---
title: "AI Feynman: a Physics-Inspired Method for Symbolic Regression"
description: "Udrescu and Tegmark argue that formulas from physics are rarely generic. Cited by 34 papers here."
authors: ["Silviu-Marian Udrescu", "Max Tegmark"]
year: 2019
venue: "arXiv:1905.11481 · Science Advances, 6:eaay2631, April 15, 2020"
source: "https://arxiv.org/abs/1905.11481"
doi: "10.48550/arxiv.1905.11481"
arxiv: "1905.11481"
licence: "arXiv non-exclusive distribution license"
licence_url: "http://arxiv.org/licenses/nonexclusive-distrib/1.0/"
summary_licence: "Elamur Cosmic License"
canonical: "https://research.elamur.ai/free/en/papers/udrescu-2019-ai-feynman-physics-inspired/"
---
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# AI Feynman: a Physics-Inspired Method for Symbolic Regression

**Authors:** Silviu-Marian Udrescu and [Max Tegmark](https://md.research.elamur.ai/free/en/authors/max-tegmark/) · **Year:** 2019 · **Venue:** arXiv:1905.11481 · Science Advances, 6:eaay2631, April 15, 2020 · **Publisher:** [American Association for the Advancement of Science](https://md.research.elamur.ai/free/en/publishers/american-association-for-the-advancement-of-science/) · **Licence:** [arXiv non-exclusive distribution license](http://arxiv.org/licenses/nonexclusive-distrib/1.0/)

**Links:** [Publisher's page](https://arxiv.org/abs/1905.11481) · [PDF](https://arxiv.org/pdf/1905.11481) · [DOI 10.48550/arxiv.1905.11481](https://doi.org/10.48550/arxiv.1905.11481) · [arXiv 1905.11481](https://arxiv.org/abs/1905.11481) · [OpenAlex](https://openalex.org/W2947630964)

**Citations:** 1,080 citations (OpenAlex, 2026-10-14) · [34](https://md.research.elamur.ai/free/en/papers/udrescu-2019-ai-feynman-physics-inspired/cited-by/) in our library, of the 149,439 papers whose bibliographies we read

## Summary
Symbolic regression means recovering an exact closed-form formula from a table of input–output values. It is likely NP-hard in general because the space of candidate expressions grows exponentially. Udrescu and Tegmark argue that formulas from physics are rarely generic. They usually have known units, low-order polynomial parts, compositional structure, smoothness, symmetries and separability. Their algorithm, AI Feynman, exploits these properties through a set of modules applied recursively:

- dimensional analysis
- polynomial fitting
- brute-force search over expressions
- a neural network fitted to the data, which serves as a probe for translational symmetry and additive or multiplicative separability

When such structure is found, the problem is split into smaller sub-problems with fewer variables, and each is solved by a fresh run of the same procedure. On 100 equations taken from the Feynman Lectures on Physics, the method recovers every one, while the strongest earlier tool (Eureqa) solves 71. On a harder set of physics formulas, the success rate rises from 15% to 90%. The work shows that combining neural fitting with physics-style simplification can make automated equation discovery practical.

## Key points
- **Benchmark results:** all 100 Feynman Lectures equations were solved, against 71 for Eureqa, a commercial genetic-algorithm tool. On a more difficult physics test set, the success rate went from 15% to 90%.
- **Dimensional analysis:** each variable's units are encoded as a vector of 5 integer exponents (meter, second, kilogram, kelvin, volt). Solving a linear system then yields dimensionless variables, which reduces how many inputs remain.
- **Polynomial and brute-force modules:**
  - Polynomials of degree 0 to 4 are fitted by linear least squares.
  - The brute-force search enumerates syntactically valid expressions in reverse Polish notation, from shortest to longest.
- **Worked example:** for Newton's gravitation law with 9 inputs, the method reduces the problem to 6 dimensionless variables. It then detects two translational symmetries and a multiplicative factorization, and finishes with polynomial fits.
- **Code:** the implementation is openly available at github.com/SJ001/AI-Feynman.

*Our summary of the paper, in our own words — not its text. The work belongs to its authors; read it at the links above.*

## Institutions

- [Massachusetts Institute of Technology](https://md.research.elamur.ai/free/en/universities/massachusetts-institute-of-technology/) — University, Cambridge, United States · 274 works · 82,013 citations

Also on the byline: [Theiss Research](https://ror.org/00scjnx30).

📚 Shelves (4): [🖥️ Computer Science](https://md.research.elamur.ai/free/en/shelves/computer-science/) · 19,503 works · [🤖 Artificial Intelligence](https://md.research.elamur.ai/free/en/shelves/computer-science/artificial-intelligence/) · 18,805 works · [⚛️ Physics and Astronomy](https://md.research.elamur.ai/free/en/shelves/physics-and-astronomy/) · 70 works · [⚛️ Statistical and Nonlinear Physics](https://md.research.elamur.ai/free/en/shelves/physics-and-astronomy/statistical-and-nonlinear-physics/) · 60 works

## Cite

Cite as: Silviu-Marian Udrescu and Max Tegmark. 2019. AI Feynman: a Physics-Inspired Method for Symbolic Regression. arXiv:1905.11481 · Science Advances, 6:eaay2631, April 15, 2020.

The paper itself, not this page. BibTeX from the library's record of the work.

```bibtex
@misc{udrescu2019ai,
  title = {{AI Feynman: a Physics-Inspired Method for Symbolic Regression}},
  author = {Silviu-Marian Udrescu and Max Tegmark},
  year = {2019},
  doi = {10.48550/arxiv.1905.11481},
  eprint = {1905.11481},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.48550/arxiv.1905.11481}
}
```

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