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We describe a neural-based method for generating exact or approximate solutions to differential equations in the form of mathematical expressions. Unlike other neural methods, our system returns symbolic expressions that can be interpreted…
In this article, we present an efficient deep learning method called coupled deep neural networks (CDNNs) for coupled physical problems. Our method compiles the interface conditions of the coupled PDEs into the networks properly and can be…
Physics-informed neural networks have been widely applied to learn general parametric solutions of differential equations. Here, we propose a neural network to discover parametric eigenvalue and eigenfunction surfaces of quantum systems. We…
Deep learning refers to the shining branch of machine learning that is based on learning levels of representations. Convolutional Neural Networks (CNN) is one kind of deep neural network. It can study concurrently. In this article, we gave…
Image segmentation is considered to be one of the critical tasks in hyperspectral remote sensing image processing. Recently, convolutional neural network (CNN) has established itself as a powerful model in segmentation and classification by…
Recent models for image processing are using the Convolutional neural network (CNN) which requires a pixel per pixel analysis of the input image. This method works well. However, it is time-consuming if we have large images. To increase the…
We proposed a framework for solving inverse problems in differential equations based on neural networks and automatic differentiation. Neural networks are used to approximate hidden fields. We analyze the source of errors in the framework…
Deep learning models face persistent challenges in training, particularly due to internal covariate shift and label shift. While single-mode normalization methods like Batch Normalization partially address these issues, they are constrained…
In this paper, we introduce a type of tensor neural network based machine learning method to solve elliptic multiscale problems. Based on the special structure, we can do the direct and highly accurate high dimensional integrations for the…
Generative Adversarial Networks (GANs) have been shown to be powerful and flexible priors when solving inverse problems. One challenge of using them is overcoming representation error, the fundamental limitation of the network in…
Causal artificial intelligence aims to enhance explainability, trustworthiness, and robustness in AI by leveraging structural causal models (SCMs). In this pursuit, recent advances formalize network sheaves and cosheaves of causal…
In this paper, we propose a Computer Assisted Diagnosis (CAD) system based on a deep Convolutional Neural Network (CNN) model, to build an end-to-end learning process that classifies breast mass lesions. We investigate the impact that has…
Integro-differential equations arise in a wide range of applications, including transport, kinetic theory, radiative transfer, and multiphysics modeling, where nonlocal integral operators couple the solution across phase space. Such…
A feedforward neural network, including hidden layers, motivated by nonlinear functions (such as Tanh, ReLU, and Sigmoid functions), exhibits uniform approximation properties in Sobolev space, and discontinuous neural networks can reduce…
The $L^2$ gradient flow of the Ginzburg-Landau free energy functional leads to the Allen Cahn equation that is widely used for modeling phase separation. Machine learning methods for solving the Allen-Cahn equation in its strong form suffer…
We develop a randomized Newton's method for solving differential equations, based on a fully connected neural network discretization. In particular, the randomized Newton's method randomly chooses equations from the overdetermined nonlinear…
Learning portable neural networks is very essential for computer vision for the purpose that pre-trained heavy deep models can be well applied on edge devices such as mobile phones and micro sensors. Most existing deep neural network…
Recent advances in Generative Artificial Intelligence have fueled numerous applications, particularly those involving Generative Adversarial Networks (GANs), which are essential for synthesizing realistic photos and videos. However,…
Recent state-of-the-art active learning methods have mostly leveraged Generative Adversarial Networks (GAN) for sample acquisition; however, GAN is usually known to suffer from instability and sensitivity to hyper-parameters. In contrast to…
We present a simple neural network model which combines a locally-connected feedforward structure, as is traditionally used to model inter-neuron connectivity, with a layer of undifferentiated connections which model the diffuse projections…