor neural network for high-dimensional Fokker-Planck equations
Sihong Shao, Zhongwei Xu
Solving high-dimensional stationary Fokker-Planck (SFP) equations remains challenging. Recently, deep learning methods have shown great potential for solving high-dimensional SFP e…
Learning a generalized Navier-Stokes model beyond the continuum regime
Sihong Shao, Yanli Wang, Zhongwei Xu
Navier-Stokes (NS) equations lose accuracy in the transition regime when the Knudsen number is large, while the Boltzmann equation provides an adequate kinetic description with a s…
A High-Dimensional Extension of Wagner's Theorem and the Geometrization of Hypergraphs
Qiming Fang, Sihong Shao
This paper introduces a geometric representation of hypergraphs by representing hyperedges as simplices. Building on this framework, we employ homotopy groups to analyze the topolo…
An adaptive Hermite spectral method for the Boltzmann equation
Sihong Shao, Yanli Wang, Jie Wu
We propose an adaptive Hermite spectral method for the three-dimensional velocity space of the Boltzmann equation guided by a newly developed frequency indicator. For the homogeneo…
Geometrization of Graphs: Towards Bounding the Chromatic Number via High-Dimensional Embedding
Qiming Fang, Sihong Shao
We establish a geometric framework by transforming a graph into a -dimensional CW complex . This construction is achieved by systematically attaching -sph…
Adaptive Hyperbolic-cross-space Mapped Jacobi Method on Unbounded Domains with Applications to Solving Multidimensional Spatiotemporal Integrodifferential Equations
Yunhong Deng, Sihong Shao, Alex Mogilner +1
In this paper, we develop a new adaptive hyperbolic-cross-space mapped Jacobi (AHMJ) method for solving multidimensional spatiotemporal integrodifferential equations in unbounded d…
Application of Causal Inference Techniques to the Maximum Weight Independent Set Problem
Jianfeng Liu, Sihong Shao, Chaorui Zhang
A powerful technique for solving combinatorial optimization problems is to reduce the search space without compromising the solution quality by exploring intrinsic mathematical pro…