SatelliteFormula: Multi-Modal Symbolic Regression from Remote Sensing Imagery for Physics Discovery

Abstract

We propose SatelliteFormula, a novel symbolic regression framework that derives physically interpretable expressions directly from multi-spectral remote sensing imagery. Unlike traditional empirical indices or black-box learning models, SatelliteFormula combines a Vision Transformer-based encoder for spatial-spectral feature extraction with physics-guided constraints to ensure consistency and interpretability. Existing symbolic regression methods struggle with the high-dimensional complexity of multi-spectral data; our method addresses this by integrating transformer representations into a symbolic optimizer that balances accuracy and physical plausibility. Extensive experiments on benchmark datasets and remote sensing tasks demonstrate superior performance, stability, and generalization compared to state-of-the-art baselines. SatelliteFormula enables interpretable modeling of complex environmental variables, bridging the gap between data-driven learning and physical understanding.