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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…

Modern power systems face significant challenges in state estimation and real-time monitoring, particularly regarding response speed and accuracy under faulty conditions or cyber-attacks. This paper proposes a hybrid approach using…

Physics-informed neural networks (PINNs) are capable of finding the solution for a given boundary value problem. We employ several ideas from the finite element method (FEM) to enhance the performance of existing PINNs in engineering…

In this study, we present and validate the predictive capability of the Physics-Informed Neural Networks (PINNs) methodology for solving a variety of engineering and biological dynamical systems governed by ordinary differential equations…

In recent years, Physics-Informed Neural Networks (PINNs) have become a representative method for solving partial differential equations (PDEs) with neural networks. PINNs provide a novel approach to solving PDEs through optimization…

In this paper, we develop a deep learning approach for the accurate solution of challenging problems of near-field microscopy that leverages the powerful framework of physics-informed neural networks (PINNs) for the inversion of the complex…

Physics-informed neural networks (PINNs) have emerged as a major research focus. However, today's PINNs encounter several limitations. Firstly, during the construction of the loss function using automatic differentiation, PINNs often…

Singularly perturbed problems are known to have solutions with steep boundary layers that are hard to resolve numerically. Traditional numerical methods, such as Finite Difference Methods (FDMs), require a refined mesh to obtain stable and…

Physics-Informed Neural Networks (PINNs) have emerged as a powerful tool for solving partial differential equations~(PDEs) in various scientific and engineering domains. However, traditional PINN architectures typically rely on large, fully…

Physics-Informed Neural Network (PINN) is a novel multi-task learning framework useful for solving physical problems modeled using differential equations (DEs) by integrating the knowledge of physics and known constraints into the…

The great success of Physics-Informed Neural Networks (PINN) in solving partial differential equations (PDEs) has significantly advanced our simulation and understanding of complex physical systems in science and engineering. However, many…

Differential equations are involved in modeling many engineering problems. Many efforts have been devoted to solving differential equations. Due to the flexibility of neural networks, Physics Informed Neural Networks (PINNs) have recently…

The transformative impact of machine learning, particularly Deep Learning (DL), on scientific and engineering domains is evident. In the context of computational fluid dynamics (CFD), Physics-Informed Neural Networks (PINNs) represent a…

We propose a new semi-analytic physics informed neural network (PINN) to solve singularly perturbed boundary value problems. The PINN is a scientific machine learning framework that offers a promising perspective for finding numerical…

Data-driven modeling of spatiotemporal physical processes with general deep learning methods is a highly challenging task. It is further exacerbated by the limited availability of data, leading to poor generalizations in standard neural…

In recent years, scientific machine learning, particularly physic-informed neural networks (PINNs), has introduced new innovative methods to understanding the differential equations that describe power system dynamics, providing a more…

Accurate modeling of drug release is essential for designing and developing controlled-release systems. Classical models (Fick, Higuchi, Peppas) rely on simplifying assumptions that limit their accuracy in complex geometries and release…

We explore the capability of physics-informed neural networks (PINNs) to discover multiple solutions. Many real-world phenomena governed by nonlinear differential equations (DEs), such as fluid flow, exhibit multiple solutions under the…

Physics-Informed Neural Networks (PINNs) are a class of deep neural networks that are trained, using automatic differentiation, to compute the response of systems governed by partial differential equations (PDEs). The training of PINNs is…

This study explores the potential of physics-informed neural networks (PINNs) for the realization of digital twins (DT) from various perspectives. First, various adaptive sampling approaches for collocation points are investigated to verify…