Related papers: Local Extreme Learning Machines and Domain Decompo…
The potential of neural networks (NN) in engineering is rooted in their capacity to understand intricate patterns and complex systems, leveraging their universal nonlinear approximation capabilities and high expressivity. Meanwhile,…
The Extreme Learning Machine (ELM) technique is a machine learning approach for constructing feed-forward neural networks with a single hidden layer and their models. The ELM model can be constructed while being trained by concurrently…
Extreme learning machine (ELM) is a new single hidden layer feedback neural network. The weights of the input layer and the biases of neurons in hidden layer are randomly generated, the weights of the output layer can be analytically…
This work considers stochastic Galerkin approximations of linear elliptic partial differential equations (PDEs) with stochastic forcing terms and stochastic diffusion coefficients, that cannot be bounded uniformly away from zero and…
Over the past few years, neural network methods have evolved in various directions for approximating partial differential equations (PDEs). A promising new development is the integration of neural networks with classical numerical…
Extreme learning machine (ELM), proposed by Huang et al., has been shown a promising learning algorithm for single-hidden layer feedforward neural networks (SLFNs). Nevertheless, because of the random choice of input weights and biases, the…
The neural network method of solving differential equations is used to approximate the electric potential and corresponding electric field in the slit-well microfluidic device. The device's geometry is non-convex, making this a challenging…
This paper investigates distributed cooperative learning algorithms for data processing in a network setting. Specifically, the extreme learning machine (ELM) is introduced to train a set of data distributed across several components, and…
In recent years, there has been an increasing interest in using deep learning and neural networks to tackle scientific problems, particularly in solving partial differential equations (PDEs). However, many neural network-based methods, such…
The tracking method based on the extreme learning machine (ELM) is efficient and effective. ELM randomly generates input weights and biases in the hidden layer, and then calculates and computes the output weights by reducing the iterative…
This paper proposes a deep-learning-based domain decomposition method (DeepDDM), which leverages deep neural networks (DNN) to discretize the subproblems divided by domain decomposition methods (DDM) for solving partial differential…
This paper is concerned with the sparsification of the input-hidden weights of ELM (Extreme Learning Machine). For ordinary feedforward neural networks, the sparsification is usually done by introducing certain regularization technique into…
We address a new numerical scheme based on a class of machine learning methods, the so-called Extreme Learning Machines with both sigmoidal and radial-basis functions, for the computation of steady-state solutions and the construction of…
Parametric partial differential equations (PDEs) are fundamental for modeling a wide range of physical and engineering systems influenced by uncertain or varying parameters. Traditional neural network-based solvers, such as Physics-Informed…
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…
Numerically solving high-dimensional partial differential equations (PDEs) is a major challenge. Conventional methods, such as finite difference methods, are unable to solve high-dimensional PDEs due to the curse-of-dimensionality. A…
The solution to partial differential equations using deep learning approaches has shown promising results for several classes of initial and boundary-value problems. However, their ability to surpass, particularly in terms of accuracy,…
ELM (Extreme Learning Machine) is a single hidden layer feed-forward network, where the weights between input and hidden layer are initialized randomly. ELM is efficient due to its utilization of the analytical approach to compute weights…
High-dimensional PDEs have been a longstanding computational challenge. We propose to solve high-dimensional PDEs by approximating the solution with a deep neural network which is trained to satisfy the differential operator, initial…
In recent years, a significant amount of attention has been paid to solve partial differential equations (PDEs) by deep learning. For example, deep Galerkin method (DGM) uses the PDE residual in the least-squares sense as the loss function…