Related papers: A Deep Fourier Residual Method for solving PDEs us…

This work proposes a solution for the problem of training physics-informed networks under partial integro-differential equations. These equations require an infinite or a large number of neural evaluations to construct a single residual for…

In this paper, we propose and study neural network based methods for solutions of high-dimensional quadratic porous medium equation (QPME). Three variational formulations of this nonlinear PDE are presented: a strong formulation and two…

We propose a numerical method for solving high dimensional fully nonlinear partial differential equations (PDEs). Our algorithm estimates simultaneously by backward time induction the solution and its gradient by multi-layer neural…

One of the oldest and most studied subject in scientific computing is algorithms for solving partial differential equations (PDEs). A long list of numerical methods have been proposed and successfully used for various applications. In…

Deep neural networks (DNNs) are widely used as surrogate models in geophysical applications; incorporating theoretical guidance into DNNs has improved the generalizability. However, most of such approaches define the loss function based on…

Recently, convolutional neural networks have shown promising performance for single-image super-resolution. In this paper, we propose Deep Artifact-Free Residual (DAFR) network which uses the merits of both residual learning and usage of…

We revisit residual algorithms in both model-free and model-based reinforcement learning settings. We propose the bidirectional target network technique to stabilize residual algorithms, yielding a residual version of DDPG that…

This paper studies an unsupervised deep learning-based numerical approach for solving partial differential equations (PDEs). The approach makes use of the deep neural network to approximate solutions of PDEs through the compositional…

Recent work has introduced a simple numerical method for solving partial differential equations (PDEs) with deep neural networks (DNNs). This paper reviews and extends the method while applying it to analyze one of the most fundamental…

Despite the power of deep neural networks for a wide range of tasks, an overconfident prediction issue has limited their practical use in many safety-critical applications. Many recent works have been proposed to mitigate this issue, but…

In this paper, we propose a deep learning-based method, deep Euler method (DEM) to solve ordinary differential equations. DEM significantly improves the accuracy of the Euler method by approximating the local truncation error with deep…

Neural Network Differential Equation (NN DE) solvers have surged in popularity due to a combination of factors: computational advances making their optimization more tractable, their capacity to handle high dimensional problems, easy…

Previous studies have shown that deep neural networks (DNNs) with common settings often capture target functions from low to high frequency, which is called Frequency Principle (F-Principle). It has also been shown that F-Principle can…

This paper presents an a priori error analysis of the Deep Mixed Residual method (MIM) for solving high-order elliptic equations with non-homogeneous boundary conditions, including Dirichlet, Neumann, and Robin conditions. We examine MIM…

Whilst the Universal Approximation Theorem guarantees the existence of approximations to Sobolev functions -- the natural function spaces for PDEs -- by Neural Networks (NNs) of sufficient size, low-regularity solutions may lead to poor…

Channel estimation is one of the main tasks in realizing practical intelligent reflecting surface-assisted multi-user communication (IRS-MC) systems. However, different from traditional communication systems, an IRS-MC system generally…

Deep learning (DL) has become an essential tool in prognosis and health management (PHM), commonly used as a regression algorithm for the prognosis of a system's behavior. One particular metric of interest is the remaining useful life (RUL)…

The numerical solution of differential equations using neural networks has become a central topic in scientific computing, with Physics-Informed Neural Networks (PINNs) emerging as a powerful paradigm for both forward and inverse problems.…

A wide range of practically important problems is nowadays efficiently solved using artificial neural networks. This gave momentum to intensive development of their optical implementations, among which, the so-called diffractive neural…

We analyze and test using Fourier extensions that minimize a Hilbert space norm for the purpose of solving partial differential equations (PDEs) on surfaces. In particular, we prove that the approach is arbitrarily high-order and also show…