BFBrain: Scalar Bounded-From-Below Conditions from Bayesian Active Learning

TL;DR

This paper introduces BFBrain, a Bayesian deep active learning method that efficiently generates accurate bounded-from-below conditions for scalar potentials, outperforming traditional analytical approaches and applicable to various models.

Contribution

The authors develop a neural network-based procedure for rapidly approximating bounded-from-below conditions, with a Python package for easy application to scalar field theories.

Findings

High accuracy classifiers for three scalar potentials.

Outperforms analytical methods in complex scenarios.

Applicable to arbitrary renormalizable scalar theories.

Abstract

We present a procedure leveraging Bayesian deep active learning to rapidly produce highly accurate approximate bounded-from-below conditions for arbitrary renormalizable scalar potentials, in the form of a neural network which may be saved and exported for use in arbitrary parameter space scans. We explore the performance of our procedure on three different scalar potentials with either highly nontrivial or unknown symbolic bounded-from-below conditions (the two-Higgs doublet model, the three-Higgs doublet model, and a version of the Georgi-Machacek model without custodial symmetry). We find that we can produce fast and highly accurate binary classifiers for all three potentials. Furthermore, for the potentials for which no known symbolic necessary and sufficient conditions on boundedness-from-below exist, our classifiers substantially outperform some common approximate analytical methods, such as producing tractable sufficient but not necessary conditions or evaluating boundedness-from-below conditions for scenarios in which only a subset of the theory's fields achieve vev's. Our methodology can be readily adapted to any renormalizable scalar field theory. For the community's use, we have developed a Python package, BFBrain, which allows for the rapid implementation of our analysis procedure on user-specified scalar potentials with a high degree of customizability.