Related papers: PIG: Physics-Informed Gaussians as Adaptive Parame…
Physics-informed neural networks (PINNs) have recently emerged as a prominent paradigm for solving partial differential equations (PDEs), yet their training strategies remain underexplored. While hard prioritization methods inspired by…
The recent rise of deep learning has led to numerous applications, including solving partial differential equations using Physics-Informed Neural Networks. This approach has proven highly effective in several academic cases. However, their…
Physics-Informed Neural Networks (PINNs) have emerged as a tool for approximating the solution of Partial Differential Equations (PDEs) in both forward and inverse problems. PINNs minimize a loss function which includes the PDE residual…
We introduce the concept of a Graph-Informed Neural Network (GINN), a hybrid approach combining deep learning with probabilistic graphical models (PGMs) that acts as a surrogate for physics-based representations of multiscale and…
Compared with conventional numerical approaches to solving partial differential equations (PDEs), physics-informed neural networks (PINN) have manifested the capability to save development effort and computational cost, especially in…
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…
Physics-informed neural networks (PINNs) have emerged as a powerful tool for solving physical systems described by partial differential equations (PDEs). However, their accuracy in dynamical systems, particularly those involving sharp…
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 Networks (PINNs) provide a mesh-free approach for solving differential equations by embedding physical constraints into neural network training. However, PINNs tend to overfit within the training domain, leading to…
Physics-Informed Neural Networks (PINNs) have emerged as a promising approach for solving Partial Differential Equations (PDEs) by incorporating physical constraints into deep learning models. However, standard PINNs often require a large…
Physics-informed neural networks (PINNs) have shown promise in solving partial differential equations (PDEs) relevant to multiscale modeling, but they often fail when applied to materials with discontinuous coefficients, such as media with…
Physics-informed neural networks (PINNs) are effective in solving integer-order partial differential equations (PDEs) based on scattered and noisy data. PINNs employ standard feedforward neural networks (NNs) with the PDEs explicitly…
Physics-Informed Neural Networks (PINNs) have emerged as a key tool in Scientific Machine Learning since their introduction in 2017, enabling the efficient solution of ordinary and partial differential equations using sparse measurements.…
In this research, the application of the Physics-Informed Neural Network (PINN) model is explored to solve transport equation-based Partial Differential Equations (PDEs). The primary objective is to analyze the impact of different…
Although physics-informed neural networks(PINNs) have progressed a lot in many real applications recently, there remains problems to be further studied, such as achieving more accurate results, taking less training time, and quantifying the…
Physics-informed neural networks (PINNs) have effectively been demonstrated in solving forward and inverse differential equation problems, but they are still trapped in training failures when the target functions to be approximated exhibit…
We apply Physics-Informed Neural Networks (PINNs) for solving identification problems of nonhomogeneous materials. We focus on the problem with a background in elasticity imaging, where one seeks to identify the nonhomogeneous mechanical…
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…
Partial differential equations (PDEs) are widely used for the description of physical and engineering phenomena. Some key parameters involved in PDEs, which represent certain physical properties with important scientific interpretations,…
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…