Fast multilabel classification of HEP constraints with deep learning

The shortcomings of the Standard Model (SM) motivate its extension to accommodate new expected phenomena, such as dark matter and neutrino masses. However, such extensions are generally more complex due to the presence of a large number of free parameters and additional phenomenology. Understanding how theoretical and experimental limits affect the parameter spaces of new models, individually and collectively, is of utmost importance for conducting model status analysis, motivating precise computations, or model-building aimed at solving certain issues. However, checking the constraints usually require a large amount of time using a chain of physics tools. We demonstrate, for the first time, the application of deep learning (DL) for the multilabel classification (MLC) of a group of theoretical and experimental constraints in the dark doublet phase of the next-to-two-Higgs-doublet model (DDP-N2HDM), as a representative 9-dimensional parameter space. We analyze the issue of class imbalance and the ability of the classifier to learn joint class distributions. We demonstrate the time advantage compared to physics tools, with the classifier achieving orders of magnitude faster checks on groups of constraints and strong performance. The classifier performed strongly in terms of identifying regions where all constraints are valid or invalid, as well as regions where one or more of the constraints are valid or invalid simultaneously. This approach can be applied to any extension beyond the SM with the potential to aid HEP tools or act as a surrogate for fast model status checks. To that end, we provide a python tool \texttt{HEPMLC} for generating and investigating multilabel classifiers for SM extensions.