Related papers: Learning Without Adversarial Training: A Physics-I…

Traffic state estimation (TSE) fundamentally involves solving high-dimensional spatiotemporal partial differential equations (PDEs) governing traffic flow dynamics from limited, noisy measurements. While Physics-Informed Neural Networks…

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…

Physics-Informed Neural Networks (PINNs) present a transformative approach for smart grid modeling by integrating physical laws directly into learning frameworks, addressing critical challenges of data scarcity and physical consistency in…

Deep learning-based surrogate modeling is becoming a promising approach for learning and simulating dynamical systems. Deep-learning methods, however, find very challenging learning stiff dynamics. In this paper, we develop DAE-PINN, 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…

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) 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…

We provide an approach enabling one to employ physics-informed neural networks (PINNs) for uncertainty quantification. Our approach is applicable to systems where observations are scarce (or even lacking), these being typical situations…

We present pseudo-differential enhanced physics-informed neural networks (PINNs), an extension of gradient enhancement but in Fourier space. Gradient enhancement of PINNs dictates that the PDE residual is taken to a higher differential…

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…

This paper addresses the challenge of transient stability in power systems with missing parameters and uncertainty propagation in swing equations. We introduce a novel application of Physics-Informed Neural Networks (PINNs), specifically an…

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…

Parameter estimation remains a challenging task across many areas of engineering. Because data acquisition can often be costly, limited, or prone to inaccuracies (noise, uncertainty) it is crucial to identify sensor configurations that…

Physics-informed neural networks (PINNs) have recently received much attention due to their capabilities in solving both forward and inverse problems. For training a deep neural network associated with a PINN, one typically constructs a…

Physics-informed neural networks (PINNs) [4, 10] are an approach for solving boundary value problems based on differential equations (PDEs). The key idea of PINNs is to use a neural network to approximate the solution to the PDE and to…

The distribution system state estimation problem seeks to determine the network state from available measurements. Widely used Gauss-Newton approaches are very sensitive to the initialization and often not suitable for real-time estimation.…

Parameter estimation for differential equations from measured data is an inverse problem prevalent across quantitative sciences. Physics-Informed Neural Networks (PINNs) have emerged as effective tools for solving such problems, especially…

We demonstrate a deep learning framework capable of recovering physical parameters from the Nonlinear Schrodinger Equation (NLSE) under severe noise conditions. By integrating Physics-Informed Neural Networks (PINNs) with automatic…

Achieving clean combustion systems is crucial in terms of solving environmental impacts, decarbonization needs and sustainability matters. Traditional combustion modeling techniques via computational fluid dynamics with accurate chemical…

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…