Related papers: Probing optimisation in physics-informed neural ne…

Physics-informed neural networks (PINNs) and their variants have been very popular in recent years as algorithms for the numerical simulation of both forward and inverse problems for partial differential equations. This article aims to…

We show that the error achievable using physics-informed neural networks for solving systems of differential equations can be substantially reduced when these networks are trained using meta-learned optimization methods rather than to using…

Physics-Informed Neural Networks (PINNs) are a powerful deep learning method capable of providing solutions and parameter estimations of physical systems. Given the complexity of their neural network structure, the convergence speed is…

A method is presented that allows to reduce a problem described by differential equations with initial and boundary conditions to the problem described only by differential equations. The advantage of using the modified problem for…

Physics-informed neural networks (PINNs) integrate fundamental physical principles with advanced data-driven techniques, driving significant advancements in scientific computing. However, PINNs face persistent challenges with stiffness in…

This dissertation investigates physics-informed neural networks (PINNs) as candidate models for encoding governing equations, and assesses their performance on experimental data from two different systems. The first system is a simple…

Physics-informed neural networks (PINNs) are a promising approach for solving partial differential equations (PDEs). Their training, however, is often difficult because multiple loss terms induced by PDE residuals and boundary or initial…

Neural networks can be trained to solve partial differential equations (PDEs) by using the PDE residual as the loss function. This strategy is called "physics-informed neural networks" (PINNs), but it currently cannot produce high-accuracy…

Physics-Informed Neural Networks (PINNs) are a class of deep neural networks that are trained, using automatic differentiation, to compute the response of systems governed by partial differential equations (PDEs). The training of PINNs is…

This research presents the development of an innovative algorithm tailored for the adaptive sampling of residual points within the framework of Physics-Informed Neural Networks (PINNs). By addressing the limitations inherent in existing…

Physics-Informed Neural Networks (PINNs) have become a kind of attractive machine learning method for obtaining solutions of partial differential equations (PDEs). Training PINNs can be seen as a semi-supervised learning task, in which only…

The importance and cost of time-domain simulations when studying power systems have exponentially increased in the last decades. With the growing share of renewable energy sources, the slow and predictable responses from large turbines are…

Physics-informed neural networks (PINNs) have recently become a popular method for solving forward and inverse problems governed by partial differential equations (PDEs). By incorporating the residual of the PDE into the loss function of a…

Physics-informed neural networks (PINNs) are known to suffer from optimization difficulty. In this work, we reveal the connection between the optimization difficulty of PINNs and activation functions. Specifically, we show that PINNs…

Concrete manufacturing projects are one of the most common ones for consulting agencies. Because of the highly non-linear dependency of input materials like ash, water, cement, superplastic, etc; with the resultant strength of concrete, it…

Approximating solutions to partial differential equations (PDEs) is fundamental for the modeling of dynamical systems in science and engineering. Physics-informed neural networks (PINNs) are a recent machine learning-based approach, for…

In this study, we utilize the emerging Physics Informed Neural Networks (PINNs) approach for the first time to predict the flow field of a compressor cascade. Different from conventional training methods, a new adaptive learning strategy…

In this paper, we investigate several techniques for modeling the one-dimensional advection equation for a specific class of problems with discontinuous initial and boundary conditions using physics-informed neural networks (PINNs). To…

In this work, we assess the ability of physics-informed neural networks (PINNs) to solve increasingly-complex coupled ordinary differential equations (ODEs). We focus on a pair of benchmarks: discretized partial differential equations and…

Recent advancements in physics-informed neural networks (PINNs) and their variants have garnered substantial focus from researchers due to their effectiveness in solving both forward and inverse problems governed by differential equations.…