Related papers: Local Randomized Neural Networks Methods for Inter…
In this paper, we propose a novel mesh-free numerical method for solving the elliptic interface problems based on deep learning. We approximate the solution by the neural networks and, since the solution may change dramatically across the…
Integro-differential equations arise in a wide range of applications, including transport, kinetic theory, radiative transfer, and multiphysics modeling, where nonlocal integral operators couple the solution across phase space. Such…
In this paper, we propose a mesh-free method to solve interface problems using the deep learning approach. Two interface problems are considered. The first one is an elliptic PDE with a discontinuous and high-contrast coefficient. While the…
In this paper, a meshfree method using the deep neural network (DNN) approach is developed for solving two kinds of dynamic two-phase interface problems governed by different dynamic partial differential equations on either side of the…
Interface problems have long been a major focus of scientific computing, leading to the development of various numerical methods. Traditional mesh-based methods often employ time-consuming body-fitted meshes with standard discretization…
Randomized neural networks (RNN) are a variation of neural networks in which the hidden-layer parameters are fixed to randomly assigned values and the output-layer parameters are obtained by solving a linear system by least squares. This…
For quasi-linear interface problems with discontinuous diffusion coefficients, the nonconvex objective functional often leads to optimization stagnation in randomized neural network approximations. This paper Proposes a…
Despite prior advances in PINNs, significant challenges remain in localized solid mechanics problems because of the limitations of single network formulations in simultaneous resolution of smooth global responses and near-tip singularities,…
Surface partial differential equations arise in numerous scientific and engineering applications. Their numerical solution on static and evolving surfaces remains challenging due to geometric complexity and, for evolving geometries, the…
Recurrent neural networks (RNNs) have recently achieved remarkable successes in a number of applications. However, the huge sizes and computational burden of these models make it difficult for their deployment on edge devices. A practically…
To overcome these obstacles and improve computational accuracy and efficiency, this paper presents the Randomized Radial Basis Function Neural Network (RRNN), an innovative approach explicitly crafted for solving multiscale elliptic…
Deep neural networks have proved very successful on archetypal tasks for which large training sets are available, but when the training data are scarce, their performance suffers from overfitting. Many existing methods of reducing…
The artificial neural network shows powerful ability of inference, but it is still criticized for lack of interpretability and prerequisite needs of big dataset. This paper proposes the Rule-embedded Neural Network (ReNN) to overcome the…
This work investigates the ways in which deep learning methods can benefit from random projection (RP), a classic linear dimensionality reduction method. We focus on two areas where, as we have found, employing RP techniques can improve…
Randomized Neural Networks explore the behavior of neural systems where the majority of connections are fixed, either in a stochastic or a deterministic fashion. Typical examples of such systems consist of multi-layered neural network…
This paper presents the benefits of using randomized neural networks instead of standard basis functions or deep neural networks to approximate the solutions of optimal stopping problems. The key idea is to use neural networks, where the…
Recurrent Neural Networks (RNNs) are a class of machine learning algorithms used for applications with time-series and sequential data. Recently, there has been a strong interest in executing RNNs on embedded devices. However, difficulties…
Traditional methods for high-dimensional diffeomorphic mapping often struggle with the curse of dimensionality. We propose a mesh-free learning framework designed for $n$-dimensional mapping problems, seamlessly combining variational…
Predicting the evolution of systems that exhibit spatio-temporal dynamics in response to external stimuli is a key enabling technology fostering scientific innovation. Traditional equations-based approaches leverage first principles to…
Non-overlapping domain decomposition methods are natural for solving interface problems arising from various disciplines, however, the numerical simulation requires technical analysis and is often available only with the use of high-quality…