从遥感影像中自动发现可解释的物理公式。
SatelliteFormula: Multi-Modal Symbolic Regression from Remote Sensing Imagery for Physics Discovery
- 用视觉变压器提取多光谱特征，结合物理约束优化符号表达式。
- 在多个基准数据集上表现优于现有方法，且模型更稳定、泛化性更强。
- 适合需要可解释性的环境建模研究者使用。
我们提出 SatelliteFormula，一种新型符号回归框架，能够直接从多光谱遥感影像中推导出具有物理可解释性的数学表达式。与传统的经验指数或黑箱学习模型不同，SatelliteFormula 采用基于视觉变压器的编码器提取空间-光谱特征，并引入物理引导约束以确保结果的一致性与可解释性。现有符号回归方法难以处理多光谱数据的高维复杂性；本方法通过将变压器表征融入符号优化器，在精度与物理合理性之间取得平衡。在多个基准数据集和遥感任务上的大量实验表明，该方法在性能、稳定性与泛化能力方面均优于当前最优基线。SatelliteFormula 实现了复杂环境变量的可解释建模，弥合了数据驱动学习与物理理解之间的鸿沟。
原文摘要 · Abstract (English)
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.
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