相关论文: Overlapping Schwarz methods with GenEO coarse spac…

This paper presents four novel domain decomposition algorithms integrated with nonlinear mapping techniques to address collocation-based solutions of eigenvalue problems involving sharp interfaces or steep gradients. The proposed methods…

Most finite element methods for solving time-harmonic wave-propagation problems lead to a linear system with a non-normal coefficient matrix. The non-normality is due to boundary conditions and losses. One way to solve these systems is to…

Pan-sharpening algorithms utilize a panchromatic image and a multispectral image to generate a high spatial and high spectral image. However, the optimizations of the algorithms are designed with different standards. We employ a simple…

Scientific machine learning has enabled the extraction of physical insights and data-driven modeling of high-dimensional spatiotemporal data, yet achieving physically interpretable latent representations and computationally efficient…

An abstract construction of coarse spaces for non-Hermitian problems and non-Hermitian domain decomposition preconditioners based on extended generalized eigenproblems was proposed in [Nataf and Parolin, arXiv:2404.02758] and analyzed on…

We develop an accelerated gradient descent algorithm on the Grassmann manifold to compute the subspace spanned by a number of leading eigenvectors of a symmetric positive semi-definite matrix. This has a constant cost per iteration and a…

In this paper, we propose oversampling strategies in the Generalized Multiscale Finite Element Method (GMsFEM) framework. The GMsFEM, which has been recently introduced in [12], allows solving multiscale parameter-dependent problems at a…

Recent advances in generative artificial intelligence have had a significant impact on diverse domains spanning computer vision, natural language processing, and drug discovery. This work extends the reach of generative models into physical…

Variational Autoencoder (VAE)-based generative models offer flexible representation learning by incorporating meta-priors, general premises considered beneficial for downstream tasks. However, the incorporated meta-priors often involve…

This paper presents a neural network--enhanced surrogate modeling approach for diffusion problems with spatially varying random field coefficients. The method builds on numerical homogenization, which compresses fine-scale coefficients into…

We propose a nonparametric procedure to achieve fast inference in generative graphical models when the number of latent states is very large. The approach is based on iterative latent variable preselection, where we alternate between…

Numerical solutions of partial differential equations (PDEs) require expensive simulations, limiting their application in design optimization, model-based control, and large-scale inverse problems. Surrogate modeling techniques seek to…

We propose a component-based (CB) parametric model order reduction (pMOR) formulation for parameterized nonlinear elliptic partial differential equations (PDEs) based on overlapping subdomains. Our approach reads as a constrained…

We present a neural network architecture based upon the Autoencoder (AE) and Generative Adversarial Network (GAN) that promotes a convex latent distribution by training adversarially on latent space interpolations. By using an AE as both…

We propose a novel algorithm based on inexact GMRES methods for linear response calculations in density functional theory. Such calculations require iteratively solving a nested linear problem $\mathcal{E} \delta\rho = b$ to obtain the…

We consider solving ill-posed imaging inverse problems without access to an explicit image prior or ground-truth examples. An overarching challenge in inverse problems is that there are many undesired images that fit to the observed…

When designing variational autoencoders (VAEs) or other types of latent space models, the dimensionality of the latent space is typically defined upfront. In this process, it is possible that the number of dimensions is under- or…

Recently deep neutral networks have achieved promising performance for filling large missing regions in image inpainting tasks. They usually adopted the standard convolutional architecture over the corrupted image, leading to meaningless…

In the field of inverse estimation for systems modeled by partial differential equations (PDEs), challenges arise when estimating high- (or even infinite-) dimensional parameters. Typically, the ill-posed nature of such problems…

Despite the empirical success of Diffusion Models (DMs) and Variational Autoencoders (VAEs), their generalization performance remains theoretically underexplored, especially lacking a full consideration of the shared encoder-generator…