Related papers: Physics-Informed Neural Networks for High-Precisio…
Physics-informed neural networks have shown significant potential in solving partial differential equations (PDEs) across diverse scientific fields. However, their performance often deteriorates when addressing PDEs with intricate and…
Physics-informed deep learning has drawn tremendous interest in recent years to solve computational physics problems, whose basic concept is to embed physical laws to constrain/inform neural networks, with the need of less data for training…
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 effectively been demonstrated in solving forward and inverse differential equation problems, but they are still trapped in training failures when the target functions to be approximated exhibit…
Solving differential equations efficiently and accurately sits at the heart of progress in many areas of scientific research, from classical dynamical systems to quantum mechanics. There is a surge of interest in using Physics-Informed…
Physics-informed neural networks (PINNs) have recently received much attention due to their capabilities in solving both forward and inverse problems. For training a deep neural network associated with a PINN, one typically constructs a…
Recently, physics-informed neural networks (PINNs) have offered a powerful new paradigm for solving problems relating to differential equations. Compared to classical numerical methods PINNs have several advantages, for example their…
We apply Physics-Informed Neural Networks (PINNs) for solving identification problems of nonhomogeneous materials. We focus on the problem with a background in elasticity imaging, where one seeks to identify the nonhomogeneous mechanical…
Physics-Informed Neural Networks (PINNs) have emerged as a key tool in Scientific Machine Learning since their introduction in 2017, enabling the efficient solution of ordinary and partial differential equations using sparse measurements.…
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…
Partial differential equations (PDEs) provide a mathematical foundation for simulating and understanding intricate behaviors in both physical sciences and engineering. With the growing capabilities of deep learning, data$-$driven approaches…
A physics-informed neural network (PINN), which has been recently proposed by Raissi et al [J. Comp. Phys. 378, pp. 686-707 (2019)], is applied to the partial differential equation (PDE) of liquid film flows. The PDE considered is the time…
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) are a class of deep learning neural networks that learn the response of a physical system without any simulation data, and only by incorporating the governing partial differential equations (PDEs) in…
Standard Physics-Informed Neural Networks (PINNs) often face challenges when modeling parameterized dynamical systems with sharp regime transitions, such as bifurcations. In these scenarios, the continuous mapping from parameters to…
The accurate modelling of structural dynamics is crucial across numerous engineering applications, such as Structural Health Monitoring (SHM), seismic analysis, and vibration control. Often, these models originate from physics-based…
Physics-Informed Neural Networks (PINNs) are a class of deep learning models aiming to approximate solutions of PDEs by training neural networks to minimize the residual of the equation. Focusing on non-equilibrium fluctuating systems, we…
We propose a new semi-analytic physics informed neural network (PINN) to solve singularly perturbed boundary value problems. The PINN is a scientific machine learning framework that offers a promising perspective for finding numerical…
Physics-Informed Neural Networks (PINNs) have demonstrated considerable success in solving complex fluid dynamics problems. However, their performance often deteriorates in regimes characterized by steep gradients, intricate boundary…
Inferring biophysical parameters and hidden state variables from partial and noisy observations is a fundamental challenge in computational neuroscience. This problem is particularly difficult for fast - slow spiking and bursting models,…