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09/01/2023
Solving multiscale elliptic problems by sparse radial basis function neural networks
Machine learning has been successfully applied to various fields of scie...
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08/08/2023
The Random Feature Method for Solving Interface Problems
Interface problems have long been a major focus of scientific computing,...
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06/03/2023
Exploring the Optimal Choice for Generative Processes in Diffusion Models: Ordinary vs Stochastic Differential Equations
The diffusion model has shown remarkable success in computer vision, but...
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04/14/2023
The Random Feature Method for Time-dependent Problems
We present a framework for solving time-dependent partial differential e...
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04/12/2023
Micromagnetics simulations and phase transitions of ferromagnetics with Dzyaloshinskii-Moriya interaction
Magnetic skyrmions widely exist in a diverse range of magnetic systems, ...
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09/07/2022
Convergence analysis of an implicit finite difference method for the inertial Landau-Lifshitz-Gilbert equation
The Landau-Lifshitz-Gilbert (LLG) equation is a widely used model for fa...
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07/27/2022
Bridging Traditional and Machine Learning-based Algorithms for Solving PDEs: The Random Feature Method
One of the oldest and most studied subject in scientific computing is al...
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11/15/2021
Convergence Analysis of A Second-order Accurate, Linear Numerical Scheme for The Landau-Lifshitz Equation with Large Damping Parameters
A second order accurate, linear numerical method is analyzed for the Lan...
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08/06/2021
A second-order semi-implicit method for the inertial Landau-Lifshitz-Gilbert equation
Recent theoretical and experimental advances show that the inertia of ma...
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03/20/2021
Understanding Loss Landscapes of Neural Network Models in Solving Partial Differential Equations
Solving partial differential equations (PDEs) by parametrizing its solut...
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01/21/2021
A Gauss-Seidel projection method with the minimal number of updates for stray field in micromagnetic simulations
Magnetization dynamics in magnetic materials is often modeled by the Lan...
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01/14/2021
A Machine-Learning Method for Time-Dependent Wave Equations over Unbounded Domains
Time-dependent wave equations represent an important class of partial di...
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08/04/2020
Enforcing exact boundary and initial conditions in the deep mixed residual method
In theory, boundary and initial conditions are important for the wellpos...
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06/07/2020
MIM: A deep mixed residual method for solving high-order partial differential equations
In recent years, a significant amount of attention has been paid to solv...
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05/10/2020
A comprehensive study of boundary conditions when solving PDEs by DNNs
Recent years have witnessed growing interests in solving partial differe...
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11/05/2019
Numerical methods for antiferromagnetics
Compared with ferromagnetic counterparts, antiferromagnetic materials ar...
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11/05/2019
Quasi-Monte Carlo sampling for machine-learning partial differential equations
Solving partial differential equations in high dimensions by deep neural...
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10/31/2019
Connecting exciton diffusion with surface roughness via deep learning
Exciton diffusion plays a vital role in the function of many organic sem...
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09/16/2019
Efficient multiscale methods for the semiclassical Schrödinger equation with time-dependent potentials
The semiclassical Schrödinger equation with time-dependent potentials is...
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07/27/2019
Two improved Gauss-Seidel projection methods for Landau-Lifshitz-Gilbert equation
In this paper, we present two improved Gauss-Seidel projection methods w...
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07/04/2019
Second-order semi-implicit projection methods for micromagnetics simulations
Micromagnetics simulations require accurate approximation of the magneti...
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06/30/2019