Related papers: An Efficient Deep Learning Approach for Approximat…

Due to the curse of dimensionality, solving high dimensional parabolic partial differential equations (PDEs) has been a challenging problem for decades. Recently, a weak adversarial network (WAN) proposed in (Y.Zang et al., 2020) offered a…

High-performance deep neural network (DNN)-based systems are in high demand in edge environments. Due to its high computational complexity, it is challenging to deploy DNNs on edge devices with strict limitations on computational resources.…

In this paper, we present a deep learning-based numerical method for approximating high dimensional stochastic partial differential equations (SPDEs). At each time step, our method relies on a predictor-corrector procedure. More precisely,…

Deep neural networks (DNNs) have been deployed in myriad machine learning applications. However, advances in their accuracy are often achieved with increasingly complex and deep network architectures. These large, deep models are often…

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…

This paper investigates deep neural network (DNN) compression from the perspective of compactly representing and storing trained parameters. We explore the previously overlooked opportunity of cross-layer architecture-agnostic…

The large computing and memory cost of deep neural networks (DNNs) often precludes their use in resource-constrained devices. Quantizing the parameters and operations to lower bit-precision offers substantial memory and energy savings for…

In this paper, we introduce a method to compress intermediate feature maps of deep neural networks (DNNs) to decrease memory storage and bandwidth requirements during inference. Unlike previous works, the proposed method is based on…

Motivated by the gap between theoretical optimal approximation rates of deep neural networks (DNNs) and the accuracy realized in practice, we seek to improve the training of DNNs. The adoption of an adaptive basis viewpoint of DNNs leads to…

Recently, the advent of deep learning has spurred interest in the development of physics-informed neural networks (PINN) for efficiently solving partial differential equations (PDEs), particularly in a parametric setting. Among all…

Training deep neural networks (DNNs) on edge devices has attracted increasing attention due to its potential to address challenges related to domain adaptation and privacy preservation. However, DNNs typically rely on large datasets for…

In this paper, we propose multi-scale deep neural networks (MscaleDNNs) using the idea of radial scaling in frequency domain and activation functions with compact support. The radial scaling converts the problem of approximation of high…

This work investigates the electrical impedance tomography (EIT) problem when only limited boundary measurements are available, which is known to be challenging due to the extreme ill-posedness. Based on the direct sampling method (DSM), we…

We present a numerical framework for approximating unknown governing equations using observation data and deep neural networks (DNN). In particular, we propose to use residual network (ResNet) as the basic building block for equation…

In this work, we present a hybrid numerical method for solving evolution partial differential equations (PDEs) by merging the time finite element method with deep neural networks. In contrast to the conventional deep learning-based…

Stochastic differential equations (SDEs) and the Kolmogorov partial differential equations (PDEs) associated to them have been widely used in models from engineering, finance, and the natural sciences. In particular, SDEs and Kolmogorov…

In this paper, we study the statistical limits of deep learning techniques for solving elliptic partial differential equations (PDEs) from random samples using the Deep Ritz Method (DRM) and Physics-Informed Neural Networks (PINNs). To…

Recently proposed numerical algorithms for solving high-dimensional nonlinear partial differential equations (PDEs) based on neural networks have shown their remarkable performance. We review some of them and study their convergence…

Partial differential equations (PDEs) with near singular solutions pose significant challenges for traditional numerical methods, particularly in complex geometries where mesh generation and adaptive refinement become computationally…

Deep neural networks (DNNs) have achieved unprecedented success in the field of artificial intelligence (AI), including computer vision, natural language processing and speech recognition. However, their superior performance comes at the…