Accurate forecasting of photovoltaic (PV) power production is crucial for the integration of more renewable energy sources into the power grid. PV power production is highly intermittent, due to the stochastic cloud behaviour and cloud dynamics. Previous works focused on predicting the dynamics by combining inputs from ground-based cameras, satellite images and numerical weather predictions with physical or statistical models. However, they are costly or have coarse resolution. The focus of this thesis is to advance the state-of-the-art on short-term solar resources forecasting. We take past PV power from a dense network of PV stations as the main input for forecasting. We leverage a graph signal processing perspective and model multi-site PV production data as signals on a graph to capture their spatio-temporal dependencies and achieve higher spatial and temporal resolution forecasts. In our first contribution two graph neural networks, based on graph convolutional layers to exploit the spatial information, are proposed for deterministic multi-site PV forecasting: the graph-convolutional long short-term memory (GCLSTM) and the graph-convolutional transformer (GCTrafo). These methods rely only on production data and exploit the intuition that PV systems provide a network of virtual weather stations. We show that the proposed models outperform state-of-the-art methods for intra-day forecasting with high spatial and temporal resolution. However, they are difficult to interpret. Utility operators and grid managers could use insights derived from interpretable models to make more informed decisions. Therefore, we introduce a novel interpretable temporal-spatial multi-windows graph attention network (TSM-GAT) for predicting future PV power. TSM-GAT captures different dynamical spatio-temporal correlations for different parts of the forecasting horizon. Thus, it is possible to interpret which PV stations have the most influence when making a prediction for short-, medium- and long-term intra-day forecasts. We show that the proposed model outperforms multi-site state-of-the-art models for four to six hours ahead predictions and that it yields predicted signals with a closer shape to ground truth. Although machine learning models for PV production achieve high resolution forecasts without loss in accuracy using only PV power data, they are often black box models, leading to overly smoothed predictions. These models might overlook the impact of variable weather conditions on PV power, indicating the model cannot fully capture cloud dynamics. Since physically informed neural networks have shown great success when modelling physical phenomena, we introduce a physics-informed graph neural network (PING) for forecasting the future concentrations in the advection-diffusion processes on an irregular grid. PING captures the dynamics by estimating historical velocities. It outperforms baseline models for forecasting cloud concentration index and when combined with GCLSTM outperforms baselines for forecasting PV production. In this thesis, we introduce state-of-the-art models for high resolution and interpretable PV power production forecasts. Even though the accuracy of the physics-informed model is not better than state of the art, it provides insight into the physical behaviour of the cloud dynamics. This insight into cloud dynamics holds potential for future integration with deep learning models to further enhance forecasting capabilities.