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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 propose a conservative energy method based on neural networks with subdomains for solving variational problems (CENN), where the admissible function satisfying the essential boundary condition without boundary penalty is constructed by…
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…
Partial differential equations have a wide range of applications in modeling multiple physical, biological, or social phenomena. Therefore, we need to approximate the solutions of these equations in computationally feasible terms. Nowadays,…
Traditional machine learning algorithms using hand-crafted feature extraction techniques (such as local binary pattern) have limited accuracy because of high variation in images of the same class (or intra-class variation) for food…
This paper presents an implementation of multilayer feed forward neural networks (NN) to optimize CMOS analog circuits. For modeling and design recently neural network computational modules have got acceptance as an unorthodox and useful…
We propose a generative Causal Adversarial Network (CAN) for learning and sampling from conditional and interventional distributions. In contrast to the existing CausalGAN which requires the causal graph to be given, our proposed framework…
Remarkable achievements have been attained by deep neural networks in various applications. However, the increasing depth and width of such models also lead to explosive growth in both storage and computation, which has restricted the…
In this work we establish the relation between optimal control and training deep Convolution Neural Networks (CNNs). We show that the forward propagation in CNNs can be interpreted as a time-dependent nonlinear differential equation and…
In this article we propose a new deep learning approach to approximate operators related to parametric partial differential equations (PDEs). In particular, we introduce a new strategy to design specific artificial neural network (ANN)…
This paper presents a deep learning approach for the classification of Engineering (CAD) models using Convolutional Neural Networks (CNNs). Owing to the availability of large annotated datasets and also enough computational power in the…
Convolutional neural network (CNN) is widely used in computer vision applications. In the networks that deal with images, CNNs are the most time-consuming layer of the networks. Usually, the solution to address the computation cost is to…
In this paper, we present a deep neural network based adaptive learning (DNN-AL) approach for switched systems. Currently, deep neural network based methods are actively developed for learning governing equations in unknown dynamic systems,…
Monte Carlo methods are widely used in particle physics to integrate and sample probability distributions (differential cross sections or decay rates) on multi-dimensional phase spaces. We present a Neural Network (NN) algorithm optimized…
This paper investigates the use of artificial neural networks (ANNs) to solve differential equations (DEs) and the construction of the loss function which meets both differential equation and its initial/boundary condition of a certain DE.…
This paper introduces a tensor neural network (TNN) to address nonparametric regression problems, leveraging its distinct sub-network structure to effectively facilitate variable separation and enhance the approximation of complex,…
Deep neural networks (DNNs) are increasingly used to solve partial differential equations (PDEs) that naturally arise while modeling a wide range of systems and physical phenomena. However, the accuracy of such DNNs decreases as the PDE…
In this paper, we present a novel framework to solve differential equations based on multilayer feedforward network. Previous works indicate that solvers based on neural network have low accuracy due to that the boundary conditions are not…
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…
Kolmogorov-Arnold Networks (KANs) have emerged as a promising alternative to Multi-layer Perceptrons (MLPs) due to their superior function-fitting abilities in data-driven modeling. In this paper, we propose a novel framework, DAE-KAN, for…