105 citations · 125 across the 35 of their papers we have counts for
5 papers · 1 filter
Two-Step Diffusion: Fast Sampling and Reliable Prediction for 3D Keller--Segel and KPP Equations in Fluid Flows
Zhenda Shen, Zhongjian Wang, Jack Xin +1
We study fast and reliable generative transport for the 3D KS (Keller-Segel) and KPP (Kolmogorov-Petrovsky-Piskunov) equations in the presence of fluid flows with the goal to appro…
A Bidirectional DeepParticle Method for Efficiently Solving Low-dimensional Transport Map Problems
Tan Zhang, Zhongjian Wang, Jack Xin +1
This paper aims to efficiently compute transport maps between probability distributions arising from particle representation of bio-physical problems. We develop a bidirectional De…
A variational neural network approach for glacier modelling with nonlinear rheology
Tiangang Cui, Zhongjian Wang, Zhiwen Zhang
In this paper, we propose a mesh-free method to solve full stokes equation which models the glacier movement with nonlinear rheology. Our approach is inspired by the Deep-Ritz meth…
A DeepParticle method for learning and generating aggregation patterns in multi-dimensional Keller-Segel chemotaxis systems
Zhongjian Wang, Jack Xin, Zhiwen Zhang
We study a regularized interacting particle method for computing aggregation patterns and near singular solutions of a Keller-Segal (KS) chemotaxis system in two and three space di…
A mesh-free method for interface problems using the deep learning approach
Zhongjian Wang, Zhiwen Zhang
In this paper, we propose a mesh-free method to solve interface problems using the deep learning approach. Two interface problems are considered. The first one is an elliptic PDE w…