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06/01/2023
High-order Moment Closure Models with Random Batch Method for Efficient Computation of Multiscale Turbulent Systems
We propose a high-order stochastic-statistical moment closure model for ...
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01/17/2023
Geometric ergodicity of SGLD via reflection coupling
We consider the geometric ergodicity of the Stochastic Gradient Langevin...
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01/03/2023
Diffusion approximations of Oja's online principal component analysis
Oja's algorithm of principal component analysis (PCA) has been one of th...
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06/02/2021
Random walk approximation for irreversible drift-diffusion process on manifold: ergodicity, unconditional stability and convergence
Irreversible drift-diffusion processes are very common in biochemical re...
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01/19/2021
Surfactant-dependent contact line dynamics and droplet adhesion on textured substrates: derivations and computations
We study the adhesion of a droplet with insoluble surfactant laid on its...
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10/20/2020
Transition path theory for Langevin dynamics on manifold: optimal control and data-driven solver
We present a data-driven point of view for the rare events, which repres...
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06/22/2020
A Proximal-Gradient Algorithm for Crystal Surface Evolution
As a counterpoint to recent numerical methods for crystal surface evolut...
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05/22/2020
Data-driven Efficient Solvers and Predictions of Conformational Transitions for Langevin Dynamics on Manifold in High Dimensions
We work on dynamic problems with collected data {x_i} that distributed o...
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05/18/2020
Inbetweening auto-animation via Fokker-Planck dynamics and thresholding
We propose an equilibrium-driven deformation algorithm (EDDA) to simulat...
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05/16/2020
Projection method for droplet dynamics on groove-textured surface with merging and splitting
We study the full dynamics of droplets placed on an inclined groove-text...
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04/12/2020
A direct simulation approach for the Poisson-Boltzmann equation using the Random Batch Method
The Poisson-Boltzmann equation is a nonlinear elliptic equation that des...
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03/25/2020
Convergence of Random Batch Method for interacting particles with disparate species and weights
We consider in this work the convergence of Random Batch Method proposed...
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01/13/2020
Gradient flow formulation and second order numerical method for motion by mean curvature and contact line dynamics on rough surface
We study the dynamics of a droplet placing on an inclined rough surface,...
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12/19/2019
Field model for complex ionic fluids: analytical properties and numerical investigation
In this paper, we consider the field model for complex ionic fluids with...
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12/19/2019
Field model for complex ionic fluids
In this paper, we consider the field model for complex ionic fluids with...
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11/18/2019
A structure preserving numerical scheme for Fokker-Planck equations of neuron networks: numerical analysis and exploration
In this work, we are concerned with the Fokker-Planck equations associat...
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10/25/2019
Towards understanding the boundary propagation speeds in tumor growth models
At the continuous level, we consider two types of tumor growth models: t...
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02/09/2019
A stochastic version of Stein Variational Gradient Descent for efficient sampling
We propose in this work RBM-SVGD, a stochastic version of Stein Variatio...
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02/02/2019
Uniform-in-Time Weak Error Analysis for Stochastic Gradient Descent Algorithms via Diffusion Approximation
Diffusion approximation provides weak approximation for stochastic gradi...
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07/22/2018
On the rate of convergence of empirical measure in ∞-Wasserstein distance for unbounded density function
We consider a sequence of identically independently distributed random s...
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09/11/2017
A Modified Levy Jump-Diffusion Model Based on Market Sentiment Memory for Online Jump Prediction
In this paper, we propose a modified Levy jump diffusion model with mark...
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05/22/2017