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This manuscript presents a complete framework for the development and verification of physics-informed neural networks with application to the alternating-current power flow (ACPF) equations. Physics-informed neural networks (PINN)s have received considerable interest within power systems communities for their ability to harness underlying physical equations to produce simple neural network architectures that achieve high accuracy using limited training data. The methodology developed in this work builds on existing methods and explores new important aspects around the implementation of PINNs including: (i) obtaining operationally relevant training data, (ii) efficiently training PINNs and using pruning techniques to reduce their complexity, and (iii) globally verifying the worst-case predictions given known physical constraints. The methodology is applied to the IEEE-14 and 118 bus systems where PINNs show substantially improved accuracy in a data-limited setting and attain better guarantees with respect to worst-case predictions. • An end-to-end framework to design, train, and validate scalable PINNs is proposed. • We formally validate the performance advantages of PINNs over traditional NNs. • We demonstrate this framework on the AC power flow problem for grid operations. [ABSTRACT FROM AUTHOR]

• Deep Neural Networks applied to estimate solar panel size, tilt and azimuth. • Solar panel size estimate with mean percentage error of 3.98%. • Tilt and azimuth estimated with absolute error of 2.55 and 4.71 degrees respectively. • Net load data resolution does not heavily impact accuracy. • Proposed approach is robust to mislabeled training data. There is an ever-growing number of photovoltaic (PV) installations in the US and worldwide. Many utilities do not have complete or up-to-date information of the PVs present within their grids. This research presents a deep neural network approach for estimating PV size, tilt, and azimuth using only behind-the-meter data. It is found that the proposed deep neural network (DNN) method can estimate PV size with an error of 2.09% in a data set with fixed tilt and azimuth values and 3.98% in a data set with varying tilt and azimuths. This is a lower error than the benchmark linear regression approach. A net load data resolution of 1 min provides the lowest error when estimating the PV size. The proposed DNN is also reasonably robust to erroneous training data. When applied to estimate PV tilt and azimuth, the proposed method achieves a mean absolute percentage error of 10.1% and 2.8% respectively. These error metrics are 2.0 × and 3.7 × lower, respectively, than the benchmark linear regression achieves. It was observed that a higher data resolution (1 min) does not provide significant gains in accuracy. It is recommended that a data resolution of 60 min is used to reduce the effects of phenomena such as cloud enhancements. The proposed deep neural network approach is also highly robust, maintaining reasonable accuracy with high levels of mislabeled training data. [ABSTRACT FROM AUTHOR]

• Strengths and limits of modeling frameworks merging first-principles and data are evaluated. • Hybrid first-principles, data-driven methods generally outperform purely data-driven models. • Recent advances in gradient evaluation and sampling methods have led to mature software implementations of hybrid modeling (HM) frameworks. • Care should be taken when extrapolating/interpreting data-driven component of HMs. • An assessment is given for improving current methods through uncertainty quantification, constraint handling and open-source publication of novel hybrid implementations. Efficiently embedding and/or integrating mechanistic information with data-driven models is essential if it is desired to simultaneously take advantage of both engineering principles and data-science. The opportunity for hybridization occurs in many scenarios, such as the development of a faster model of an accurate high-fidelity computer model; the correction of a mechanistic model that does not fully-capture the physical phenomena of the system; or the integration of a data-driven component approximating an unknown correlation within a mechanistic model. At the same time, different techniques have been proposed and applied in different literatures to achieve this hybridization, such as hybrid modeling, physics-informed Machine Learning (ML) and model calibration. In this paper we review the methods, challenges, applications and algorithms of these three research areas and discuss them in the context of the different hybridization scenarios. Moreover, we provide a comprehensive comparison of the hybridization techniques with respect to their differences and similarities, as well as advantages and limitations and future perspectives. Finally, we apply and illustrate hybrid modeling, physics-informed ML and model calibration via a chemical reactor case study. [ABSTRACT FROM AUTHOR]