10 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…
Iterative bounds on effective transport for advection diffusion in periodic flow fields
N. B. Murphy, D. Hallman, E. Cherkaev +2
Over three decades ago a Stieltjes integral representation for the effective diffusivity of a tracer in a steady fluid velocity field was developed, involving the spectral measure…
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…
An Efficient Particle-Field Algorithm with Neural Interpolation based on a Parabolic-Hyperbolic Chemotaxis System in 3D
Jongwon David Kim, Jack Xin
Tumor angiogenesis involves a collection of tumor cells moving towards blood vessels for nutrients to grow. Angiogenesis, and in general chemotaxis systems have been modeled using…
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…