# From Kepler to Newton: Explainable AI for Science

arXiv: https://arxiv.org/abs/2111.12210 · HTML: https://mlsanity.com/paper/2111.12210/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 60 references that are in the map.
- First posted on arXiv 24 Nov 2021.

## Builds on (most cited first, 14 of 14)

- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [Attention is not Explanation](https://mlsanity.com/paper/1902.10186/) (2019)
- [Attention is not not Explanation](https://mlsanity.com/paper/1908.04626/) (2019)
- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [The many Shapley values for model explanation](https://mlsanity.com/paper/1908.08474/) (2019)
- [Discovering Symbolic Models from Deep Learning with Inductive Biases](https://mlsanity.com/paper/2006.11287/) (2020)
- [Explainable Recommendation: A Survey and New Perspectives](https://mlsanity.com/paper/1804.11192/) (2018)
- [AI Feynman 2.0: Pareto-optimal symbolic regression exploiting graph modularity](https://mlsanity.com/paper/2006.10782/) (2020)
- [Bayesian Symbolic Regression](https://mlsanity.com/paper/1910.08892/) (2019)
- [Counterfactual Explainable Recommendation](https://mlsanity.com/paper/2108.10539/) (2021)
- [Logic Guided Genetic Algorithms](https://mlsanity.com/paper/2010.11328/) (2020)
- [Symbolic regression by uniform random global search](https://mlsanity.com/paper/1906.07848/) (2019)
- [Recreation of the Periodic Table with an Unsupervised Machine Learning Algorithm](https://mlsanity.com/paper/1912.10708/) (2019)

## Built on by (most cited first, 13 of 13)

- [Automated Scientific Discovery: From Equation Discovery to Autonomous Discovery Systems](https://mlsanity.com/paper/2305.02251/) (2023)
- [Towards Explainable Artificial Intelligence (XAI): A Data Mining Perspective](https://mlsanity.com/paper/2401.04374/) (2024)
- [Creativity in AI: Progresses and Challenges](https://mlsanity.com/paper/2410.17218/) (2024)
- [Advancing the Scientific Method with Large Language Models: From Hypothesis to Discovery](https://mlsanity.com/paper/2505.16477/) (2025)
- [Interpretability Can Be Actionable](https://mlsanity.com/paper/2605.11161/) (2026)
- [Sum-of-Parts: Self-Attributing Neural Networks with End-to-End Learning of Feature Groups](https://mlsanity.com/paper/2310.16316/) (2023)
- [AI-Newton: A Concept-Driven Physical Law Discovery System without Prior Physical Knowledge](https://mlsanity.com/paper/2504.01538/) (2025)
- [Learn Basic Skills and Reuse: Modularized Adaptive Neural Architecture Search (MANAS)](https://mlsanity.com/paper/2208.11083/) (2022)
- [ExplainableFold: Understanding AlphaFold Prediction with Explainable AI](https://mlsanity.com/paper/2301.11765/) (2023)
- [Counterfactual Collaborative Reasoning](https://mlsanity.com/paper/2307.00165/) (2023)
- [D'etection d'objets c'elestes dans des images astronomiques par IA explicable](https://mlsanity.com/paper/2311.10592/) (2023)
- [Self-explainable Operator Learning for Discovering Spatial Patterns in Functional Data](https://mlsanity.com/paper/2607.02203/) (2026)
- [Why We Care About Understanding: Competence through Predictive Compression](https://mlsanity.com/paper/2609.04962/) (2026)

## Abstract (arXiv)

The Observation--Hypothesis--Prediction--Experimentation loop paradigm for scientific research has been practiced by researchers for years towards scientific discoveries. However, with data explosion in both mega-scale and milli-scale scientific research, it has been sometimes very difficult to manually analyze the data and propose new hypotheses to drive the cycle for scientific discovery. In this paper, we discuss the role of Explainable AI in scientific discovery process by demonstrating an Explainable AI-based paradigm for science discovery. The key is to use Explainable AI to help derive data or model interpretations, hypotheses, as well as scientific discoveries or insights. We show how computational and data-intensive methodology -- together with experimental and theoretical methodology -- can be seamlessly integrated for scientific research. To demonstrate the AI-based science discovery process, and to pay our respect to some of the greatest minds in human history, we show how Kepler's laws of planetary motion and Newton's law of universal gravitation can be rediscovered by (Explainable) AI based on Tycho Brahe's astronomical observation data, whose works were leading the scientific revolution in the 16-17th century. This work also highlights the important role of Explainable AI (as compared to Blackbox AI) in science discovery to help humans prevent or better prepare for the possible technological singularity that may happen in the future, since science is not only about the know how, but also the know why. Presentation of the work is available at https://slideslive.com/38986142/from-kepler-to-newton-explainable-ai-for-science-discovery.