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08/28/2023
A convergent interacting particle method for computing KPP front speeds in random flows
We aim to efficiently compute spreading speeds of reaction-diffusion-adv...
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04/11/2023
One-Shot High-Fidelity Talking-Head Synthesis with Deformable Neural Radiance Field
Talking head generation aims to generate faces that maintain the identit...
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01/19/2023
Understanding the diffusion models by conditional expectations
This paper provide several mathematical analyses of the diffusion model ...
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09/05/2022
A variational neural network approach for glacier modelling with nonlinear rheology
In this paper, we propose a mesh-free method to solve full stokes equati...
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08/31/2022
A DeepParticle method for learning and generating aggregation patterns in multi-dimensional Keller-Segel chemotaxis systems
We study a regularized interacting particle method for computing aggrega...
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06/17/2022
Asymmetric transport computations in Dirac models of topological insulators
This paper presents a fast algorithm for computing transport properties ...
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11/02/2021
DeepParticle: learning invariant measure by a deep neural network minimizing Wasserstein distance on data generated from an interacting particle method
We introduce the so called DeepParticle method to learn and generate inv...
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06/02/2021
Convergence analysis of a Lagrangian numerical scheme in computing effective diffusivity of 3D time-dependent flows
In this paper, we study the convergence analysis for a robust stochastic...
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03/27/2021
A convergent interacting particle method and computation of KPP front speeds in chaotic flows
In this paper, we study the propagation speeds of reaction-diffusion-adv...
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09/10/2019
A class of robust numerical methods for solving dynamical systems with multiple time scales
In this paper, we develop a class of robust numerical methods for solvin...
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08/12/2019
Solving high-dimensional nonlinear filtering problems using a tensor train decomposition method
In this paper, we propose an efficient numerical method to solve high-di...
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06/21/2019
Convergence of stochastic structure-preserving schemes for computing effective diffusivity in random flows
In this paper, we propose stochastic structure-preserving schemes to com...
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01/03/2019