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A physics-informed neural network (PINN) uses physics-augmented loss functions, e.g., incorporating the residual term from governing partial differential equations (PDEs), to ensure its output is consistent with fundamental physics laws.…

PDEs arise ubiquitously in science and engineering, where solutions depend on parameters (physical properties, boundary conditions, geometry). Traditional numerical methods require re-solving the PDE for each parameter, making parameter…

Numerical methods such as finite element have been flourishing in the past decades for modeling solid mechanics problems via solving governing partial differential equations (PDEs). A salient aspect that distinguishes these numerical…

Physics-informed neural networks (PINNs) are at the forefront of scientific machine learning, making possible the creation of machine intelligence that is cognizant of physical laws and able to accurately simulate them. However, today's…

We propose a self-supervised physics-informed neural network (PINN) framework that adaptively balances physics-based and data-driven supervision for scientific machine learning under data scarcity. Unlike prior PINNs that rely on fixed or…

Physics informed neural networks (PINNs) have recently been very successfully applied for efficiently approximating inverse problems for PDEs. We focus on a particular class of inverse problems, the so-called data assimilation or unique…

I provide an introduction to the application of deep learning and neural networks for solving partial differential equations (PDEs). The approach, known as physics-informed neural networks (PINNs), involves minimizing the residual of the…

Deep learning is a powerful tool for solving data driven differential problems and has come out to have successful applications in solving direct and inverse problems described by PDEs, even in presence of integral terms. In this paper, we…

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…

Thanks to their universal approximation properties and new efficient training strategies, Deep Neural Networks are becoming a valuable tool for the approximation of mathematical operators. In the present work, we introduce Mesh-Informed…

We introduce adaptive-basis physics-informed neural networks (AB-PINNs), a novel approach to domain decomposition for training PINNs in which existing subdomains dynamically adapt to the intrinsic features of the unknown solution. Drawing…

Physics-informed neural networks (PINNs) have emerged as a transformative framework for addressing operator learning and inverse problems involving the Korteweg-de Vries (KdV) equation for internal solitary waves. By integrating physical…

Physics-Informed Neural Networks (PINNs) recast PDE solving as an optimisation problem in function space by minimising a residual-based objective, yet many applications require additional derivative-based relations that are just as…

Machine learning techniques are employed to perform the full characterization of a quantum system. The particular artificial intelligence technique used to learn the Hamiltonian is called physics informed neural network (PINN). The idea…

Efficient and robust optimization is essential for neural networks, enabling scientific machine learning models to converge rapidly to very high accuracy -- faithfully capturing complex physical behavior governed by differential equations.…

Physics-informed neural networks (PINNs) are an emerging technique to solve partial differential equations (PDEs). In this work, we propose a simple but effective PINN approach for the phase-field model of ferroelectric microstructure…

Physics-informed neural networks (PINNs) have been demonstrated to be efficient in solving partial differential equations (PDEs) from a variety of experimental perspectives. Some recent studies have also proposed PINN algorithms for PDEs on…

Regular physics-informed neural networks (PINNs) predict the solution of partial differential equations using sparse labeled data but only over a single domain. On the other hand, fully supervised learning models are first trained usually…

How to solve inverse problems is the challenge of many engineering and industrial applications. Recently, physics-informed neural networks (PINNs) have emerged as a powerful approach to solve inverse problems efficiently. However, it is…

Physics-informed neural networks (PINNs) represent a new paradigm for solving partial differential equations (PDEs) by integrating physical laws into the learning process of neural networks. However, ensuring that such frameworks fully…