Applications of Machine Learning in Constraining Multi-Scalar Models

TL;DR

This work addresses the computational challenge of enforcing unitarity and vacuum-stability constraints in Standard Model extensions with extra $SU(2)$ multiplets. It employs four progressively larger fully connected networks to predict unitarity and bounded-from-below conditions simultaneously, achieving high accuracy while delivering substantial speedups over traditional scalar potential minimization. Results demonstrate significant improvements across models with a $4$-plet and a $6$-plet, with final true-positive rates exceeding $99.0\%$ and computation times reduced by factors exceeding $400$–$600\times$. The approach enables efficient, scalable parameter-space scanning for complex multi-scalar theories and can be extended to scenarios with more intricate hypercharge assignments or larger multiplets where analytical conditions are not readily available.

Abstract

Machine learning techniques are used to predict theoretical constraints such as unitarity and boundedness from below in extensions of the Standard Model. This approach has proven effective for models incorporating additional SU(2) scalar multiplets, in particular the quadruplet and sixplet cases. High predictive performance is achieved through the use of suitable neural network architectures and well-prepared training datasets. Moreover, machine learning provides a substantial computational advantage, enabling significantly faster evaluations compared to scalar potential minimization.

Figures (1)

• Figure 1: The architecture of the networks used in the analysis of the G2HDM is shown as an example. The ten input parameters correspond to the G2HDM potential couplings, with their real and imaginary parts treated separately.