相关论文: Physics-informed Neural Network for Nonlinear Dyna…
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…
Recently developed physics-informed neural network (PINN) has achieved success in many science and engineering disciplines by encoding physics laws into the loss functions of the neural network, such that the network not only conforms to…
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…
Physics-informed Neural Networks (PINNs) have been shown as a promising approach for solving both forward and inverse problems of partial differential equations (PDEs). Meanwhile, the neural operator approach, including methods such as Deep…
The physics informed neural network (PINN) is evolving as a viable method to solve partial differential equations. In the recent past PINNs have been successfully tested and validated to find solutions to both linear and non-linear partial…
As a typical application of deep learning, physics-informed neural network (PINN) {has been} successfully used to find numerical solutions of partial differential equations (PDEs), but how to improve the limited accuracy is still a great…
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.…
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…
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…
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…
This paper investigates data-driven solutions and parameter discovery to (2+1)-dimensional coupled nonlinear Schr\"odinger equations with variable coefficients (VC-CNLSEs), which describe transverse effects in optical fiber systems under…
Physics-informed neural networks (PINNs) impose known physical laws into the learning of deep neural networks, making sure they respect the physics of the process while decreasing the demand of labeled data. For systems represented by…
A physics-informed neural network (PINN) is used to produce a variety of self-trapped necklace solutions of the (2+1)-dimensional nonlinear Schr\"{o}dinger/Gross-Pitaevskii equation. We elaborate the analysis for the existence and evolution…
Physics-informed neural networks (PINNs) [31] use automatic differentiation to solve partial differential equations (PDEs) by penalizing the PDE in the loss function at a random set of points in the domain of interest. Here, we develop a…
A method for solving elasticity problems based on separable physics-informed neural networks (SPINN) in conjunction with the deep energy method (DEM) is presented. Numerical experiments have been carried out for a number of problems showing…
We revisit the original approach of using deep learning and neural networks to solve differential equations by incorporating the knowledge of the equation. This is done by adding a dedicated term to the loss function during the optimization…
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…
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) have great potential for flexibility and effectiveness in forward modeling and inversion of seismic waves. However, coordinate-based neural networks (NNs) commonly suffer from the "spectral bias"…
Machine learning techniques have proven to be effective in addressing the structure of atomic nuclei. Physics$-$Informed Neural Networks (PINNs) are a promising machine learning technique suitable for solving integro-differential problems…