105 citations · 125 across the 35 of their papers we have counts for
37 papers
Posterior sampling by source-space MCMC via prior-based few-step transport maps
Hoang Phuc Hau Luu, Marcelo Hartmann, Zhongjian Wang
Bayesian inference increasingly uses informative but implicit priors represented only by samples, such as historical ensembles, simulator outputs, and pretrained generative models.…
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…
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…
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…
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-…
Pathway to Complexity bound under Wasserstein metric of flow-based models
Xiangjun Meng, Zhongjian Wang
We provide attainable analytical tools to estimate the error of flow-based generative models under the Wasserstein metric and to establish the optimal sampling iteration complexity…
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…
COFM: Consistent Optimal Transport Flow Matching via Partially Input Convex Neural Networks
Fanghui Song, Zhongjian Wang, Jiebao Sun
Optimal transport (OT) provides a principled framework for learning mappings between probability distributions, and has found broad applications in generative modeling, inverse pro…
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…
DPOT: A DeepParticle method for Computation of Optimal Transport with convergence guarantee
Yingyuan Li, Aokun Wang, Zhongjian Wang
In this work, we propose a novel machine learning approach to compute the optimal transport map between two continuous distributions from their unpaired samples, based on the DeepP…
PODNO: Proper Orthogonal Decomposition Neural Operators
Zilan Cheng, Zhongjian Wang, Li-Lian Wang +1
In this paper, we introduce Proper Orthogonal Decomposition Neural Operators (PODNO) for solving partial differential equations (PDEs) dominated by high-frequency components. Build…
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 systems with normal Lindblad operators
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 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…
Global Well-posedness and Convergence Analysis of Score-based Generative Models via Sharp Lipschitz Estimates
Connor Mooney, Zhongjian Wang, Jack Xin +1
We establish global well-posedness and convergence of the score-based generative models (SGM) under minimal general assumptions of initial data for score estimation. For the smooth…
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…
A Novel Stochastic Interacting Particle-Field Algorithm for 3D Parabolic-Parabolic Keller-Segel Chemotaxis System
Zhongjian Wang, Jack Xin, Zhiwen Zhang
We introduce an efficient stochastic interacting particle-field (SIPF) algorithm with no history dependence for computing aggregation patterns and near singular solutions of parabo…
A convergent interacting particle method for computing KPP front speeds in random flows
Tan Zhang, Zhongjian Wang, Jack Xin +1
We aim to efficiently compute spreading speeds of reaction-diffusion-advection (RDA) fronts in divergence free random flows under the Kolmogorov-Petrovsky-Piskunov (KPP) nonlineari…
Mathematical analysis of singularities in the diffusion model under the submanifold assumption
Yubin Lu, Zhongjian Wang, Guillaume Bal
This paper concerns the mathematical analyses of the diffusion model in machine learning. The drift term of the backward sampling process is represented as a conditional expectatio…
Randomized methods for computing optimal transport without regularization and their convergence analysis
Yue Xie, Zhongjian Wang, Zhiwen Zhang
The optimal transport (OT) problem can be reduced to a linear programming (LP) problem through discretization. In this paper, we introduced the random block coordinate descent (RBC…
Long time asymptotics of mixed-type Kimura diffusions
Guillaume Bal, Binglu Chen, Zhongjian Wang
This paper concerns the long-time asymptotics of diffusions with degenerate coefficients at the domain's boundary. Degenerate diffusion operators with mixed linear and quadratic de…