Related papers: Machine learning-based parameter optimization for …
In this paper, an innovative Physical Model-driven Neural Network (PMNN) method is proposed to solve time-fractional differential equations. It establishes a temporal iteration scheme based on physical model-driven neural networks which…
Parameter estimation remains a challenging task across many areas of engineering. Because data acquisition can often be costly, limited, or prone to inaccuracies (noise, uncertainty) it is crucial to identify sensor configurations that…
The main aim of this study is to introduce a 2-layered Artificial Neural Network (ANN) for solving the Black-Scholes partial differential equation (PDE) of either fractional or ordinary orders. Firstly, a discretization method is employed…
We introduce and analyze a method of learning-informed parameter identification for partial differential equations (PDEs) in an all-at-once framework. The underlying PDE model is formulated in a rather general setting with three unknowns:…
Parametric optimal control problems governed by partial differential equations (PDEs) are widely found in scientific and engineering applications. Traditional grid-based numerical methods for such problems generally require repeated…
This paper establishes an approximation theorem for randomized neural networks (RaNNs) whose hidden-layer parameters are uniformly sampled from a prescribed bounded domain. Our analysis shows that, for RaNNs of the form $\mathop{\sum}_i W_i…
We introduce a novel approach to automatic unstructured mesh generation using machine learning to predict an optimal finite element mesh for a previously unseen problem. The framework that we have developed is based around training an…
With the rapid development of Deep Learning, more and more applications on the cloud and edge tend to utilize large DNN (Deep Neural Network) models for improved task execution efficiency as well as decision-making quality. Due to memory…
Physics-informed neural networks (PINNs) as a means of discretizing partial differential equations (PDEs) are garnering much attention in the Computational Science and Engineering (CS&E) world. At least two challenges exist for PINNs at…
Physics-informed neural networks (PINNs) have emerged as a promising approach to solving partial differential equations (PDEs) using neural networks, particularly in data-scarce scenarios, due to their unsupervised training capability.…
Randomized neural network (RaNN) methods have been proposed for solving various partial differential equations (PDEs), demonstrating high accuracy and efficiency. However, initializing the fixed parameters remains challenging. Additionally,…
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…
Recent research has used deep learning to develop partial differential equation (PDE) models in science and engineering. The functional form of the PDE is determined by a neural network, and the neural network parameters are calibrated to…
Compared with conventional numerical approaches to solving partial differential equations (PDEs), physics-informed neural networks (PINN) have manifested the capability to save development effort and computational cost, especially in…
To solve high-dimensional parameter-dependent partial differential equations (pPDEs), a neural network architecture is presented. It is constructed to map parameters of the model data to corresponding finite element solutions. To improve…
Traditionally, an artificial neural network (ANN) is trained slowly by a gradient descent algorithm such as the backpropagation algorithm since a large number of hyperparameters of the ANN need to be fine-tuned with many training epochs. To…
We analyse and compare various empirical models of wall pressure spectra beneath turbulent boundary layers and propose an alternative machine learning approach using Artificial Neural Networks (ANN). The analysis and the training of the ANN…
The study of parametric differential equations plays a crucial role in weather forecasting and epidemiological modeling. These phenomena are better represented using fractional derivatives due to their inherent memory or hereditary effects.…
We introduce Neural Parameter Regression (NPR), a novel framework specifically developed for learning solution operators in Partial Differential Equations (PDEs). Tailored for operator learning, this approach surpasses traditional DeepONets…
This paper presents the concept of "model-based neural network"(MNN), which is inspired by the classic artificial neural network (ANN) but for different usages. Instead of being used as a data-driven classifier, a MNN serves as a modeling…