Machine Learning with Renormalization Group for Lattice QCD

This project combines machine learning and fundamental physics to gain a deeper understanding of the basic building blocks of matter that make up protons, neutrons, and atomic nuclei. Lattice QCD (Quantum Chromodynamics) is a method used to simulate the dynamics of quarks and gluons, the fundamental interactions of the strong nuclear force, on a discrete lattice. These simulations are computationally demanding and face significant challenges with traditional approaches. The project explores new methods to make lattice QCD more efficient and precise. A key concept is the so-called fixed point action, a specialized mathematical formulation that significantly reduces lattice artifacts. Using modern machine learning techniques, particularly lattice gauge equivariant convolutional neural networks (L-CNNs), the project aims to automatically learn these fixed point actions, surpassing previously manually developed methods. The renormalization group plays a central role in this context: This theoretical tool helps preserve the essential information of a system across different energy scales while filtering out less relevant details. This is crucial for achieving high-precision simulations of quantum chromodynamics on a lattice while reducing computational costs compared to traditional methods. In addition, the project investigates diffusion models, a modern method from the field of machine learning. These models use stochastic processes to efficiently generate physical configurations. Of particular interest is the connection between diffusion models and renormalization group concepts. Studying these links could improve our understanding of underlying physical principles and enable more targeted applications of machine learning techniques. By combining physics with modern artificial intelligence technologies, the project opens new perspectives for fundamental research and may lead to technological innovations in the long term.