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Physics-informed neural networks (PINNs) are one popular approach to incorporate a priori knowledge about physical systems into the learning framework. PINNs are known to be robust for smaller training sets, derive better generalization…

Physics-informed neural networks (PINNs) provide a promising framework for solving inverse problems governed by partial differential equations (PDEs) by integrating observational data and physical constraints in a unified optimization…

Stiff differential equations are prevalent in various scientific domains, posing significant challenges due to the disparate time scales of their components. As computational power grows, physics-informed neural networks (PINNs) have led to…

The paper presents an efficient and robust data-driven deep learning (DL) computational framework developed for linear continuum elasticity problems. The methodology is based on the fundamentals of the Physics Informed Neural Networks…

Quantifying and propagating modeling uncertainties is crucial for reliability analysis, robust optimization, and other model-based algorithmic processes in engineering design and control. Now, physics-informed machine learning (PIML)…

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…

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…

Partial differential equations (PDEs) form the backbone of simulations of many natural phenomena, for example in climate modeling, material science, and even financial markets. The application of physics-informed neural networks to…

Effective inclusion of physics-based knowledge into deep neural network models of dynamical systems can greatly improve data efficiency and generalization. Such a-priori knowledge might arise from physical principles (e.g., conservation…

This paper presents a PINN training framework that employs (1) pre-training steps that accelerates and improve the robustness of the training of physics-informed neural network with auxiliary data stored in point clouds, (2) a net-to-net…

Physics-informed neural networks (PINNs) are a new tool for solving boundary value problems by defining loss functions of neural networks based on governing equations, boundary conditions, and initial conditions. Recent investigations have…

This paper presents a physics-informed neural network approach for dynamic modeling of saturable synchronous machines, including cases with spatial harmonics. We introduce an architecture that incorporates gradient networks directly into…

The integration of physics-based knowledge with machine learning models is increasingly shaping the monitoring, diagnostics, and prognostics of electrical transformers. In this two-part series, the first paper introduced the foundations of…

Physically informed neural networks (PINNs) are a promising emerging method for solving differential equations. As in many other deep learning approaches, the choice of PINN design and training protocol requires careful craftsmanship. Here,…

This work presents a two-stage adaptive framework for progressively developing deep neural network (DNN) architectures that generalize well for a given training data set. In the first stage, a layerwise training approach is adopted where a…

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…

We characterize and remedy a failure mode that may arise from multi-scale dynamics with scale imbalances during training of deep neural networks, such as Physics Informed Neural Networks (PINNs). PINNs are popular machine-learning templates…

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,…

We develop improved physics-informed neural networks (PINNs) for high-order and high-dimensional power system models described by nonlinear ordinary differential equations. We propose some novel enhancements to improve PINN training and…

Physics-informed neural networks (PINNs) are numerical solvers that embed all the physical information of a system into the loss function of a neural network. In this way the learned solution accounts for data (if available), the governing…