A Bayesian machine scientist to aid in the solution of challenging scientific problems

Abstract

Closed-form, interpretable mathematical models have been instrumental for advancing our understanding of the world; with the data revolution, we may now be in a position to uncover new such models for many systems from physics to the social sciences. However, to deal with increasing amounts of data, we need "machine scientists" that are able to extract these models automatically from data. Here, we introduce a Bayesian machine scientist, which establishes the plausibility of models using explicit approximations to the exact marginal posterior over models and establishes its prior expectations about models by learning from a large empirical corpus of mathematical expressions. It explores the space of models using Markov chain Monte Carlo. We show that this approach uncovers accurate models for synthetic and real data and provides out-of-sample predictions that are more accurate than those of existing approaches and of other nonparametric methods.

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Cited by in corpus (27)

• Discovering Symbolic Models from Deep Learning with Inductive Biases
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• Probabilistic Grammars for Equation Discovery
• SINDy for delay-differential equations: application to model bacterial zinc response
• Human mobility is well described by closed-form gravity-like models learned automatically from data
• Percolation on feature-enriched interconnected systems
• Fundamental limits to learning closed-form mathematical models from data
• Catch-22s of reservoir computing
• Augmenting astrophysical scaling relations with machine learning: application to reducing the Sunyaev-Zeldovich flux-mass scatter
• Evolving Scientific Discovery by Unifying Data and Background Knowledge with AI Hilbert
• Efficient Generator of Mathematical Expressions for Symbolic Regression
• Priors for symbolic regression
• Is the Machine Smarter than the Theorist: Deriving Formulas for Particle Kinematics with Symbolic Regression
• Optimal Inflationary Potentials
• Bayesian machine scientist to compare data collapses for the Nikuradse dataset
• The Inefficiency of Genetic Programming for Symbolic Regression
• Using machine learning to find exact analytic solutions to analytically posed physics problems
• From reductionism to realism: Holistic mathematical modelling for complex biological systems
• Discovering Symmetries of ODEs by Symbolic Regression
• Dimension Reduction for Symbolic Regression
• KAN-SR: A Kolmogorov-Arnold Network Guided Symbolic Regression Framework
• Statistical Patterns in the Equations of Physics and the Emergence of a Meta-Law of Nature
• The hidden architecture of connections: How do multidimensional identities shape our social networks?
• LMFD: Latent Monotonic Feature Discovery
• The Limits of Inference in Complex Systems: When Stochastic Models Become Indistinguishable