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We describe the class of convexified convolutional neural networks (CCNNs), which capture the parameter sharing of convolutional neural networks in a convex manner. By representing the nonlinear convolutional filters as vectors in a…

Many problems in science and engineering can be represented by a set of partial differential equations (PDEs) through mathematical modeling. Mechanism-based computation following PDEs has long been an essential paradigm for studying topics…

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…

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,…

Recently, there has been significant progress in solving quantum many-particle problem via machine learning based on the restricted Boltzmann machine. However, it is still highly challenging to solve frustrated models via machine learning,…

Recent works have shown that deep neural networks can be employed to solve partial differential equations, giving rise to the framework of physics informed neural networks. We introduce a generalization for these methods that manifests as a…

We propose the physics-constrained convolutional neural network (PC-CNN) to infer the high-resolution solution from sparse observations of spatiotemporal and nonlinear partial differential equations. Results are shown for a chaotic and…

The customizable nature of deep learning models have allowed them to be successful predictors in various disciplines. These models are often trained with respect to thousands or millions of instances for complicated problems, but the…

Neural network based methods have emerged as a promising paradigm for scientific computing, yet they face critical bottlenecks in high frequency function approximation and partial differential equation (PDE) solving.

Deep learning utilizing deep neural networks (DNNs) has achieved a lot of success recently in many important areas such as computer vision, natural language processing, and recommendation systems. The lack of convexity for DNNs has been…

Many physical processes such as weather phenomena or fluid mechanics are governed by partial differential equations (PDEs). Modelling such dynamical systems using Neural Networks is an active research field. However, current methods are…

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…

Deep neural networks are powerful tools for solving nonlinear problems in science and engineering, but training highly accurate models becomes challenging as problem complexity increases. Non-convex optimization and sensitivity to…

The escalating energy demands and parallel-processing bottlenecks of electronic neural networks underscore the need for alternative computing paradigms. Optical neural networks, capitalizing on the inherent parallelism and speed of light…

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.…

This paper presents an adaptive convolutional neural network (CNN) architecture that can automate diverse topology optimization (TO) problems having different underlying physics. The architecture uses the encoder-decoder networks with dense…

In this work we introduce a convolutional neural network (CNN) that jointly handles low-, mid-, and high-level vision tasks in a unified architecture that is trained end-to-end. Such a universal network can act like a `swiss knife' for…

Signal-background classification is a central problem in High-Energy Physics (HEP), that plays a major role for the discovery of new fundamental particles. A recent method -- the Parametric Neural Network (pNN) -- leverages multiple signal…

Prostate cancer is one of the most common causes of cancer deaths in men. There is a growing demand for noninvasively and accurately diagnostic methods that facilitate the current standard prostate cancer risk assessment in clinical…

The use of machine learning methods to tackle challenging physical layer signal processing tasks has attracted significant attention. In this work, we focus on the use of neural networks (NNs) to perform pilot-assisted channel estimation in…