52 citations · 59 across the 13 of their papers we have counts for
8 papers · 1 filter
Neural Sampling with Reweighted Normalizing Flows via the Wasserstein--Fisher--Rao JKO Scheme
Chenguang Duan, Johannes Hertrich, Gabriele Steidl
We propose a neural algorithm for sampling from distributions specified by unnormalized Boltzmann densities. Our approach is based on the Jordan--Kinderlehrer--Otto scheme for the…
Preconditioning and Numerical Stability in Neural Network Training for Parametric PDEs
Markus Bachmayr, Wolfgang Dahmen, Chenguang Duan +1
In the context of training neural network-based approximations of solutions of parameter-dependent PDEs, we investigate the effect of preconditioning via well-conditioned frame rep…
Sampling via Stochastic Interpolants by Langevin-based Velocity and Initialization Estimation in Flow ODEs
Chenguang Duan, Yuling Jiao, Gabriele Steidl +3
We propose a novel method for sampling from unnormalized Boltzmann densities based on a probability flow ordinary differential equation (ODE) derived from linear stochastic interpo…
Nonlinear Assimilation via Score-based Sequential Langevin Sampling
Zhao Ding, Chenguang Duan, Yuling Jiao +3
This paper introduces score-based sequential Langevin sampling (SSLS), a novel approach to nonlinear data assimilation within a recursive Bayesian filtering framework. The proposed…
Current density impedance imaging with PINNs
Chenguang Duan, Yuling Jiao, Xiliang Lu +1
In this paper, we introduce CDII-PINNs, a computationally efficient method for solving CDII using PINNs in the framework of Tikhonov regularization. This method constructs a physic…
Deep Neural Network Approximation of Composition Functions: with application to PINNs
Chenguang Duan, Yuling Jiao, Xiliang Lu +2
In this paper, we focus on approximating a natural class of functions that are compositions of smooth functions. Unlike the low-dimensional support assumption on the covariate, we…
Analysis of Deep Ritz Methods for Laplace Equations with Dirichlet Boundary Conditions
Chenguang Duan, Yuling Jiao, Yanming Lai +3
Deep Ritz methods (DRM) have been proven numerically to be efficient in solving partial differential equations. In this paper, we present a convergence rate in norm for dee…
Convergence Rate Analysis for Deep Ritz Method
Chenguang Duan, Yuling Jiao, Yanming Lai +2
Using deep neural networks to solve PDEs has attracted a lot of attentions recently. However, why the deep learning method works is falling far behind its empirical success. In thi…