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01/24/2023
On the convergence of Sobolev gradient flow for the Gross-Pitaevskii eigenvalue problem
We study the convergences of three projected Sobolev gradient flows to t...
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12/17/2022
Two-Scale Gradient Descent Ascent Dynamics Finds Mixed Nash Equilibria of Continuous Games: A Mean-Field Perspective
Finding the mixed Nash equilibria (MNE) of a two-player zero sum continu...
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12/09/2022
Transfer Learning Enhanced DeepONet for Long-Time Prediction of Evolution Equations
Deep operator network (DeepONet) has demonstrated great success in vario...
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11/01/2022
Birth-death dynamics for sampling: Global convergence, approximations and their asymptotics
Motivated by the challenge of sampling Gibbs measures with nonconvex pot...
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01/25/2022
A Regularity Theory for Static Schrödinger Equations on ℝ^d in Spectral Barron Spaces
Spectral Barron spaces have received considerable interest recently as i...
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10/13/2021
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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06/14/2021
On the Representation of Solutions to Elliptic PDEs in Barron Spaces
Numerical solutions to high-dimensional partial differential equations (...
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05/04/2021
A Priori Generalization Error Analysis of Two-Layer Neural Networks for Solving High Dimensional Schrödinger Eigenvalue Problems
This paper analyzes the generalization error of two-layer neural network...
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01/05/2021
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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09/04/2020
Density estimation and modeling on symmetric spaces
In many applications, data and/or parameters are supported on non-Euclid...
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04/19/2020
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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03/11/2020
A Mean-field 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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05/23/2019
Accelerating Langevin Sampling with Birth-death
A fundamental problem in Bayesian inference and statistical machine lear...
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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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05/10/2018
