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      "statement": "# AI Feynman: use learned structure to turn formula search into smaller problems\n\nUdrescu and Tegmark combine neural-network interpolation with dimensional analysis, symmetry and separability tests, polynomial fitting and symbolic search to recover known physics formulas from generated numerical data.\n\nA table of measurements can fit many different formulas. AI Feynman searches for an understandable symbolic expression by first looking for structure. Known physical units reduce the number of variables; a trained neural network helps test whether variables can be combined or whether the function separates into smaller pieces. Polynomial fitting or symbolic search then solves the reduced problems. The authors report recovering all 100 selected Feynman formulas, and 18 of 20 more difficult formulas selected after the method was finalized. They explicitly call the first 100 a training set for their algorithm and settings. Success is checked against the known answer by symbolic simplification, rather than numerical fit alone. These experiments demonstrate automated recovery of known equations under the chosen data and search assumptions. They do not report a previously unknown physical law, and a good fit on finitely many samples is not a general proof of the recovered formula.\n\n## Scientific scope\n\nOriginal 2019 preprint and AI Feynman 2.0 are separate versions/works. Physics-generated known algebraic functions,1-9 variables; derivatives/integrals excluded. Samples generally uniform 1-5 with adjusted physical domains; units optionally supplied. First 100 equations were used to tune implementation/hyperparameters;20 bonus equations held out until finalization. Reported 100/100 and 18/20 are author results, not WRS replay. Eureqa baseline is 71% in abstract/results but 68% in conclusion: unresolved discrepancy, no single verified baseline asserted. Table timings omit earlier alphabet-search hours in four cases; budgets are not a uniform total-runtime comparison. Neural symmetry/separability tests use empirical error thresholds, not global identity proofs. Scoring uses simplification against known formulas; domains/branches still matter. Noise tested in dependent outputs, with threshold changes; independent-variable noise/real measurements remain future work. Mc Dermott subset report 66.7%vs 48.9% is separate. Two bonus failures and feature/grammar dependencies retained. No unknown-law discovery, polynomial-time solver or model/provider correctness guarantee. April 15 manuscript vs April 17 publisher print date retained.\n\n## People and systems\n\nSilviu-Marian Udrescu; Max Tegmark\n\n\n\n## Original sources\n\n- [Udrescu and Tegmark, AI Feynman; exact arXiv1905.11481v2 author manuscript](https://arxiv.org/pdf/1905.11481v2)\n- [Publisher-deposited identity of the exact2020 AI Feynman paper](https://api.crossref.org/works/10.1126%2Fsciadv.aay2631)\n",
      "summary": "Udrescu and Tegmark combine neural-network interpolation with dimensional analysis, symmetry and separability tests, polynomial fitting and symbolic search to recover known physics formulas from generated numerical data.\n\nA table of measurements can fit many different formulas. AI Feynman searches for an understandable symbolic expression by first looking for structure. Known physical units reduce the number of variables; a trained neural network helps test whether variables can be combined or whether the function separates into smaller pieces. Polynomial fitting or symbolic search then solves the reduced problems. The authors report recovering all 100 selected Feynman formulas, and 18 of 20 more difficult formulas selected after the method was finalized. They explicitly call the first 100 a training set for their algorithm and settings. Success is checked against the known answer by symbolic simplification, rather than numerical fit alone. These experiments demonstrate automated recovery of known equations under the chosen data and search assumptions. They do not report a previously unknown physical law, and a good fit on finitely many samples is not a general proof of the recovered formula.",
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