Related papers: Numerical Computation of Partial Differential Equa…

A hybrid computational approach that integrates the finite element method (FEM) with least squares support vector regression (LSSVR) is introduced to solve partial differential equations. The method combines FEM's ability to provide the…

Recent developments in mechanical, aerospace, and structural engineering have driven a growing need for efficient ways to model and analyse structures at much larger and more complex scales than before. While established numerical methods…

Convolutional neural network (CNN) has achieved impressive success in computer vision during the past few decades. The image convolution operation helps CNNs to get good performance on image-related tasks. However, it also has high…

In the present work, a multi-scale framework for neural network enhanced methods is proposed for approximation of function and solution of partial differential equations (PDEs). By introducing the multi-scale concept, the total solution of…

We are delighted to see the recent development of physics-informed extreme learning machine (PIELM) for its higher computational efficiency and accuracy compared to other physics-informed machine learning (PIML) paradigms. Since a…

In this paper, we study a machine-learning-based solver for high-dimensional partial differential equations (PDEs). Computing accurate solutions efficiently for such problems remains challenging because of the curse of dimensionality, which…

Partial differential equations (PDEs) involving high contrast and oscillating coefficients are common in scientific and industrial applications. Numerical approximation of these PDEs is a challenging task that can be addressed, for example,…

We present a novel layerwise optimization algorithm for the learning objective of Piecewise-Linear Convolutional Neural Networks (PL-CNNs), a large class of convolutional neural networks. Specifically, PL-CNNs employ piecewise linear…

Neural networks with randomly generated hidden weights (RaNNs) have been extensively studied, both as a standalone learning method and as an initialization for fully trainable deep learning methods. In this work, we study RaNN expressivity…

We propose a simplified, biologically inspired predictive local learning rule that eliminates the need for global backpropagation in conventional neural networks and membrane integration in event-based training. Weight updates are triggered…

We propose machine learning methods for solving fully nonlinear partial differential equations (PDEs) with convex Hamiltonian. Our algorithms are conducted in two steps. First the PDE is rewritten in its dual stochastic control…

Physics-informed machine learning frameworks such as Physics-Informed Neural Networks (PINNs) and Physics-Informed Extreme Learning Machines (PI-ELMs) have shown great promise for solving partial differential equations (PDEs) but struggle…

We utilize extreme-learning machines for the prediction of partial differential equations (PDEs). Our method splits the state space into multiple windows that are predicted individually using a single model. Despite requiring only few data…

Deep learning utilizing deep neural networks (DNNs) has achieved a lot of success recently in many important areas such as computer vision, natural language processing, and recommendation systems. The lack of convexity for DNNs has been…

In this paper, based on the combination of finite element mesh and neural network, a novel type of neural network element space and corresponding machine learning method are designed for solving partial differential equations. The…

We introduce a rapid and precise analytical approach for analyzing cerebral blood flow (CBF) using Diffuse Correlation Spectroscopy (DCS) with the application of the Extreme Learning Machine (ELM). Our evaluation of ELM and existing…

We present a closed form expression for initializing the input weights in a multi-layer perceptron, which can be used as the first step in synthesis of an Extreme Learning Ma-chine. The expression is based on the standard function for a…

The optical domain is a promising field for physical implementation of neural networks, due to the speed and parallelism of optics. Extreme Learning Machines (ELMs) are feed-forward neural networks in which only output weights are trained,…

Deep learning with a convolutional neural network (CNN) has been proved to be very effective in feature extraction and representation of images. For image classification problems, this work aim at finding which classifier is more…

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…