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Identifying governing equations for a dynamical system is a topic of critical interest across an array of disciplines, from mathematics to engineering to biology. Machine learning -- specifically deep learning -- techniques have shown their…

Probabilistic power flow (PPF) plays a critical role in power system analysis. However, the high computational burden makes it challenging for the practical implementation of PPF. This paper proposes a model-based deep learning approach to…

In this paper, we consider approximating the parameter-to-solution maps of parametric partial differential equations (PPDEs) using deep neural networks (DNNs). We propose an efficient approach combining reduced collocation methods (RCMs)…

In this paper we apply neural networks with local converging inputs (NNLCI), originally introduced in [arXiv:2109.09316], to solve the two dimensional Maxwell's equation around perfect electric conductors (PECs). The input to the networks…

Recently, deep learning techniques have been extensively studied for pansharpening, which aims to generate a high resolution multispectral (HRMS) image by fusing a low resolution multispectral (LRMS) image with a high resolution…

By replacing standard non-linearities with polynomial activations, Polynomial Neural Networks (PNNs) are pivotal for applications such as privacy-preserving inference via Homomorphic Encryption (HE). However, training PNNs effectively…

Neural networks have been identified as powerful tools for the study of complex systems. A noteworthy example is the neural network differential equation (NN DE) solver, which can provide functional approximations to the solutions of a wide…

Deep neural networks (DNNs) have been used to model complex optimization problems in many applications, yet have difficulty guaranteeing solution optimality and feasibility, despite training on large datasets. Training a NN as a surrogate…

In recent years, surrogate models based on deep neural networks (DNN) have been widely used to solve partial differential equations, which were traditionally handled by means of numerical simulations. This kind of surrogate models, however,…

As the scale and complexity of integrated circuits continue to increase, traditional modeling methods are struggling to address the nonlinear challenges in radio frequency (RF) chips. Deep learning has been increasingly applied to RF device…

Computational drug discovery provides an efficient tool helping large scale lead molecules screening. One of the major tasks of lead discovery is identifying molecules with promising binding affinities towards a target, a protein in…

Deep Convolutional Neural Networks (CNNs) achieve high accuracy but often rely on purely global, gradient-based optimisation, which can lead to overfitting, redundant filters, and reduced interpretability. To address these limitations, we…

Neural networks have shown promising potential in accelerating the numerical simulation of systems governed by partial differential equations (PDEs). Different from many existing neural network surrogates operating on high-dimensional…

We propose a new semi-analytic physics informed neural network (PINN) to solve singularly perturbed boundary value problems. The PINN is a scientific machine learning framework that offers a promising perspective for finding numerical…

Neural Networks (NN) has been used in many areas with great success. When a NN's structure (Model) is given, during the training steps, the parameters of the model are determined using an appropriate criterion and an optimization algorithm…

Autoregressive next-step prediction models have become the de-facto standard for building data-driven neural solvers to forecast time-dependent partial differential equations (PDEs). Denoise training that is closely related to diffusion…

Despite the impressive performance of biological and artificial networks, an intuitive understanding of how their local learning dynamics contribute to network-level task solutions remains a challenge to this date. Efforts to bring learning…

Deep neural networks (DNNs) have been widely applied to solve real-world regression problems. However, selecting optimal network structures remains a significant challenge. This study addresses this issue by linking neuron selection in DNNs…

Deep Neural Nets (DNNs) learn latent representations induced by their downstream task, objective function, and other parameters. The quality of the learned representations impacts the DNN's generalization ability and the coherence of the…

Solving high dimensional partial differential equations (PDEs) has historically posed a considerable challenge when utilizing conventional numerical methods, such as those involving domain meshes. Recent advancements in the field have seen…