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05/21/2023
On optimal bases for multiscale PDEs and Bayesian homogenization
PDE solutions are numerically represented by basis functions. Classical ...
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03/21/2023
Convergence of stochastic gradient descent on parameterized sphere with applications to variational Monte Carlo simulation
We analyze stochastic gradient descent (SGD) type algorithms on a high-d...
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01/10/2022
High-frequency limit of the inverse scattering problem: asymptotic convergence from inverse Helmholtz to inverse Liouville
We investigate the asymptotic relation between the inverse problems rely...
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11/03/2021
A reduced order Schwarz method for nonlinear multiscale elliptic equations based on two-layer neural networks
Neural networks are powerful tools for approximating high dimensional da...
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10/06/2021
On the Global Convergence of Gradient Descent for multi-layer ResNets in the mean-field regime
Finding the optimal configuration of parameters in ResNet is a nonconvex...
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05/30/2021
Overparameterization of deep ResNet: zero loss and mean-field analysis
Finding parameters in a deep neural network (NN) that fit training data ...
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02/08/2021
Constrained Ensemble Langevin Monte Carlo
The classical Langevin Monte Carlo method looks for i.i.d. samples from ...
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10/22/2020
Random Coordinate Underdamped Langevin Monte Carlo
The Underdamped Langevin Monte Carlo (ULMC) is a popular Markov chain Mo...
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10/03/2020
Random Coordinate Langevin Monte Carlo
Langevin Monte Carlo (LMC) is a popular Markov chain Monte Carlo samplin...
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07/26/2020
Langevin Monte Carlo: random coordinate descent and variance reduction
Sampling from a log-concave distribution function on ℝ^d (with d≫ 1) is ...
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06/10/2020
Variance reduction for Langevin Monte Carlo in high dimensional sampling problems
Sampling from a log-concave distribution function is one core problem th...
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03/04/2020
Ensemble Kalman Inversion for nonlinear problems: weights, consistency, and variance bounds
Ensemble Kalman Inversion (EnKI), originally derived from Enseble Kalman...
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10/28/2019
Ensemble Kalman Sampling: mean-field limit and convergence analysis
Ensemble Kalman sampling (EKS) is a method to find i.i.d. samples from a...
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10/18/2019
Error Lower Bounds of Constant Step-size Stochastic Gradient Descent
Stochastic Gradient Descent (SGD) plays a central role in modern machine...
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08/15/2019
Mean-field limit and numerical analysis for Ensemble Kalman Inversion: linear setting
Ensemble Kalman inversion (EKI) is a method introduced in [14] to find s...
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07/09/2019