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Physics-informed neural networks (PINNs) have emerged as a powerful tool for solving inverse problems, especially in cases where no complete information about the system is known and scatter measurements are available. This is especially…

The application of deep learning methods to speed up the resolution of challenging power flow problems has recently shown very encouraging results. However, power system dynamics are not snap-shot, steady-state operations. These dynamics…

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…

Deep learning has been shown to be an effective tool in solving partial differential equations (PDEs) through physics-informed neural networks (PINNs). PINNs embed the PDE residual into the loss function of the neural network, and have been…

Physics-informed neural networks (PINNs) [31] use automatic differentiation to solve partial differential equations (PDEs) by penalizing the PDE in the loss function at a random set of points in the domain of interest. Here, we develop a…

Inverse problems arise across scientific and engineering domains, where the goal is to infer hidden parameters or physical fields from indirect and noisy observations. Classical approaches, such as variational regularization and Bayesian…

Compared to physics-based computational manufacturing, data-driven models such as machine learning (ML) are alternative approaches to achieve smart manufacturing. However, the data-driven ML's "black box" nature has presented a challenge to…

Physics-informed neural networks (PINNs) have emerged as a new learning paradigm for solving partial differential equations (PDEs) by enforcing the constraints of physical equations, boundary conditions (BCs), and initial conditions (ICs)…

Accurate vessel trajectory prediction is crucial for navigational safety, route optimization, traffic management, search and rescue operations, and autonomous navigation. Traditional data-driven models lack real-world physical constraints,…

Physics-informed neural networks (PINNs) are an increasingly powerful way to solve partial differential equations, generate digital twins, and create neural surrogates of physical models. In this manuscript we detail the inner workings of…

The identification of material parameters occurring in constitutive models has a wide range of applications in practice. One of these applications is the monitoring and assessment of the actual condition of infrastructure buildings, as the…

Physics-Informed Neural Networks (PINN) are neural networks (NNs) that encode model equations, like Partial Differential Equations (PDE), as a component of the neural network itself. PINNs are nowadays used to solve PDEs, fractional…

Physics-informed neural networks (PINNs) impose known physical laws into the learning of deep neural networks, making sure they respect the physics of the process while decreasing the demand of labeled data. For systems represented by…

The effectiveness of the Physics Informed Neural Networks (PINNs) for learning the dynamics of constrained Hamiltonian systems is demonstrated using the Dirac theory of constraints for regular systems with holonomic constraints and systems…

Many physical systems are described by partial differential equations (PDEs), and solving these equations and estimating their coefficients or boundary conditions (BCs) from observational data play a crucial role in understanding the…

The numerical approximation of partial differential equations (PDEs) using neural networks has seen significant advancements through Physics-Informed Neural Networks (PINNs). Despite their straightforward optimization framework and…

Modeled Reynolds stress is a major source of model-form uncertainties in Reynolds-averaged Navier-Stokes (RANS) simulations. Recently, a physics-informed machine-learning (PIML) approach has been proposed for reconstructing the…

Deep learning has been highly successful in some applications. Nevertheless, its use for solving partial differential equations (PDEs) has only been of recent interest with current state-of-the-art machine learning libraries, e.g.,…

As a typical application of deep learning, physics-informed neural network (PINN) {has been} successfully used to find numerical solutions of partial differential equations (PDEs), but how to improve the limited accuracy is still a great…

Physics-informed neural networks (PINN) is a machine learning (ML)-based method to solve partial differential equations that has gained great popularity due to the fast development of ML libraries in the last few years. The…