Two-stage residual learning for calibrated uncertainty in solar irradiance forecasts

Accurate forecasting of renewable generation requires not only point predictions but also reliable estimates of the uncertainty attached to them, particularly at extended horizons. Machine learning models are increasingly used to predict solar output, but they typically report a single value and capture the associated uncertainty poorly. The standard remedy is to train a model to predict the parameters of an assumed probability distribution directly. Here we develop an alternative two-stage method, motivated by synthetic solar signal generation, in which the forecast error is modeled separately from the expected irradiance. A first long short-term memory (LSTM) network predicts the expected global horizontal irradiance, and a second network models the distribution of the forecast error, which is added back to the mean to give both the forecast and its uncertainty. Using historical weather data from the National Solar Radiation Database and a probability integral transform evaluation, we show that explicitly modeling the error brings the predicted standard deviation markedly closer to the historical value, reducing the deviation between the two by 34.6 percent for a standalone LSTM and by 56.5 percent when the LSTM is coupled to Gaussian process regression, the most reliable of the configurations tested. Because the method models the total forecast error directly, it captures the full predictive uncertainty that matters for decisions, rather than only the model contribution that dropout-based approaches estimate.