Related papers: Taylor-Model Physics-Informed Neural Networks (PIN…

Deep learning has achieved remarkable success in diverse applications; however, its use in solving partial differential equations (PDEs) has emerged only recently. Here, we present an overview of physics-informed neural networks (PINNs),…

Physics-informed neural networks (PINNs) as a means of discretizing partial differential equations (PDEs) are garnering much attention in the Computational Science and Engineering (CS&E) world. At least two challenges exist for PINNs at…

As is well known, differential algebraic equations (DAEs), which are able to describe dynamic changes and underlying constraints, have been widely applied in engineering fields such as fluid dynamics, multi-body dynamics, mechanical systems…

Evolution equations, including both ordinary differential equations (ODEs) and partial differential equations (PDEs), play a pivotal role in modeling dynamic systems. However, achieving accurate long-time integration for these equations…

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…

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…

Recently, a class of machine learning methods called physics-informed neural networks (PINNs) has been proposed and gained prevalence in solving various scientific computing problems. This approach enables the solution of partial…

Recent work in deep learning focuses on solving physical systems in the Ordinary Differential Equation or Partial Differential Equation. This current work proposed a variant of Convolutional Neural Networks (CNNs) that can learn the hidden…

Partial differential equations (PDEs) are central to scientific modeling. Modern workflows increasingly rely on learning-based components to support model reuse, inference, and integration across large computational processes. Despite the…

Physics-informed deep learning has drawn tremendous interest in recent years to solve computational physics problems, whose basic concept is to embed physical laws to constrain/inform neural networks, with the need of less data for training…

Physics-informed neural networks (PINNs) have been widely applied to solve partial differential equations (PDEs) by enforcing outputs and gradients of deep models to satisfy target equations. Due to the limitation of numerical computation,…

Inverse problems involving differential equations often require identifying unknown parameters or functions from data. Existing approaches, such as Physics-Informed Neural Networks (PINNs), Universal Differential Equations (UDEs) and…

Physics-informed neural networks (PINNs) encode physical conservation laws and prior physical knowledge into the neural networks, ensuring the correct physics is represented accurately while alleviating the need for supervised learning to a…

Despite their ubiquity, the rich physics present in a plasma sheath has inhibited the development of a generally applicable description of this critical region. The present study utilizes a physics-informed neural network (PINN) to evaluate…

Physics-Informed Neural Networks (PINNs) and their variational counterparts (VPINNs) are neural networks that incorporate physical laws, making them useful for scientific problems. Existing generalization analyses for PINNs and VPINNs…

Classical Physics-informed neural networks (PINNs) approximate solutions to PDEs with the help of deep neural networks trained to satisfy the differential operator and the relevant boundary conditions. We revisit this idea in the quantum…

In this study, we explore the application of Physics-Informed Neural Networks (PINNs) to the analysis of bifurcation phenomena in ecological migration models. By integrating the fundamental principles of diffusion-advection-reaction…

Scientific machine learning (SciML) represents a significant advancement in integrating machine learning (ML) with scientific methodologies. At the forefront of this development are Physics-Informed Neural Networks (PINNs), which offer a…

The utilization of Deep Neural Networks (DNNs) in physical science and engineering applications has gained traction due to their capacity to learn intricate functions. While large datasets are crucial for training DNN models in fields like…

The rise of Physics-Informed Neural Networks (PINNs) has popularized the concept of solving differential equations via residual minimization. However, neural networks are often viewed as ``black boxes" requiring significant computational…