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…
A Stochastic Genetic Interacting Particle Method for Reaction-Diffusion-Advection Equations
Boyi Hu, Zhongjian Wang, Jack Xin +1
We develop and analyze a stochastic genetic interacting particle method (SGIP) for reaction-diffusion-advection (RDA) equations. The SGIP method employs operator splitting to appro…
Regularity estimate and sparse approximation of pathwise robust Duncan-Mortensen-Zakai equation
Yuhua Meng, Zhongjian Wang, Stephen S. T. Yau +1
In this paper, we establish an \textit{a priori} estimate for arbitrary-order derivatives of the solution to the pathwise robust Duncan-Mortensen-Zakai (DMZ) equation within the fr…
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 direct algebraic proof for the non-positivity of Liouvillian spectral values and controlling the dissipative gap of unital systems
Yikang Zhang, Thomas Barthel
Markovian open quantum systems are described by the Lindblad master equation , where denotes the system's density operator and the Lio…
A Stochastic Interacting Particle-Field Algorithm for a Haptotaxis Advection-Diffusion System Modeling Cancer Cell Invasion
Boyi Hu, Zhongjian Wang, Jack Xin +1
The investigation of tumor invasion and metastasis dynamics is crucial for advancements in cancer biology and treatment. Many mathematical models have been developed to study the i…
A novel model reduction method to solve inverse problems of parabolic type
Wenlong Zhang, Zhiwen Zhang
In this paper, we propose novel proper orthogonal decomposition (POD)--based model reduction methods that effectively address the issue of inverse crime in solving parabolic invers…
A structure-preserving scheme for computing effective diffusivity and anomalous diffusion phenomena of random flows
Tan Zhang, Zhongjian Wang, Jack Xin +1
This paper aims to investigate the diffusion behavior of particles moving in stochastic flows under a structure-preserving scheme. We compute the effective diffusivity for normal d…
Stochastic convergence of regularized solutions for backward heat conduction problems
Zhongjian Wang, Wenlong Zhang, Zhiwen Zhang
In this paper, we study the stochastic convergence of regularized solutions for backward heat conduction problems. These problems are recognized as ill-posed due to the exponential…