Related papers: ALM-PINNs Algorithms for Solving Nonlinear PDEs an…

Physics-informed neural networks (PINNs) have shown promise for solving partial differential equations (PDEs) by directly embedding them into the loss function. Despite their notable success, existing PINNs often exhibit training…

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,…

The solution of partial differential equations (PDES) on irregular domains has long been a subject of significant research interest. In this work, we present an approach utilizing physics-informed neural networks (PINNs) to achieve…

Sparse identification of nonlinear dynamical systems is a topic of continuously increasing significance in the dynamical systems community. Here we explore it at the level of lattice nonlinear dynamical systems of many degrees of freedom.…

Despite the significant progress over the last 50 years in simulating flow problems using numerical discretization of the Navier-Stokes equations (NSE), we still cannot incorporate seamlessly noisy data into existing algorithms,…

Over the past few years, neural network methods have evolved in various directions for approximating partial differential equations (PDEs). A promising new development is the integration of neural networks with classical numerical…

Successfully training Physics Informed Neural Networks (PINNs) for highly nonlinear PDEs on complex 3D domains remains a challenging task. In this paper, PINNs are employed to solve the 3D incompressible Navier-Stokes (NS) equations at…

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…

Coupling physics with machine learning models has shown great potential for solving fluid dynamics problems governed by partial differential equations. However, conventional methods, such as physics-informed neural networks, often suffer…

Physically informed neural networks (PINNs) are a promising emerging method for solving differential equations. As in many other deep learning approaches, the choice of PINN design and training protocol requires careful craftsmanship. Here,…

Physics-informed neural networks (PINNs) are able to solve partial differential equations (PDEs) by incorporating the residuals of the PDEs into their loss functions. Variational Physics-Informed Neural Networks (VPINNs) and hp-VPINNs use…

Phase field models, in particular, the Allen-Cahn type and Cahn-Hilliard type equations, have been widely used to investigate interfacial dynamic problems. Designing accurate, efficient, and stable numerical algorithms for solving the phase…

Physics-informed neural networks (PINN) have recently become attractive for solving partial differential equations (PDEs) that describe physics laws. By including PDE-based loss functions, physics laws such as mass balance are enforced…

Physics-Informed Neural Networks (PINNs) have emerged as a promising approach for solving partial differential equations (PDEs) by embedding the governing physics into the loss function associated with a deep neural network. In this work, a…

The use of Physics-informed neural networks (PINNs) has shown promise in solving forward and inverse problems of fractional diffusion equations. However, due to the fact that automatic differentiation is not applicable for fractional…

Physics-informed neural networks (PINNs) have gained prominence for their capability to tackle supervised learning tasks that conform to physical laws, notably nonlinear partial differential equations (PDEs). This paper presents…

In aerodynamics, accurately modeling subsonic compressible flow over airfoils is critical for aircraft design. However, solving the governing nonlinear perturbation velocity potential equation presents computational challenges. Traditional…

In this paper, local H\"older regularization is incorporated into a physics-informed neural networks (PINNs) framework for solving elliptic partial differential equations (PDEs). Motivated by the interior regularity properties of linear…

Physics-Informed Neural Networks (PINNs) recast PDE solving as an optimisation problem in function space by minimising a residual-based objective, yet many applications require additional derivative-based relations that are just as…

Physics-Informed Neural Networks (PINNs) are regarded as state-of-the-art tools for addressing highly nonlinear problems based on partial differential equations. Despite their broad range of applications, PINNs encounter several performance…