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

arXiv: https://arxiv.org/abs/2506.06176 · HTML: https://mlsanity.com/paper/2506.06176/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 53 references that are in the map.
- First posted on arXiv 6 Jun 2025.

## Builds on (most cited first, 24 of 24)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [Multimodal Learning with Transformers: A Survey](https://mlsanity.com/paper/2206.06488/) (2022)
- [End-to-end symbolic regression with transformers](https://mlsanity.com/paper/2204.10532/) (2022)
- [Neural Symbolic Regression that Scales](https://mlsanity.com/paper/2106.06427/) (2021)
- [SymbolicGPT: A Generative Transformer Model for Symbolic Regression](https://mlsanity.com/paper/2106.14131/) (2021)
- [Interpretable Scientific Discovery with Symbolic Regression: A Review](https://mlsanity.com/paper/2211.10873/) (2022)
- [Vision-Language Models in Remote Sensing: Current Progress and Future Trends](https://mlsanity.com/paper/2305.05726/) (2023)
- [Transformer-based Planning for Symbolic Regression](https://mlsanity.com/paper/2303.06833/) (2023)
- [A Survey on Object Detection in Optical Remote Sensing Images](https://mlsanity.com/paper/1603.06201/) (2016)
- [SymFormer: End-to-end symbolic regression using transformer-based architecture](https://mlsanity.com/paper/2205.15764/) (2022)
- [EarthVQA: Towards Queryable Earth via Relational Reasoning-Based Remote Sensing Visual Question Answering](https://mlsanity.com/paper/2312.12222/) (2023)
- [A Survey on Neural-symbolic Learning Systems](https://mlsanity.com/paper/2111.08164/) (2021)
- [Discovering a reaction-diffusion model for Alzheimer's disease by combining PINNs with symbolic regression](https://mlsanity.com/paper/2307.08107/) (2023)
- [MMSR: Symbolic Regression is a Multi-Modal Information Fusion Task](https://mlsanity.com/paper/2402.18603/) (2024)
- [Who is Responsible? The Data, Models, Users or Regulations? A Comprehensive Survey on Responsible Generative AI for a Sustainable Future](https://mlsanity.com/paper/2502.08650/) (2025)
- [A Diffusion-Based Framework for Terrain-Aware Remote Sensing Image Reconstruction](https://mlsanity.com/paper/2504.12112/) (2025)
- [Rainy: Unlocking Satellite Calibration for Deep Learning in Precipitation](https://mlsanity.com/paper/2504.10776/) (2025)
- [SatelliteCalculator: A Multi-Task Vision Foundation Model for Quantitative Remote Sensing Inversion](https://mlsanity.com/paper/2504.13442/) (2025)
- [Interpretable Multimodal Learning for Tumor Protein-Metal Binding: Progress, Challenges, and Perspectives](https://mlsanity.com/paper/2504.03847/) (2025)
- [DanceText: A Training-Free Layered Framework for Controllable Multilingual Text Transformation in Images](https://mlsanity.com/paper/2504.14108/) (2025)

## Built on by (most cited first, 3 of 3)

- [From Physics to Foundation Models: A Review of AI-Driven Quantitative Remote Sensing Inversion](https://mlsanity.com/paper/2507.09081/) (2025)
- [Multi-Modal Machine Learning Framework for Predicting Early Recurrence of Brain Tumors Using MRI and Clinical Biomarkers](https://mlsanity.com/paper/2509.01161/) (2025)
- [A Multimodal Deep Learning Framework for Early Diagnosis of Liver Cancer via Optimized BiLSTM-AM-VMD Architecture](https://mlsanity.com/paper/2509.01164/) (2025)

## Abstract (arXiv)

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.