Related papers: PINN-DG: Residual neural network methods trained w…
In this work, we present a study combining two approaches in the context of solving PDEs: the continuous finite element method (FEM) and more recent techniques based on neural networks. In recent years, physics-informed neural networks…
We propose a meta-learning technique for offline discovery of physics-informed neural network (PINN) loss functions. We extend earlier works on meta-learning, and develop a gradient-based meta-learning algorithm for addressing diverse task…
We extend the finite element interpolated neural network (FEINN) framework from partial differential equations (PDEs) with weak solutions in $H^1$ to PDEs with weak solutions in $H(\textbf{curl})$ or $H(\textbf{div})$. To this end, we…
Physics-Informed Neural Networks (PINNs) seek to solve partial differential equations (PDEs) with deep learning. Mainstream approaches that deploy fully-connected multi-layer deep learning architectures require prolonged training to achieve…
The physics-informed neural network (PINN) is effective in solving the partial differential equation (PDE) by capturing the physics constraints as a part of the training loss function through the Automatic Differentiation (AD). This study…
In this study, we introduce a method based on Separable Physics-Informed Neural Networks (SPINNs) for effectively solving the BGK model of the Boltzmann equation. While the mesh-free nature of PINNs offers significant advantages in handling…
In this study, we propose a new numerical scheme for physics-informed neural networks (PINNs) that enables precise and inexpensive solution for partial differential equations (PDEs) in case of arbitrary geometries while strictly enforcing…
Accurate computational modeling of damage and fracture remains a central challenge in solid mechanics. The finite element method (FEM) is widely used for numerical modeling of fracture problems; however, classical damage models without…
Machine learning methods have been lately used to solve partial differential equations (PDEs) and dynamical systems. These approaches have been developed into a novel research field known as scientific machine learning in which techniques…
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…
We propose gradient-enhanced PINNs based on transfer learning (TL-gPINNs) for inverse problems of the function coefficient discovery in order to overcome deficiency of the discrete characterization of the PDE loss in neural networks and…
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…
Solving time-dependent partial differential equations (PDEs) that exhibit sharp gradients or local singularities is computationally demanding, as traditional physics-informed neural networks (PINNs) often suffer from inefficient point…
Physics-Informed Neural Networks (PINN) are neural networks encoding the problem governing equations, such as Partial Differential Equations (PDE), as a part of the neural network. PINNs have emerged as a new essential tool to solve various…
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…
We present a unified convergence theory for gradient-based training of neural network methods for partial differential equations (PDEs), covering both physics-informed neural networks (PINNs) and the Deep Ritz method. For linear PDEs, we…
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…
Parametric partial differential equations (PDEs) are fundamental for modeling a wide range of physical and engineering systems influenced by uncertain or varying parameters. Traditional neural network-based solvers, such as Physics-Informed…
Recently, a class of machine learning methods called physics-informed neural networks (PINNs) has been proposed and gained prevalence in solving various scientific computing problems. This approach enables the solution of partial…
Physics-informed neural networks (PINNs) approximate solutions of partial differential equations (PDEs) by embedding physical laws into the loss function. In parameterized PDE families, variations in coefficients or boundary/initial…