Related papers: A deep domain decomposition method based on Fourie…

The classical development of neural networks has primarily focused on learning mappings between finite-dimensional Euclidean spaces. Recently, this has been generalized to neural operators that learn mappings between function spaces. For…

Solving high-dimensional parabolic partial differential equations (PDEs) with deep learning methods is often computationally and memory intensive, primarily due to the need for automatic differentiation (AD) to compute large Hessian…

Image Representation learning via input reconstruction is a common technique in machine learning for generating representations that can be effectively utilized by arbitrary downstream tasks. A well-established approach is using…

We present the Deep Picard Iteration (DPI) method, a new deep learning approach for solving high-dimensional partial differential equations (PDEs). The core innovation of DPI lies in its use of Picard iteration to reformulate the typically…

Partial Differential Equation (PDE) problems often exhibit strong local spatial structures, and effectively capturing these structures is critical for approximating their solutions. Recently, the Fourier Neural Operator (FNO) has emerged as…

Recent works have shown that traditional Neural Network (NN) architectures display a marked frequency bias in the learning process. Namely, the NN first learns the low-frequency features before learning the high-frequency ones. In this…

We present an effective and efficient method that explores the properties of Transformers in the frequency domain for high-quality image deblurring. Our method is motivated by the convolution theorem that the correlation or convolution of…

In recent years, SPDEs have become a well-studied field in mathematics. With their increase in popularity, it becomes important to efficiently approximate their solutions. Thus, our goal is a contribution towards the development of…

This study presents a discrete physics-informed neural network (dPINN) framework, enhanced with enforced interface constraints (EIC), for modeling physical systems using the domain decomposition method (DDM). Built upon finite element-style…

A parallel direct solution approach based on domain decomposition method (DDM) and directed acyclic graph (DAG) scheduling is outlined. Computations are represented as a sequence of small tasks that operate on domains of DDM or dense matrix…

Deep neural networks (DNNs) sustain high performance in today's data processing applications. DNN inference is resource-intensive thus is difficult to fit into a mobile device. An alternative is to offload the DNN inference to a cloud…

While diffusion-based generative models have made significant strides in visual content creation, conventional approaches face computational challenges, especially for high-resolution images, as they denoise the entire image from noisy…

We present an improved neural field architecture for solving partial differential equations (PDEs). Current physics-informed neural networks (PINNs) provide a flexible framework for solving PDEs, but they struggle to achieve highly accurate…

We develop a novel deep contour detection algorithm with a top-down fully convolutional encoder-decoder network. Our proposed method, named TD-CEDN, solves two important issues in this low-level vision problem: (1) learning multi-scale and…

Frequency estimation is a fundamental problem in many areas. The well-known A&M and its variant estimators have established an estimation framework by iteratively interpolating the discrete Fourier transform (DFT) coefficients. In general,…

Solving Singularly Perturbed Differential Equations (SPDEs) poses computational challenges arising from the rapid transitions in their solutions within thin regions. The effectiveness of deep learning in addressing differential equations…

In this paper, we present a novel image inpainting technique using frequency domain information. Prior works on image inpainting predict the missing pixels by training neural networks using only the spatial domain information. However,…

To address the sensitivity of parameters and limited precision for physics-informed extreme learning machines (PIELM) with common activation functions, such as sigmoid, tangent, and Gaussian, in solving high-order partial differential…

This paper is concerned with the analysis of convergent sequential and parallel overlapping domain decomposition methods for the minimization of functionals formed by a discrepancy term with respect to data and a total variation constraint.…

Fourier ptychography is a recently explored imaging method for overcoming the diffraction limit of conventional cameras with applications in microscopy and yielding high-resolution images. In order to splice together low-resolution images…