2023
DOI: 10.1038/s41467-023-37236-y
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Combining data and theory for derivable scientific discovery with AI-Descartes

Abstract: Scientists aim to discover meaningful formulae that accurately describe experimental data. Mathematical models of natural phenomena can be manually created from domain knowledge and fitted to data, or, in contrast, created automatically from large datasets with machine-learning algorithms. The problem of incorporating prior knowledge expressed as constraints on the functional form of a learned model has been studied before, while finding models that are consistent with prior knowledge expressed via general log… Show more

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Cited by 24 publications
(18 citation statements)
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“…An early example of this is AI-Descartes, in which a symbolic regression algorithm generates equations to match experimental data, which is then combined with an automated theorem prover to establish the equations' “derivability” with respect to a scientific theory. 33 However, in this work, each theory required human expertise to be expressed in formal language, and reliance on an automated theorem prover limited the scope of theories to those expressible in first-order logic. AI tools that can autoformalize the informal scientific literature, generate novel theories, and auto-complete complex proofs could open new avenues for automating theory discovery.…”
Section: Discussionmentioning
confidence: 99%
See 1 more Smart Citation
“…An early example of this is AI-Descartes, in which a symbolic regression algorithm generates equations to match experimental data, which is then combined with an automated theorem prover to establish the equations' “derivability” with respect to a scientific theory. 33 However, in this work, each theory required human expertise to be expressed in formal language, and reliance on an automated theorem prover limited the scope of theories to those expressible in first-order logic. AI tools that can autoformalize the informal scientific literature, generate novel theories, and auto-complete complex proofs could open new avenues for automating theory discovery.…”
Section: Discussionmentioning
confidence: 99%
“…Artificial intelligence tools for scientific discovery have also used theorem provers in designing optical quantum experiments, 32 as well as for rediscovering and deriving scientific equations from data and background theory. 33…”
Section: Introductionmentioning
confidence: 99%
“…16 The theory-infused neural network (TinNet) exhibits emergent behaviors in interpretability, whereas it is fundamentally limited in generalizability of the underlying neural network architectures, especially with out-of-distribution samples. Imposing constraints or scientific rules through other means, e.g., physics-inspired graph kernels, 15 symbolic regression with logical reasoning, 59 might provide improved accuracy while attaining interpretability.…”
Section: Conclusion and Perspectivementioning
confidence: 99%
“…Incorporating adequate prior knowledge is critical for developing generalizable deep learning models in data-deficient scientific problems 1 – 3 . The domain-specific prior knowledge of a particular task can help a model featurize generalizable patterns across its training data, leading to noteworthy successes 4 7 . For instance, AlphaFold2 8 utilized the co-evolutionary information to narrow down the extensive conformational space of protein folding on a macroscopic scale and the residue pair representation to reduce the structural complexity on a microscopic scale.…”
Section: Introductionmentioning
confidence: 99%