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We revisit the analogy between feed-forward deep neural networks (DNNs) and discrete dynamical systems derived from neural integral equations and their corresponding partial differential equation (PDE) forms. A comparative analysis between…

Physics-informed neural networks (PINNs) have been applied to simulate multiphase flows, yet they are limited in modeling phase changes and sharp interfaces due to optimization conflicts in the strongly coupled Allen-Cahn, Cahn-Hilliard,…

We introduce a method to convert Physics-Informed Neural Networks (PINNs), commonly used in scientific machine learning, to Spiking Neural Networks (SNNs), which are expected to have higher energy efficiency compared to traditional…

Signal processing, communications, and control have traditionally relied on classical statistical modeling techniques. Such model-based methods utilize mathematical formulations that represent the underlying physics, prior information and…

Deep neural networks (DNNs) are powerful tools for compressing and distilling information. Their scale and complexity, often involving billions of inter-dependent parameters, render direct microscopic analysis difficult. Under such…

Emergence of deep neural networks (DNNs) has raised enormous attention towards artificial neural networks (ANNs) once again. They have become the state-of-the-art models and have won different machine learning challenges. Although these…

Physics-Informed Neural Networks (PINNs) have emerged as a promising approach for solving Partial Differential Equations (PDEs) by incorporating physical constraints into deep learning models. However, standard PINNs often require a large…

Many types of physics-informed neural network models have been proposed in recent years as approaches for learning solutions to differential equations. When a particular task requires solving a differential equation at multiple…

Physics-informed neural networks (PINNs) have emerged as a promising mesh-free paradigm for solving partial differential equations, yet adoption in science and engineering is limited by slow training and modest accuracy relative to modern…

The concepts and techniques of physics-informed neural networks (PINNs) is studied and limitations are identified to make it efficient to approximate dynamical equations. Potential working research domains are explored for increasing the…

This paper introduces Progressively Diffused Networks (PDNs) for unifying multi-scale context modeling with deep feature learning, by taking semantic image segmentation as an exemplar application. Prior neural networks, such as ResNet, tend…

Physics-informed neural networks (PINNs) [31] use automatic differentiation to solve partial differential equations (PDEs) by penalizing the PDE in the loss function at a random set of points in the domain of interest. Here, we develop a…

Recent advancements in recurrent neural network (RNN) research have demonstrated the superiority of utilizing multiscale structures in learning temporal representations of time series. Currently, most of multiscale RNNs use fixed scales,…

Deep Neural Networks (DNNs) are powerful tools for various computer vision tasks, yet they often struggle with reliable uncertainty quantification - a critical requirement for real-world applications. Bayesian Neural Networks (BNN) are…

A method for solving elasticity problems based on separable physics-informed neural networks (SPINN) in conjunction with the deep energy method (DEM) is presented. Numerical experiments have been carried out for a number of problems showing…

This paper introduces a Bi-fidelity Asymptotic-Preserving Neural Network (BI-APNNs) framework, designed to efficiently solve forward and inverse problems for the semiconductor Boltzmann equation. Our approach builds upon the…

Physics-Informed Neural Networks (PINNs) are a new family of numerical methods, based on deep learning, for modeling boundary value problems. They offer an advantage over traditional numerical methods for high-dimensional, parametric, and…

Physics-informed neural networks (PINNs), rooted in deep learning, have emerged as a promising approach for solving partial differential equations (PDEs). By embedding the physical information described by PDEs into feedforward neural…

Motivated by the gap between theoretical optimal approximation rates of deep neural networks (DNNs) and the accuracy realized in practice, we seek to improve the training of DNNs. The adoption of an adaptive basis viewpoint of DNNs leads to…

Physics-Informed Neural Networks (PINNs) offer a promising approach to solving differential equations and, more generally, to applying deep learning to problems in the physical sciences. We adopt a recently developed transfer learning…