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Abstract:

When choosing between competing symbolic models for a data set, a human will naturally prefer the “simpler” expression or the one which more closely resembles equations previously seen in a similar context. This suggests a non-uniform prior on functions, which is, however, rarely considered within a symbolic regression (SR) framework. In this paper we develop methods to incorporate detailed prior information on both functions and their parameters into SR. Our prior on the structure of a function is based on a ngram language model, which is sensitive to the arrangement of operators relative to one another in addition to the frequency of occurrence of each operator. We also develop a formalism based on the Fractional Bayes Factor to treat numerical parameter priors in such a way that models may be fairly compared though the Bayesian evidence, and explicitly compare Bayesian, Minimum Description Length and heuristic methods for model selection. We demonstrate the performance of our priors relative to literature standards on benchmarks and a real-world dataset from the field of cosmology.

Abstract:

<jats:p>The non-linear dynamics of scalar fields coupled to matter and gravity can lead to remarkable density-dependent screening effects. In this short review, we present the main classes of screening mechanisms, and discuss their tests in laboratory and astrophysical systems. We particularly focused on reviewing numerical and technical aspects involved in modeling the non-linear dynamics of screening and on tests using laboratory experiments and astrophysical systems, such as stars, galaxies, and dark matter halos.</jats:p>