Related papers: SetPINNs: Set-based Physics-informed Neural Networ…

Physics-Informed Neural Networks (PINNs) have emerged as a promising framework for solving forward and inverse problems governed by differential equations. However, their reliability when used in ill-posed inverse problems remains poorly…

Physics-Informed Neural Networks (PINNs) have emerged as a promising computational framework for solving differential equations by integrating deep learning with physical constraints. However, their application in gas turbines is still in…

Physics-informed neural networks (PINNs) offer a unified framework for solving both forward and inverse problems of differential equations, yet their performance and physical consistency strongly depend on how governing laws are…

Physics-Informed Neural Networks (PINNs) have recently been proposed to solve scientific and engineering problems, where physical laws are introduced into neural networks as prior knowledge. With the embedded physical laws, PINNs enable the…

A Physics-Informed Neural Network (PINN) provides a distinct advantage by synergizing neural networks' capabilities with the problem's governing physical laws. In this study, we introduce an innovative approach for solving seepage problems…

Physics informed neural networks (PINNs) are nowadays used as efficient machine learning methods for solving differential equations. However, vanilla-PINNs fail to learn complex problems as ones involving stiff ordinary differential…

In this paper, we introduce the SPINNs (stochastic physics-informed neural networks) in a systematic manner. This provides a mathematical framework for approximating the solution of stochastic differential equations (SDEs) driven by Levy…

In recent years, scientific machine learning, particularly physic-informed neural networks (PINNs), has introduced new innovative methods to understanding the differential equations that describe power system dynamics, providing a more…

Physics-Informed Neural Networks (PINNs) have emerged as a promising deep learning framework for approximating numerical solutions to partial differential equations (PDEs). However, conventional PINNs, relying on multilayer perceptrons…

Deep learning models trained on finite data lack a complete understanding of the physical world. On the other hand, physics-informed neural networks (PINNs) are infused with such knowledge through the incorporation of mathematically…

This paper puts forward the vision of creating a library of neural-network-based models for power system simulations. Traditional numerical solvers struggle with the growing complexity of modern power systems, necessitating faster and more…

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 deep learning has emerged as a promising framework for solving partial differential equations (PDEs). Nevertheless, training these models on complex problems remains challenging, often leading to limited accuracy and…

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…

Physics-informed neural networks (PINNs) incorporate physical laws into their training to efficiently solve partial differential equations (PDEs) with minimal data. However, PINNs fail to guarantee adherence to conservation laws, which are…

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…

Inverse problems are extensively studied in applied mathematics, with applications ranging from acoustic tomography for medical diagnosis to geophysical exploration. Physics informed neural networks (PINNs) have emerged as a powerful tool…

In this work, we study physics-informed neural networks (PINNs) constrained by partial differential equations (PDEs) and their application in approximating PDEs with two characteristic scales. From a continuous perspective, our formulation…

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 attracted significant attention for solving partial differential equations (PDEs) in recent years because they alleviate the curse of dimensionality that appears in traditional methods. However,…