14 papers
A Pseudo-time Data-Driven Framework for Model Reduction of Linear Operator Equations
Zhentong Wei, Tingen Xiong, Wenlong Zhang +1
This paper proposes a novel Pseudo-time Proper Orthogonal Decomposition (POD) framework to enable model reduction for stationary problems lacking temporal snapshot data. By recasti…
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…
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…
A Bernoulli Phase-Fitted finite difference method with wavenumber-explicit analysis for the Helmholtz problem
Ansgar Jüngel, Panchi Li, Zhiwei Sun +1
A new Bernoulli phase-fitted finite difference method for the Helmholtz equation is introduced, obtained by applying a complexified Scharfetter--Gummel flux to the one-way factors…
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 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…