相关论文: Error analysis for physics informed neural network…

I provide an introduction to the application of deep learning and neural networks for solving partial differential equations (PDEs). The approach, known as physics-informed neural networks (PINNs), involves minimizing the residual of the…

This study investigates the potential accuracy boundaries of physics-informed neural networks, contrasting their approach with previous similar works and traditional numerical methods. We find that selecting improved optimization algorithms…

Physics Informed Neural Networks (PINNs) is a promising application of deep learning. The smooth architecture of a fully connected neural network is appropriate for finding the solutions of PDEs; the corresponding loss function can also be…

Deep learning has been highly successful in some applications. Nevertheless, its use for solving partial differential equations (PDEs) has only been of recent interest with current state-of-the-art machine learning libraries, e.g.,…

Physics-informed neural networks (PINNs) have recently become a powerful tool for solving partial differential equations (PDEs). However, finding a set of neural network parameters that lead to fulfilling a PDE can be challenging and…

Physics-Informed Neural Networks (PINNs) can be regarded as general-purpose PDE solvers, but it might be slow to train PINNs on particular problems, and there is no theoretical guarantee of corresponding error bounds. In this manuscript, we…

Complex physical systems are often described by partial differential equations (PDEs) that depend on parameters such as the Reynolds number in fluid mechanics. In applications such as design optimization or uncertainty quantification,…

We present the hidden-layer concatenated physics informed neural network (HLConcPINN) method, which combines hidden-layer concatenated feed-forward neural networks, a modified block time marching strategy, and a physics informed approach…

Partial differential equations (PDEs) serve as the cornerstone of mathematical physics. In recent years, Physics-Informed Neural Networks (PINNs) have significantly reduced the dependence on large datasets by embedding physical laws…

Physics-informed Neural Networks (PINNs) have been shown to be effective in solving partial differential equations by capturing the physics induced constraints as a part of the training loss function. This paper shows that a PINN can be…

PDEs arise ubiquitously in science and engineering, where solutions depend on parameters (physical properties, boundary conditions, geometry). Traditional numerical methods require re-solving the PDE for each parameter, making parameter…

Physics-Informed Neural Networks (PINNs) have revolutionized the computation of PDE solutions by integrating partial differential equations (PDEs) into the neural network's training process as soft constraints, becoming an important…

We propose a novel algorithm, based on physics-informed neural networks (PINNs) to efficiently approximate solutions of nonlinear dispersive PDEs such as the KdV-Kawahara, Camassa-Holm and Benjamin-Ono equations. The stability of solutions…

Physics-Informed Neural Networks (PINNs) have emerged as a powerful mesh-free framework for solving ordinary and partial differential equations by embedding the governing physical laws directly into the loss function. However, their…

Deep learning models trained on finite data lack a complete understanding of the physical world. On the other hand, physics-informed neural networks (PINNs) are infused with such knowledge through the incorporation of mathematically…

Physics-Informed Neural Networks (PINNs) encounter accuracy limitations when solving the Allen--Cahn (AC) and Cahn--Hilliard (CH) partial differential equations (PDEs). To overcome this, we employ a novel loss function, Residuals-weighted…

This work compares the advantages and limitations of the Finite Difference Method with Physics-Informed Neural Networks, showing where each can best be applied for different problem scenarios. Analysis on the L2 relative error based on…

Physics-Informed Neural Networks (PINN) are neural networks (NNs) that encode model equations, like Partial Differential Equations (PDE), as a component of the neural network itself. PINNs are nowadays used to solve PDEs, fractional…

Physics-Informed Neural Networks (PINNs) have become a popular and powerful framework for solving partial differential equations (PDEs), leveraging neural networks to approximate solutions while embedding PDE constraints, boundary…

In this work, we study physics-informed neural networks (PINNs) constrained by partial differential equations (PDEs) and their application in approximating PDEs with two characteristic scales. From a continuous perspective, our formulation…