Related papers: Physics-informed neural networks to solve inverse …
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…
Solving inverse problems in dynamical systems governed by high-dimensional coupled ordinary differential equations (ODEs) is a ubiquitous challenge in scientific machine learning. In many real-world applications, researchers seek to uncover…
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…
Kolmogorov-Arnold Networks (KANs) have gained attention as an alternative to traditional multilayer perceptrons (MLPs) for deep learning applications in computational physics, particularly for solving inverse problems with sparse data, as…
Physics-informed neural networks (PINNs) is an emerging category of neural networks which can be trained to solve supervised learning tasks while taking into consideration given laws of physics described by general nonlinear partial…
Numerical modeling errors are unavoidable in finite element analysis. The presence of model errors inherently reflects both model accuracy and uncertainty. To date there have been few methods for explicitly quantifying errors at points of…
In this paper, the physics-informed neural networks (PINN) is applied to high-dimensional system to solve the (N+1)-dimensional initial boundary value problem with 2N+1 hyperplane boundaries. This method is used to solve the most classic…
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…
Differential equations are indispensable to engineering and hence to innovation. In recent years, physics-informed neural networks (PINN) have emerged as a novel method for solving differential equations. PINN method has the advantage of…
Physics-informed neural network (PINN) is a data-driven solver for partial and ordinary differential equations(ODEs/PDEs). It provides a unified framework to address both forward and inverse problems. However, the complexity of the…
The research in Artificial Intelligence methods with potential applications in science has become an essential task in the scientific community last years. Physics Informed Neural Networks (PINNs) is one of this methods and represent a…
Deep learning has been shown to be an effective tool in solving partial differential equations (PDEs) through physics-informed neural networks (PINNs). PINNs embed the PDE residual into the loss function of the neural network, and have been…
Physics-informed neural networks (PINNs) leverage neural-networks to find the solutions of partial differential equation (PDE)-constrained optimization problems with initial conditions and boundary conditions as soft constraints. These soft…
In this study, we present and validate the predictive capability of the Physics-Informed Neural Networks (PINNs) methodology for solving a variety of engineering and biological dynamical systems governed by ordinary differential equations…
We apply physics-informed machine learning (PIML) to solve inverse problems in holography and classical mechanics, focusing on neural ordinary differential equations (Neural ODEs) and physics-informed neural networks (PINNs) for solving…
In this paper, we develop a deep learning approach for the accurate solution of challenging problems of near-field microscopy that leverages the powerful framework of physics-informed neural networks (PINNs) for the inversion of the complex…
We develop improved physics-informed neural networks (PINNs) for high-order and high-dimensional power system models described by nonlinear ordinary differential equations. We propose some novel enhancements to improve PINN training and…
Addressing high-dimensional partial differential equations to derive effective actions within the functional renormalization group is formidable, especially when considering various field configurations, including inhomogeneous states, even…
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…
A physics informed neural network (PINN) incorporates the physics of a system by satisfying its boundary value problem through a neural network's loss function. The PINN approach has shown great success in approximating the map between the…