4 papers · 1 filter
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…
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…
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…