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Automated Scientific Discovery: From Equation Discovery to Autonomous Discovery Systems

Paper · 2023 · Stefan Kramer, Mattia Cerrato, Jannis Brugger et al.

Summary

This survey maps the field of automated scientific discovery along two strands that have so far developed largely apart. The first is the extraction of human-interpretable knowledge, mostly equations, from data. The second is automating and increasing the autonomy of the research process itself. The authors follow equation discovery and symbolic regression from the early BACON systems to grammar-guided and sparse-regression methods, and list open problems. They also examine the roles neural networks play: learning representations, guiding equation search, and serving as neural operators that give up interpretability entirely. They then turn to closed-loop systems, starting with the robot scientist Adam. Autonomy is framed with levels borrowed from self-driving cars, and the paper catalogues benchmarks and testbeds. The main conclusion is a clear gap: few systems both act autonomously and report their findings in formalisms scientists use, which would let humans steer the search. Bridging this gap is presented as necessary for the Nobel Turing Grand Challenge, which asks for AI scientists capable of Nobel-level discoveries by 2050.

Key points

  • Lineage of equation discovery:
    • BACON (built on PRISM, with versions BACON.2–5) rederived laws such as Kepler's third law by constructing new terms.
    • Lagrange learned ODEs from observational data.
    • Lagramge was the first system to constrain the search with a context-free grammar encoding domain knowledge.
    • SINDy later applied sparse regression, and SINDy-SHRED extended it to nonlinear dynamics.
  • Adam, the first robot scientist, automated hypothesis–experiment cycles in functional genomics; a third generation of robot scientists is now being developed.
  • Autonomy is graded on five levels, as in autonomous driving; level five means scientific knowledge is produced with no human intervention.
  • The paper cites Jan Zytkow's coupling of the FAHRENHEIT discovery system with real experiments as rare early work bridging both strands.
  • Benchmarks reviewed include:
    • ScienceWorld: 30 text-based tasks.
    • DiscoveryBench: over 1,000 tasks, scored with an LLM judge.
    • Open Catalyst 2020 (OC20): over a million DFT relaxations.
    • Others: Feynman, Nguyen, ChemGymRL, BoxingGym, Science-Gym, Matbench, SCP-116K and The Well. Of these, only The Well is rated fully open-ended.

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

🎓University of CambridgeCambridge · United Kingdom287 works · 125,174 citations🎓Technische Universität DarmstadtDarmstadt · Germany123 works · 36,745 citations🎓Chalmers University of TechnologyGothenburg · Sweden15 works · 3,169 citations🔬Jožef Stefan InstituteLjubljana · Slovenia18 works · 2,178 citations🔬Hessian Center for Artificial IntelligenceDarmstadt · Germany17 works · 787 citations🎓Johannes Gutenberg University MainzMainz · Germany8 works · 837 citations🎓Jožef Stefan International Postgraduate SchoolLjubljana · Slovenia12 works · 1,789 citations

 Fields, topics and concepts

📚 Shelves 4The field of science this work belongs to (OpenAlex fields).Computer Science · 19,503 worksArtificial Intelligence · 18,805 worksMaterials Science · 58 worksMaterials Chemistry · 58 works

Cite

Cite as Stefan Kramer, Mattia Cerrato, Jannis Brugger, Sašo Džeroski and Ross King. 2023. Automated Scientific Discovery: From Equation Discovery to Autonomous Discovery Systems. arXiv:2305.02251 · Machine Learning (2026) 115:109.

The paper itself, not this page. BibTeX from the library's record of the work. DOI 10.1007/s10994-025-06955-2 · arXiv 2305.02251

@misc{kramer2023automated,
  title = {{Automated Scientific Discovery: From Equation Discovery to Autonomous Discovery Systems}},
  author = {Stefan Kramer, Mattia Cerrato, Jannis Brugger, Sašo Džeroski and Ross King},
  year = {2023},
  doi = {10.1007/s10994-025-06955-2},
  eprint = {2305.02251},
  archivePrefix = {arXiv},
  url = {https://doi.org/10.1007/s10994-025-06955-2}
}

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