Estimating narrowband solar irradiance with physically constrained multi-output neural network

Solar narrowband irradiance data, although necessary in solar energy engineering and applications, are scarce due to its high-cost measurement. To obtain such data indirectly, building models with machine learning (ML) methods is recognized as an effective and practical approach. Considering the need for the irradiance data across multiple bands in certain scenarios, along with the importance of improving physical consistency of ML models, a physically constrained multi-output neural network is developed in this study. The model is based on shared bottom structure, with a specialized constraint layer added to ensure the estimations satisfy a simple physical inequality. Compared to several conventional single-output ML methods, the proposed model shows the best overall performance on the test set with a normalized root mean square error, normalized mean absolute error and R2 averaged across all target variables being 2.8970%, 1.7301% and 0.9975, slightly superior to XGBoost, one of the powerful and popular methods on related tasks, of which the corresponding metrics being 2.9358%, 1.7568% and 0.9975, respectively.