相关论文: Neuro-Spectral Architectures for Causal Physics-In…

Physics-Informed Neural Networks (PINNs) solve partial differential equations using deep learning. However, conventional PINNs perform pointwise predictions that neglect dependencies within a domain, which may result in suboptimal…

Machine learning and neural networks have advanced numerous research domains, but challenges such as large training data requirements and inconsistent model performance hinder their application in certain scientific problems. To overcome…

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) 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…

Physics-informed neural networks (PINNs) have recently been used to solve various computational problems which are governed by partial differential equations (PDEs). In this paper, we propose a multi-output physics-informed neural network…

We address the neutral inclusion problem with imperfect boundary conditions, focusing on designing interface functions for inclusions of arbitrary shapes. Traditional Physics-Informed Neural Networks (PINNs) struggle with this inverse…

While the popularity of physics-informed neural networks (PINNs) is steadily rising, to this date PINNs have not been successful in simulating dynamical systems whose solution exhibits multi-scale, chaotic or turbulent behavior. In this…

Learning the solution of partial differential equations (PDEs) with a neural network is an attractive alternative to traditional solvers due to its elegance, greater flexibility and the ease of incorporating observed data. However, training…

As an emerging technology in deep learning, physics-informed neural networks (PINNs) have been widely used to solve various partial differential equations (PDEs) in engineering. However, PDEs based on practical considerations contain…

Accurately and efficiently solving nonlinear differential equations is crucial for modeling dynamic behavior across science and engineering. Physics-Informed Neural Networks (PINNs) have emerged as a powerful solution that embeds physical…

Physics-Informed Neural Networks (PINNs) provide a learning-based framework for solving partial differential equations (PDEs) by embedding governing physical laws into neural network training. In practice, however, their performance is…

With the rapid advancement of graphical processing units, Physics-Informed Neural Networks (PINNs) are emerging as a promising tool for solving partial differential equations (PDEs). However, PINNs are not well suited for solving PDEs with…

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…

In various engineering and applied science applications, repetitive numerical simulations of partial differential equations (PDEs) for varying input parameters are often required (e.g., aircraft shape optimization over many design…

Physics-Informed Neural Networks (PINNs) have emerged as a powerful, mesh-free paradigm for solving partial differential equations (PDEs). However, they notoriously struggle with stiff, multi-scale, and nonlinear systems due to the inherent…

Physics-Informed Neural Networks (PINNs) are a useful framework for approximating partial differential equation solutions using deep learning methods. In this paper, we propose a principled redesign of the PINNsformer, a Transformer-based…

We present a novel numerical approach aiming at computing equilibria and dynamics structures of magnetized plasmas in coronal environments. A technique based on the use of neural networks that integrates the partial differential equations…

Physics-informed neural networks (PINNs) commonly address ill-posed inverse problems by uncovering unknown physics. This study presents a novel unsupervised learning framework that identifies spatial subdomains with specific governing…

Mathematical models in neural networks are powerful tools for solving complex differential equations and optimizing their parameters; that is, solving the forward and inverse problems, respectively. A forward problem predicts the output of…

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…