Related papers: Surface profile recovery from electromagnetic fiel…

In recent engineering applications using deep learning, physics-informed neural network (PINN) is a new development as it can exploit the underlying physics of engineering systems. The novelty of PINN lies in the use of partial differential…

We present a new technique for the accelerated training of physics-informed neural networks (PINNs): discretely-trained PINNs (DT-PINNs). The repeated computation of partial derivative terms in the PINN loss functions via automatic…

Solving time-dependent Partial Differential Equations (PDEs) is one of the most critical problems in computational science. While Physics-Informed Neural Networks (PINNs) offer a promising framework for approximating PDE solutions, their…

Large-scale river models are being refined over coastal regions to improve the scientific understanding of coastal processes, hazards and responses to climate change. However, coarse mesh resolutions and approximations in physical…

Physics-Informed Neural Networks (PINNs) have emerged as a powerful tool for integrating physics-based constraints and data to address forward and inverse problems in machine learning. Despite their potential, the implementation of PINNs…

Physics-informed neural networks (PINNs) are a new tool for solving boundary value problems by defining loss functions of neural networks based on governing equations, boundary conditions, and initial conditions. Recent investigations have…

Physics-informed neural networks (PINNs) are an increasingly powerful way to solve partial differential equations, generate digital twins, and create neural surrogates of physical models. In this manuscript we detail the inner workings of…

Physics-informed neural networks (PINNs) are employed to solve the Dyson--Schwinger equations of quantum electrodynamics (QED) in Euclidean space, with a focus on the non-perturbative generation of the fermion's dynamical mass function in…

Traditional cortical surface reconstruction is time consuming and limited by the resolution of brain Magnetic Resonance Imaging (MRI). In this work, we introduce Pial Neural Network (PialNN), a 3D deep learning framework for pial surface…

Data-driven modeling of spatiotemporal physical processes with general deep learning methods is a highly challenging task. It is further exacerbated by the limited availability of data, leading to poor generalizations in standard neural…

Partial differential equations (PDEs) are an essential computational kernel in physics and engineering. With the advance of deep learning, physics-informed neural networks (PINNs), as a mesh-free method, have shown great potential for fast…

In this study, the capabilities of the Physics-Informed Neural Network (PINN) method are investigated for three major tasks: modeling, simulation, and optimization in the context of the heat conduction problem. In the modeling phase, the…

Physics-informed neural networks (PINNs) commonly address ill-posed inverse problems by uncovering unknown physics. This study presents a novel unsupervised learning framework that identifies spatial subdomains with specific governing…

Physics-Informed Neural Networks (PINNs) are effective methods for solving inverse problems and discovering governing equations from observational data. However, their performance degrades significantly under complex measurement noise and…

Physics-Informed Neural Networks (PINNs) represent a significant advancement in Scientific Machine Learning (SciML), which integrate physical domain knowledge into an empirical loss function as soft constraints and apply existing machine…

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) have emerged as a promising approach for solving partial differential equations (PDEs) by embedding the governing physics into the loss function associated with a deep neural network. In this work, a…

Physics-informed neural networks (PINNs) are extensively employed to solve partial differential equations (PDEs) by ensuring that the outputs and gradients of deep learning models adhere to the governing equations. However, constrained by…

Physics-Informed Neural Networks (PINNs) are machine learning tools that approximate the solution of general partial differential equations (PDEs) by adding them in some form as terms of the loss/cost function of a Neural Network. Most…

Solving differential equations efficiently and accurately sits at the heart of progress in many areas of scientific research, from classical dynamical systems to quantum mechanics. There is a surge of interest in using Physics-Informed…