Generating particle physics Lagrangians with transformers

In physics, Lagrangians provide a systematic way to describe laws governing physical systems. In the context of particle physics, they encode the interactions and behavior of the fundamental building blocks of our universe. By treating Lagrangians as complex, rule-based constructs similar to linguistic expressions, we trained a transformer model -- proven to be effective in natural language tasks -- to predict the Lagrangian corresponding to a given list of particles. We report on the transformer's performance in constructing Lagrangians respecting the Standard Model $\mathrm{SU}(3)\times \mathrm{SU}(2)\times \mathrm{U}(1)$ gauge symmetries. The resulting model is shown to achieve high accuracies (over 90\%) with Lagrangians up to six matter fields, with the capacity to generalize beyond the training distribution, albeit within architectural constraints. We show through an analysis of input embeddings that the model has internalized concepts such as group representations and conjugation operations as it learned to generate Lagrangians. We make the model and training datasets available to the community. An interactive demonstration can be found at: \url{https://huggingface.co/spaces/JoseEliel/generate-lagrangians}.

A diversity-enhanced genetic algorithm for efficient exploration of parameter spaces

We present a Python package together with a practical guide for the implementation of a lightweight diversity-enhanced genetic algorithm (GA) approach for the exploration of multi-dimensional parameter spaces. Searching a parameter space for regions with desirable properties, e.g. compatibility with experimental data, poses a type of optimization problem wherein the focus lies on pinpointing all "good enough" solutions, rather than a single "best solution". Our approach dramatically outperforms random scans and other GA-based implementations in this aspect. We validate the effectiveness of our approach by applying it to a particle physics problem, showcasing its ability to identify promising parameter points in isolated, viable regions meeting experimental constraints. The companion Python package is applicable to optimization problems beyond those considered in this work, including scanning over discrete parameters (categories). A detailed guide for its usage is provided.