Related papers: ST-PINN: A Self-Training Physics-Informed Neural N…
In recent years the study of deep learning for solving differential equations has grown substantially. The use of physics-informed neural networks (PINNs) and deep operator networks (DeepONets) have emerged as two of the most useful…
Physics-informed neural networks (PINNs) offer a promising avenue for tackling both forward and inverse problems in partial differential equations (PDEs) by incorporating deep learning with fundamental physics principles. Despite their…
This paper presents a deep learning strategy to simultaneously solve Partial Differential Equations (PDEs) and back-calculate their parameters in the context of deep tunnel excavation. A Physics-Informed Neural Network (PINN) model is…
This paper presents a comprehensive review of the design of experiments used in the surrogate models. In particular, this study demonstrates the necessity of the design of experiment schemes for the Physics-Informed Neural Network (PINN),…
Physics-informed neural networks (PINNs) are a newly emerging research frontier in machine learning, which incorporate certain physical laws that govern a given data set, e.g., those described by partial differential equations (PDEs), into…
Physics-Informed Neural Networks (PINNs) offer a promising approach to solving differential equations and, more generally, to applying deep learning to problems in the physical sciences. We adopt a recently developed transfer learning…
Physics informed neural network (PINN) based solution methods for differential equations have recently shown success in a variety of scientific computing applications. Several authors have reported difficulties, however, when using PINNs to…
Solving inverse problems in dynamical systems governed by high-dimensional coupled ordinary differential equations (ODEs) is a ubiquitous challenge in scientific machine learning. In many real-world applications, researchers seek to uncover…
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…
Physics-informed neural networks based on automatic differentiation (AD-PINNs) and their finite-difference counterparts (FD-PINNs) are widely used for solving partial differential equations (PDEs), yet their analytical properties remain…
Solving high-frequency oscillatory partial differential equations (PDEs) is a critical challenge in scientific computing, with applications in fluid mechanics, quantum mechanics, and electromagnetic wave propagation. Traditional…
With growing investigations into solving partial differential equations by physics-informed neural networks (PINNs), more accurate and efficient PINNs are required to meet the practical demands of scientific computing. One bottleneck of…
Physics-informed neural networks (PINNs) are extensively employed to solve partial differential equations (PDEs) by ensuring that the outputs and gradients of deep learning models adhere to the governing equations. However, constrained by…
Physics-informed Neural Networks (PINNs) have been shown as a promising approach for solving both forward and inverse problems of partial differential equations (PDEs). Meanwhile, the neural operator approach, including methods such as Deep…
Physics-informed neural networks (PINNs) have recently emerged as an alternative way of solving partial differential equations (PDEs) without the need of building elaborate grids, instead, using a straightforward implementation. In…
Physics-informed neural networks (PINN) have recently emerged as a promising application of deep learning in a wide range of engineering and scientific problems based on partial differential equation (PDE) models. However, evidence shows…
Physics-informed neural networks (PINNs) have been proposed to learn the solution of partial differential equations (PDE). In PINNs, the residual form of the PDE of interest and its boundary conditions are lumped into a composite objective…
In this paper, we propose a novel Physics-Informed Neural Network (PINN) framework based on the Cord\`{e}s condition for solving both linear and fully nonlinear partial differential equations (PDEs) in non-divergence form, together with…
Physics-informed neural networks (PINNs) have lately received significant attention as a representative deep learning-based technique for solving partial differential equations (PDEs). Most fully connected network-based PINNs use automatic…
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…