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09/19/2023
Γ-convergence of Nonlocal Dirichlet Energies With Penalty Formulations of Dirichlet Boundary Data
We study nonlocal Dirichlet energies associated with a class of nonlocal...
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07/23/2023
An axiomatized PDE model of deep neural networks
Inspired by the relation between deep neural network (DNN) and partial d...
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09/30/2022
Point Normal Orientation and Surface Reconstruction by Incorporating Isovalue Constraints to Poisson Equation
Oriented normals are common pre-requisites for many geometric algorithms...
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09/06/2022
Semi-Supervised Clustering via Dynamic Graph Structure Learning
Most existing semi-supervised graph-based clustering methods exploit the...
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05/16/2022
A scalable deep learning approach for solving high-dimensional dynamic optimal transport
The dynamic formulation of optimal transport has attracted growing inter...
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04/28/2022
BI-GreenNet: Learning Green's functions by boundary integral network
Green's function plays a significant role in both theoretical analysis a...
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04/24/2022
M2N: Mesh Movement Networks for PDE Solvers
Mainstream numerical Partial Differential Equation (PDE) solvers require...
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04/14/2022
Unsupervised Deep Learning Meets Chan-Vese Model
The Chan-Vese (CV) model is a classic region-based method in image segme...
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03/28/2022
A nonlocal Stokes system with volume constraints
In this paper, we introduce a nonlocal model for linear steady Stokes sy...
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03/04/2022
Truncation Error Analysis for an Accurate Nonlocal Manifold Poisson Model with Dirichlet Boundary
In this work, we introduced a class of nonlocal models to accurately app...
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02/10/2022
A non-local gradient based approach of infinity Laplacian with Γ-convergence
We propose an infinity Laplacian method to address the problem of interp...
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11/18/2021
Learning Modified Indicator Functions for Surface Reconstruction
Surface reconstruction is a fundamental problem in 3D graphics. In this ...
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10/18/2021
Training Deep Neural Networks with Adaptive Momentum Inspired by the Quadratic Optimization
Heavy ball momentum is crucial in accelerating (stochastic) gradient-bas...
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10/01/2021
BINet: Learning to Solve Partial Differential Equations with Boundary Integral Networks
We propose a method combining boundary integral equations and neural net...
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05/07/2021
Diff-ResNets for Few-shot Learning – an ODE Perspective
Interpreting deep neural networks from the ordinary differential equatio...
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01/04/2021
A Second-Order Nonlocal Approximation for Surface Poisson Model with Dirichlet Boundary
Partial differential equations on manifolds have been widely studied and...
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12/31/2020
Discontinuous Galerkin methods for the Laplace-Beltrami operator on point cloud
A generic geometric error analysis framework for numerical solution of P...
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06/10/2020
Interpolation between Residual and Non-Residual Networks
Although ordinary differential equations (ODEs) provide insights for des...
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01/28/2019
CURE: Curvature Regularization For Missing Data Recovery
Missing data recovery is an important and yet challenging problem in ima...
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11/26/2018
EnResNet: ResNet Ensemble via the Feynman-Kac Formalism
We propose a simple yet powerful ResNet ensemble algorithm which consist...
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09/23/2018
Adversarial Defense via Data Dependent Activation Function and Total Variation Minimization
We improve the robustness of deep neural nets to adversarial attacks by ...
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02/01/2018
Deep Learning with Data Dependent Implicit Activation Function
Though deep neural networks (DNNs) achieve remarkable performances in ma...
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01/31/2018
Weighted Nonlocal Total Variation in Image Processing
In this paper, a novel weighted nonlocal total variation (WNTV) method i...
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08/21/2017