2D Time-varying functional modeling framework for multi-scale solar irradiance forecasting

Considering the inherent multi-scale nature of solar irradiance data is essential for accurate long-term forecasting. However, when temporal dynamics at multiple scales are represented in 1D space, critical time dependencies become deeply obscured, making them difficult to capture with existing methods. To overcome the limitations of 1D representations, this paper introduces a novel 2D Time-Varying Function Modeling (2D-TFM) framework that transforms 1D time series into functional sequences, enabling the modeling of time-varying patterns across different scales in 2D space. This transformation leverages B-spline basis function expansion, which is optimized through our Adaptive Local Complexity (ALC) knot placement algorithm to enhance functional representation. Our framework incorporates a functional Long Short-Term Memory (LSTM) network to learn the mappings between function sequences in parameter spaces, facilitating segment-wise operations. Comprehensive benchmark experiments demonstrate that our proposed 2D-TFM outperforms existing methods, effectively capturing both short-term fluctuations and long-term trends, achieving superior forecasting accuracy, computational efficiency, and interpretability. For hourly forecasts, our model reduces RMSE by 13.8 % and MAPE by 21.8 % compared to Seq2Seq-LSTM, whereas for minutely forecasts, it reduces RMSE by 7.6 % and MAPE by 21.1 % compared to Seq2Seq-LSTM. Furthermore, our framework provides mesh-free predictions at arbitrary time resolutions through a single trained model, enhancing the practical applicability of solar irradiance prediction in energy management systems.