Related papers: Accelerating multigrid solver with generative supe…

We study multilevel techniques, commonly used in PDE multigrid literature, to solve structured optimization problems. For a given hierarchy of levels, we formulate a coarse model that approximates the problem at each level and provides a…

Anatomical landmark segmentation and pathology localization are important steps in automated analysis of medical images. They are particularly challenging when the anatomy or pathology is small, as in retinal images and cardiac MRI, or when…

Although the inherently ambiguous task of predicting what resides beyond all four edges of an image has rarely been explored before, we demonstrate that GANs hold powerful potential in producing reasonable extrapolations. Two outpainting…

In this paper we analyse the convergence properties of V-cycle multigrid algorithms for the numerical solution of the linear system of equations arising from discontinuous Galerkin discretization of second-order elliptic partial…

Multigrid algorithms are among the fastest iterative methods known today for solving large linear and some non-linear systems of equations. Greatly optimized for serial operation, they still have a great potential for parallelism not fully…

In recent years, sub-grid models for turbulent mixing have been developed by data-driven methods for large eddy simulation (LES). Super-resolution is a data-driven deconvolution technique in which deep convolutional neural networks are…

The advent of generative adversarial networks (GAN) has enabled new capabilities in synthesis, interpolation, and data augmentation heretofore considered very challenging. However, one of the common assumptions in most GAN architectures is…

Machine learning, especially physics-informed neural networks (PINNs) and their neural network variants, has been widely used to solve problems involving partial differential equations (PDEs). The successful deployment of such methods…

We propose the interpolatory hybridizable discontinuous Galerkin (Interpolatory HDG) method for a class of scalar parabolic semilinear PDEs. The Interpolatory HDG method uses an interpolation procedure to efficiently and accurately…

We present a tailored multigrid method for linear problems stemming from a Nitsche-based extended finite element method (XFEM). Our multigrid method is robust with respect to highly varying coefficients and the number of interfaces in a…

This article introduces a general purpose framework and software to approximate partial differential equations (PDEs). The sparsity patterns of finite element discretized operators is identified automatically using the tools from…

Generative adversarial networks (GANs) have been a popular deep generative model for real-world applications. Despite many recent efforts on GANs that have been contributed, mode collapse and instability of GANs are still open problems…

We propose a data-driven and machine-learning-based approach to compute non-Galerkin coarse-grid operators in algebraic multigrid (AMG) methods, addressing the well-known issue of increasing operator complexity. Guided by the AMG theory on…

Multi-level preconditioners for Discontinuous Galerkin (DG) discretizations are widely used to solve elliptic equations, and a main ingredient of such solvers is the interpolation operator to transfer information from the coarse to the fine…

The paper proposes a method to effectively fuse multi-exposure inputs and generate high-quality high dynamic range (HDR) images with unpaired datasets. Deep learning-based HDR image generation methods rely heavily on paired datasets. The…

Generative Adversarial Networks (GANs) have extended deep learning to complex generation and translation tasks across different data modalities. However, GANs are notoriously difficult to train: Mode collapse and other instabilities in the…

The support vector machine is a flexible optimization-based technique widely used for classification problems. In practice, its training part becomes computationally expensive on large-scale data sets because of such reasons as the…

Generative adversarial networks (GANs) has gained tremendous popularity lately due to an ability to reinforce quality of its predictive model with generated objects and the quality of the generative model with and supervised feedback. GANs…

This paper constitutes our initial effort in developing sparse grid discontinuous Galerkin (DG) methods for high-dimensional partial differential equations (PDEs). Over the past few decades, DG methods have gained popularity in many…

Recent work introduced progressive network growing as a promising way to ease the training for large GANs, but the model design and architecture-growing strategy still remain under-explored and needs manual design for different image data.…