The Utility of Physics-Informed Machine Learning in Solar Power Production Forecasting
Authors: Peter Pavlík, Franz M. Rohrhofer, Bernhard C. Geiger
Organizations: Kempelen Institute of Intelligent Technologies, Sky Park Offices, Bottova 7939/2A, Bratislava, 811 09, Slovakia · Faculty of Information Technology, Brno University of Technology, Božetěchova 2, Brno, 612 00, Czech Republic · Know Center Research GmbH, Sandgasse 34, Graz, 8010, Austria · Signal Processing and Speech Communication Laboratory, Graz University of Technology, Inffeldgasse 16c, Graz, 8010, Austria · Research Center ENERGETIC, Graz University of Technology, Rechbauerstraße 12, Graz, 8010, Austria
Physics-informed machine learning (PIML) and hybrid modeling have attracted significant attention as approaches for combining physical knowledge with the flexibility of deep learning. In this work, we investigate whether these approaches deliver their commonly claimed benefits for large-scale photovoltaic (PV) power forecasting. We develop two hybrid forecasting architectures that integrate the ADR physical PV efficiency model with the TSMixer neural forecasting architecture through feature augmentation and residual learning. The proposed models are evaluated on a dataset comprising over 3 million samples from 3,713 PV installations across 33 European countries. We assess convergence speed, forecasting accuracy, transferability across geographical regions, and data efficiency. Although the physics-informed models seem to exhibit slightly faster convergence during training, they do not achieve consistent improvements in test-set accuracy, generalization, or performance under limited training data compared to the purely data-driven baseline. These findings suggest that, for modern deep forecasting architectures trained on large datasets, explicitly incorporating the ADR physical model provides limited practical benefit for day-ahead PV forecasting.
Figures & tables
Figure 1: The map shows the geographical distribution of PV installations in the used dataset. Each dot represents one site with at least one day of production data available.
Model
Weather
History
ADR Features
ADR
✓
✗
–
TSMixer-Baseline
✓
✓
✗
TSMixer-ADRAugment
✓
✓
✓
TSMixer-ADRResidual
✓
✓
✓
Table 1: Comparison of evaluated forecasting models’ inputs.
Figure 2: Validation loss (MSE) during training for the evaluated models, averaged over ten independent training runs for each. Lines represent the mean validation loss at each training epoch, while the error bars indicate one standard deviation of the loss across the 10 runs. The horizontal axis is shown on a logarithmic scale to emphasize the convergence behavior during the initial stages of training.
Figure 3: Performance of the evaluated models across ten independent training runs. (a) Per-observation normalized MSE, (b) total daily normalized MSE, (c) per-observation denormalized MAE (W), and (d) total daily denormalized MAE (kWh). Red horizontal lines indicate medians, boxes show the interquartile range (IQR), and whiskers extend to the minimum and maximum observed values (excluding outliers beyond 1.5-times the inter-quartile range).
Figure 4: Performance of the evaluated models trained on data from different countries on Czechia test set. (a) Per-observation normalized MSE, (b) total daily normalized MSE, (c) per-observation denormalized MAE (W), and (d) total daily denormalized MAE (kWh). The country code in the label indicates a country whose train data was used to train the model (DE - Germany, CZ - Czechia, SK - Slovakia). Blue bars show the performance of the baseline TSMixer models while the brown bars show the physics-informed TSMixer-ADRResidual models.
Figure 5: Performance of the evaluated models trained on data from different countries on Slovakia test set. (a) Per-observation normalized MSE, (b) total daily normalized MSE, (c) per-observation denormalized MAE (W), and (d) total daily denormalized MAE (kWh). The country code in the label indicates a country whose train data was used to train the model (DE - Germany, CZ - Czechia, SK - Slovakia). Blue bars show the performance of the baseline TSMixer models while the brown bars show the physics-informed TSMixer-ADRResidual models.
Figure 6: Performance of the evaluated models trained on different fractions of the training dataset. (a) Per-observation normalized MSE, (b) total daily normalized MSE, (c) per-observation denormalized MAE (W), and (d) total daily denormalized MAE (kWh). For each dataset fraction, the standalone ADR model, baseline TSMixer, and physics-informed TSMixer-ADRResidual are compared.
Solar power forecasting predicts photovoltaic generation and irradiance from weather, imagery, plant data, and recent output to support reliable grid and energy decisions.
School of Economics and Management, North China Electric Power University, 102206, Beijing, China · School of Electrical and Electronic Engineering, Nanyang Technological University, 639798, 50 Nanyang Avenue, Singapore · Department of Electrical Engineering, Tsinghua University, 100084, Beijing, China
CSEM, Rue de Jaquet-Droz 1, 2002 Neuchâtel, Switzerland · Department of Electrical Engineering, École Polytechnique Fédérale de Lausanne (EPFL), Rte Cantonale, 1015 Lausanne, Switzerland.