Related papers: Efficient Training of Physics-Informed Neural Netw…
Physics-Informed Neural Networks (PINNs) solve physical systems by incorporating governing partial differential equations directly into neural network training. In electromagnetism, where well-established methodologies such as FDTD and FEM…
In recent years, with the advancements in machine learning and neural networks, algorithms using physics-informed neural networks (PINNs) to solve PDEs have gained widespread applications. While these algorithms are well-suited for a wide…
Physics-informed neural networks (PINN) is a extremely powerful paradigm used to solve equations encountered in scientific computing applications. An important part of the procedure is the minimization of the equation residual which…
Physics informed neural networks (PINNs) have recently been widely used for robust and accurate approximation of PDEs. We provide rigorous upper bounds on the generalization error of PINNs approximating solutions of the forward problem for…
Physics-Informed Neural Network (PINN) is a novel multi-task learning framework useful for solving physical problems modeled using differential equations (DEs) by integrating the knowledge of physics and known constraints into the…
Material identification is critical for understanding the relationship between mechanical properties and the associated mechanical functions. However, material identification is a challenging task, especially when the characteristic of the…
While physics-informed neural networks (PINNs) have become a popular deep learning framework for tackling forward and inverse problems governed by partial differential equations (PDEs), their performance is known to degrade when larger and…
A novel comparison is presented of the effect of optimiser choice on the accuracy of physics-informed neural networks (PINNs). To give insight into why some optimisers are better, a new approach is proposed that tracks the training…
This work aims to provide an effective deep learning framework to predict the vector-soliton solutions of the coupled nonlinear equations and their interactions. The method we propose here is a physics-informed neural network (PINN)…
How to develop slim and accurate deep neural networks has become crucial for real- world applications, especially for those employed in embedded systems. Though previous work along this research line has shown some promising results, most…
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…
In recent years, Scientific Machine Learning (SciML) methods for solving partial differential equations (PDEs) have gained increasing popularity. Within such a paradigm, Physics-Informed Neural Networks (PINNs) are novel deep learning…
Recently, physics-informed neural networks (PINNs) and their variants have gained significant popularity as a scientific computing method for solving partial differential equations (PDEs), whereas accuracy is still its main shortcoming.…
Physics-Informed Neural Networks (PINN) has evolved into a powerful tool for solving partial differential equations, which has been applied to various fields such as energy, environment, en-gineering, etc. When utilizing PINN to solve…
We employ adaptive activation functions for regression in deep and physics-informed neural networks (PINNs) to approximate smooth and discontinuous functions as well as solutions of linear and nonlinear partial differential equations. In…
Recent work in scientific machine learning has developed so-called physics-informed neural network (PINN) models. The typical approach is to incorporate physical domain knowledge as soft constraints on an empirical loss function and use…
This article introduces Perception-Informed Neural Networks (PrINNs), a framework designed to incorporate perception-based information into neural networks, addressing both systems with known and unknown physics laws or differential…
Physics-informed neural networks (PINNs) show great advantages in solving partial differential equations. In this paper, we for the first time propose to study conformable time fractional diffusion equations by using PINNs. By solving the…
Systems biology and systems neurophysiology in particular have recently emerged as powerful tools for a number of key applications in the biomedical sciences. Nevertheless, such models are often based on complex combinations of multiscale…
Efficient and robust optimization is essential for neural networks, enabling scientific machine learning models to converge rapidly to very high accuracy -- faithfully capturing complex physical behavior governed by differential equations.…