Related papers: Numerical Computation of Partial Differential Equa…

In this article, a stochastic gradient based online learning algorithm for Extreme Learning Machines (ELM) is developed (SG-ELM). A stability criterion based on Lyapunov approach is used to prove both asymptotic stability of estimation…

The physics-informed neural network (PINN) is effective in solving the partial differential equation (PDE) by capturing the physics constraints as a part of the training loss function through the Automatic Differentiation (AD). This study…

Random functional-linked types of neural networks (RFLNNs), e.g., the extreme learning machine (ELM) and broad learning system (BLS), which avoid suffering from a time-consuming training process, offer an alternative way of learning in deep…

We develop in this paper a multi-grade deep learning method for solving nonlinear partial differential equations (PDEs). Deep neural networks (DNNs) have received super performance in solving PDEs in addition to their outstanding success in…

We describe and analyze a hybrid finite element/neural network method for predicting solutions of partial differential equations. The methodology is designed for obtaining fine scale fluctuations from neural networks in a local manner. The…

This work concerns receiver design for light emitting diode (LED) communications where the LED nonlinearity can severely degrade the performance of communications. We propose extreme learning machine (ELM) based non-iterative receivers and…

The phenomena of Spectral Bias, where the higher frequency components of a function being learnt in a feedforward Artificial Neural Network (ANN) are seen to converge more slowly than the lower frequencies, is observed ubiquitously across…

Accurate approximation of scalar-valued functions from sample points is a key task in computational science. Recently, machine learning with Deep Neural Networks (DNNs) has emerged as a promising tool for scientific computing, with…

According to conventional neural network theories, the feature of single-hidden-layer feedforward neural networks(SLFNs) resorts to parameters of the weighted connections and hidden nodes. SLFNs are universal approximators when at least the…

Recent years have witnessed the great advance of deep learning in a variety of vision tasks. Many state-of-the-art deep neural networks suffer from large size and high complexity, which makes it difficult to deploy in resource-limited…

In this work, we present a machine learning approach for reducing the error when numerically solving time-dependent partial differential equations (PDE). We use a fully convolutional LSTM network to exploit the spatiotemporal dynamics of…

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…

Machine learning based partial differential equations (PDEs) solvers have received great attention in recent years. Most progress in this area has been driven by deep neural networks such as physics-informed neural networks (PINNs) and…

Training implicit neural representations (INRs) to capture fine-scale details typically relies on iterative backpropagation and is often hindered by spectral bias when the target exhibits highly non-uniform frequency content. We propose…

The least squares method with deep neural networks as function parametrization has been applied to solve certain high-dimensional partial differential equations (PDEs) successfully; however, its convergence is slow and might not be…

We introduce generalised finite difference methods for solving fully nonlinear elliptic partial differential equations. Methods are based on piecewise Cartesian meshes augmented by additional points along the boundary. This allows for…

With a recent trend of using Large Language Models (LLMs) for different applications within smart cities, there is a need for pushing these models toward the edge of network while still preserving their performance. Edge Computing (EC) as a…

Modeling stiff partial differential equations (PDEs) with sharp gradients remains a significant challenge for scientific machine learning. While Physics-Informed Neural Networks (PINNs) struggle with spectral bias and slow training times,…

In this paper, we introduce a tensor neural network based machine learning method for solving the elliptic partial differential equations with random coefficients in a bounded physical domain. With the help of tensor product structure, we…

Graph representation learning methods are highly effective in handling complex non-Euclidean data by capturing intricate relationships and features within graph structures. However, traditional methods face challenges when dealing with…