Chenguang Duan
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View article: Nonlinear Assimilation via Score-based Sequential Langevin Sampling
Nonlinear Assimilation via Score-based Sequential Langevin Sampling Open
This paper presents score-based sequential Langevin sampling (SSLS), a novel approach to nonlinear data assimilation within a recursive Bayesian filtering framework. The proposed method decomposes the assimilation process into alternating …
View article: Adv-SSL: Adversarial Self-Supervised Representation Learning with Theoretical Guarantees
Adv-SSL: Adversarial Self-Supervised Representation Learning with Theoretical Guarantees Open
Learning transferable data representations from abundant unlabeled data remains a central challenge in machine learning. Although numerous self-supervised learning methods have been proposed to address this challenge, a significant class o…
View article: Recovering the Source Term in Elliptic Equation via Deep Learning: Method and Convergence Analysis
Recovering the Source Term in Elliptic Equation via Deep Learning: Method and Convergence Analysis Open
In this paper, we present a deep learning approach to tackle elliptic inverse source problems.Our method combines Tikhonov regularization with physics-informed neural networks, utilizing separate neural networks to approximate the source t…
View article: Characteristic Learning for Provable One Step Generation
Characteristic Learning for Provable One Step Generation Open
We propose the characteristic generator, a novel one-step generative model that combines the efficiency of sampling in Generative Adversarial Networks (GANs) with the stable performance of flow-based models. Our model is driven by characte…
View article: Semi-Supervised Deep Sobolev Regression: Estimation and Variable Selection by ReQU Neural Network
Semi-Supervised Deep Sobolev Regression: Estimation and Variable Selection by ReQU Neural Network Open
We propose SDORE, a Semi-supervised Deep Sobolev Regressor, for the nonparametric estimation of the underlying regression function and its gradient. SDORE employs deep ReQU neural networks to minimize the empirical risk with gradient norm …
View article: Current density impedance imaging with PINNs
Current density impedance imaging with PINNs Open
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 physics-informed loss function by merging the regularized least-s…
View article: Deep Ritz Methods for Laplace Equations with Dirichlet Boundary Condition
Deep Ritz Methods for Laplace Equations with Dirichlet Boundary Condition Open
View article: Convergence Rate Analysis for Deep Ritz Method
Convergence Rate Analysis for Deep Ritz Method Open
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 this paper, we provide a rigorous numerical analysis on deep R…
View article: Analysis of Deep Ritz Methods for Laplace Equations with Dirichlet Boundary Conditions
Analysis of Deep Ritz Methods for Laplace Equations with Dirichlet Boundary Conditions Open
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 $H^{1}$ norm for deep Ritz methods for Laplace equations with Dirichlet boundar…