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

2025-06-06

AI Summary

Existing symbolic regression methods for physical modeling of multispectral remote sensing imagery suffer from poor interpretability of empirical indices, lack of transparency in black-box models, and inability to handle high-dimensional spectral data. Method: This paper proposes a physics-guided, Vision Transformer (ViT)-enhanced symbolic regression framework. It innovatively integrates a ViT encoder into the symbolic optimization pipeline to jointly model spectral-spatial multimodal features, while incorporating physics-based constraints to co-optimize both expression accuracy and physical plausibility. Results: Experiments across multiple remote sensing benchmark tasks demonstrate significant improvements over state-of-the-art methods. The framework consistently discovers interpretable, physically meaningful expressions—for instance, for chlorophyll content and land surface temperature—while enhancing cross-scene generalization and modeling robustness. This work establishes a novel, interpretable, and verifiable paradigm for physics-driven discovery in remote sensing.

Technology Category

• Computer Vision: Visual Reasoning & Symbolic Representations
• Cognitive Modeling & Cognitive Systems: Symbolic Representations
• Intelligent Robots: Multimodal Perception & Sensor Fusion

Application Category

• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs

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.

Problem

• Derives interpretable physics expressions from multi-spectral imagery
• Addresses high-dimensional complexity in symbolic regression
• Bridges data-driven learning with physical understanding

Innovation

• Multi-modal symbolic regression from remote sensing
• Vision Transformer encoder for feature extraction
• Physics-guided constraints for interpretable expressions