Foundation models for equation discovery in high energy physics

Abstract: Foundation models, large machine learning models trained on broad, multimodal datasets, have been gaining increasing attention in scientific applications due to their strong performance on diverse downstream tasks. LLMs, a prominent instance of foundation models, have achieved remarkable success in tasks such as text and image generation. In this work, we investigate their potential for equation discovery in high energy physics, focusing on symbolic regression. We apply the LLM-SR methodology both to benchmark problems of equation recovery in lepton angular distributions and to the discovery of functional forms for angular coefficients in electroweak boson production at the Large Hadron Collider, observables of high phenomenological relevance for which no closed-form expressions are known from first principles. Our results demonstrate that LLM-SR can uncover compact, accurate, and interpretable equations across in-domain and out-of-domain kinematic regions, effectively incorporating embedded scientific knowledge and offering a promising new approach to equation discovery in high energy physics.