Related papers: Multi-scale Deep Neural Networks for Solving High …

We present approximation results and numerical experiments for the use of randomized neural networks within physics-informed extreme learning machines to efficiently solve high-dimensional PDEs, demonstrating both high accuracy and low…

A tandem deep neural network approach is presented for the inverse design of reactively loaded metasurfaces with prescribed far-field radiation characteristics. The proposed approach integrates a deep neural network (DNN) with a…

We present a novel method for using Neural Networks (NNs) for finding solutions to a class of Partial Differential Equations (PDEs). Our method builds on recent advances in Neural Radiance Field research (NeRFs) and allows for a NN to…

The intrinsically infinite-dimensional features of the functional observations over multidimensional domains render the standard classification methods effectively inapplicable. To address this problem, we introduce a novel multiclass…

Deep convolutional neural networks (DCNN) have enjoyed great successes in many signal processing applications because they can learn complex, non-linear causal relationships from input to output. In this light, DCNNs are well suited for the…

Diffractive neural networks leverage the high-dimensional characteristics of electromagnetic (EM) fields for high-throughput computing. However, the existing architectures face challenges in integrating large-scale multidimensional…

This paper proposes two efficient approximation methods to solve high-dimensional fully nonlinear partial differential equations (NPDEs) and second-order backward stochastic differential equations (2BSDEs), where such high-dimensional fully…

We are interested to explore the limit in using deep learning (DL) to study the electromagnetic response for complex and random metasurfaces, without any specific applications in mind. For simplicity, we focus on a simple pure reflection…

Developing algorithms for solving high-dimensional partial differential equations (PDEs) has been an exceedingly difficult task for a long time, due to the notoriously difficult problem known as the "curse of dimensionality". This paper…

Many scientific and industrial applications require solving Partial Differential Equations (PDEs) to describe the physical phenomena of interest. Some examples can be found in the fields of aerodynamics, astrodynamics, combustion and many…

Recently, several deep learning (DL) methods for approximating high-dimensional partial differential equations (PDEs) have been proposed. The interest that these methods have generated in the literature is in large part due to simulations…

We consider learning deep neural networks (DNNs) that consist of low-precision weights and activations for efficient inference of fixed-point operations. In training low-precision networks, gradient descent in the backward pass is performed…

Deep models have achieved impressive progress in solving partial differential equations (PDEs). A burgeoning paradigm is learning neural operators to approximate the input-output mappings of PDEs. While previous deep models have explored…

We propose a novel framework for representing neural fields on triangle meshes that is multi-resolution across both spatial and frequency domains. Inspired by the Neural Fourier Filter Bank (NFFB), our architecture decomposes the spatial…

Deep Convolutional Neural Networks (DCNNs) and their variants have been widely used in large scale face recognition(FR) recently. Existing methods have achieved good performance on many FR benchmarks. However, most of them suffer from two…

Neural networks have shown significant potential in solving partial differential equations (PDEs). While deep networks are capable of approximating complex functions, direct one-shot training often faces limitations in both accuracy and…

Numerical simulation is dominant in solving partial difference equations (PDEs), but balancing fine-grained grids with low computational costs is challenging. Recently, solving PDEs with neural networks (NNs) has gained interest, yet…

We investigate the potential of applying (D)NN ((deep) neural networks) for approximating nonlinear mappings arising in the finite element discretization of nonlinear PDEs (partial differential equations). As an application, we apply the…

The Deep Material Network (DMN) has emerged as a powerful framework for multiscale materials modeling, enabling efficient and accurate prediction of material behavior across different length scales. Unlike conventional data-driven…

We use elliptic partial differential equations (PDEs) as examples to show various properties and behaviors when shallow neural networks (SNNs) are used to represent the solutions. In particular, we study the numerical ill-conditioning,…