17 papers
A Novel Stochastic Particle-Field Algorithm for a Reaction-Diffusion-Advection Cancer Invasion Model
Jingyuan Hu, Zhongjian Wang, Jack Xin +1
In this paper, we present a novel numerical framework for solving a specific biological reaction-diffusion-advection system of cancer growth in three dimensions (3D) using particle…
Preconditioned One-Step Generative Modeling for Bayesian Inverse Problems in Function Spaces
Zilan Cheng, Li-Lian Wang, Zhongjian Wang
We propose a machine-learning algorithm for Bayesian inverse problems in the function-space regime. Based on one-step generative transport, the method learns an amortized neural op…
On the Regularity and Generalization of One-Step Wasserstein-guided Generative Models for PDE-Induced Measures
Likun Lin, Zhongjian Wang, Jack Xin +1
Despite the remarkable empirical success of generative models, the available theory on their statistical accuracy in scientific computing remains largely pessimistic. This paper de…
DC-LA: Difference-of-Convex Langevin Algorithm
Hoang Phuc Hau Luu, Zhongjian Wang
We study a sampling problem whose target distribution is where the data fidelity term is Lipschitz smooth while the regularizer term is a non…
A fast stochastic interacting particle-field method for 3D parabolic parabolic Chemotaxis systems: numerical algorithms and error analysis
Jingyuan Hu, Zhongjian Wang, Jack Xin +1
In this paper, we develop a novel numerical framework, namely the stochastic interacting particle-field method with particle-in-cell acceleration (SIPF-PIC), for the efficient simu…
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…