  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.
