Comprehensive and Comparative Analysis of GAM-Based PV Power Forecasting Models Using Multidimensional Tensor Product Splines against Machine Learning Techniques

In recent years, as photovoltaic (PV) power generation has rapidly increased on a global scale, there is a growing need for a highly accurate power generation forecasting model that is easy to implement for a wide range of electric utilities. Against this background, this study proposes a PV power forecasting model based on the generalized additive model (GAM) and compares its forecasting accuracy with four popular machine learning methods: k-nearest neighbor, artificial neural networks, support vector regression, and random forest. The empirical analysis provides an intuitive interpretation of the multidimensional smooth trends estimated by the GAM as tensor product splines and confirms the validity of the proposed modeling structure. The effectiveness of GAM is particularly evident in trend completion for missing data, where it is able to flexibly express the tangled trend structure inherent in time series data, and thus has an advantage not only in interpretability but also in improving forecast accuracy.

On particles and splines in bounded domains

We propose numerical schemes that enable the application of particle methods for advection problems in general bounded domains. These schemes combine particle fields with Cartesian tensor product splines and a fictitious domain approach. Their implementation only requires a fitted mesh of the domain's boundary, and not the domain itself, where an unfitted Cartesian grid is used. We establish the stability and consistency of these schemes in $W^{s,p}$-norms, $s\in\mathbb{R}$, $1\leq p\leq\infty$.