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arXiv:1905.11481physics.comp-ph

AI Feynman: a Physics-Inspired Method for Symbolic Regression

Silviu-Marian Udrescu, Max Tegmark

Abstract

A core challenge for both physics and artificial intellicence (AI) is symbolic regression: finding a symbolic expression that matches data from an unknown function. Although this problem is likely to be NP-hard in principle, functions of practical interest often exhibit symmetries, separability, compositionality and other simplifying properties. In this spirit, we develop a recursive multidimensional symbolic regression algorithm that combines neural network fitting with a suite of physics-inspired techniques. We apply it to 100 equations from the Feynman Lectures on Physics, and it discovers all of them, while previous publicly available software cracks only 71; for a more difficult test set, we improve the state of the art success rate from 15% to 90%.

arXiv comments
15 pages, 2 figs. Our code is available at https://github.com/SJ001/AI-Feynman and our Feynman Symbolic Regression Database for benchmarking can be downloaded at https://space.mit.edu/home/tegmark/aifeynman.html
Journal reference
Science Advances, 6:eaay2631, April 15, 2020
DOI
Subjects
physics.comp-phComputational Physics cs.AIArtificial Intelligence cs.LGMachine Learning hep-thHigh Energy Physics, Theory

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Linked by 3 identifiable commenters in 3 comments across 3 threads, from Nov 2019 to Apr 2026. Found in 4 HN submissions from May 2019 to Nov 2025. Open submission discussions.

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Discussed in comments3 threads

  1. All elementary functions from a single binary operator 1 comment

    • Yes, metamath uses a large collection of specialized but reusable building blocks, so it doesn't blow up exponentially. However, if you want to "just do gradient descent" on general trees built from a single universal primitive, you now have to rediscover all those building…

      yorwbaView on HNParent context

  2. DALL-E 2 generates images of Kermit The Frog in various films 1 comment

    • Indeed: • https://news.ycombinator.com/item?id=31609839 • https://arxiv.org/pdf/1810.10525.pdf • https://arxiv.org/pdf/1905.11481.pdf

      ben_wView on HNParent context

  3. The revolution of machine learning has been exaggerated 1 comment

    • This is exactly it. Earlier this year there was a hyped up paper [0] going around claiming that they could derive physics with AI. On inspection I found that what they actually did was this: 1. Take one simple physics equation, such as F = ma 2. Generate 10^6 tuples exactly…

      knzhouView on HNParent context

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