
Solving multiscale steady radiative transfer equation using neural networks with uniform stability
This paper concerns solving the steady radiative transfer equation with ...
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On the Representation of Solutions to Elliptic PDEs in Barron Spaces
Numerical solutions to highdimensional partial differential equations (...
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A Priori Generalization Error Analysis of TwoLayer Neural Networks for Solving High Dimensional Schrödinger Eigenvalue Problems
This paper analyzes the generalization error of twolayer neural network...
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A Priori Generalization Analysis of the Deep Ritz Method for Solving High Dimensional Elliptic Equations
This paper concerns the a priori generalization analysis of the Deep Rit...
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Density estimation and modeling on symmetric spaces
In many applications, data and/or parameters are supported on nonEuclid...
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A Universal Approximation Theorem of Deep Neural Networks for Expressing Distributions
This paper studies the universal approximation property of deep neural n...
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A Meanfield Analysis of Deep ResNet and Beyond: Towards Provable Optimization Via Overparameterization From Depth
Training deep neural networks with stochastic gradient descent (SGD) can...
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Accelerating Langevin Sampling with Birthdeath
A fundamental problem in Bayesian inference and statistical machine lear...
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UniforminTime Weak Error Analysis for Stochastic Gradient Descent Algorithms via Diffusion Approximation
Diffusion approximation provides weak approximation for stochastic gradi...
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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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Scaling limit of the Stein variational gradient descent part I: the mean field regime
We study an interacting particle system in R^d motivated by Stein variat...
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Yulong Lu
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