Upscaling Glasma simulations using machine learning

Machine learning is a novel tool for studying various aspects of physical systems. Using deep learning one is able to extract hierarchical information from big data and predict evolutions of nonlinear dynamics to an astonishing degree. In this project, we want to explore how deep neural networks can be utilized to unravel the rich dynamics of gauge theories. We want to apply deep learning to Glasma simulations which simulate the earliest stages of heavy ion collisions. The Glasma is a precursor to the quark-gluon plasma, which is a plasma-like state of matter at energies where protons and neutrons melt into their constituents, the quarks and gluons. The quark-gluon plasma prevailed the early universe up to ten microseconds after the big bang. Nowadays, the quark-gluon plasma can be produced in heavy-ion colliders like the Relativistic Heavy Ion Collider (RHIC) at Brookhaven or the Large Hadron Collider (LHC) at CERN. The quark-gluon plasma that is created in such heavy-ion collisions differs from the equilibrated quark- gluon plasma in the early universe by its creation process. Due to its glass-like flux-tube structure at the time of creation in heavy-ion collisions, it is called Glasma - a combination of glass and plasma. A central role in the numerical simulation is fulfilling the symmetry of gauge-invariance exactly, regardless of random color-charge fluctuations. The simulation of the evolution of the Glasma is numerically expensive and memory-intensive. When applying machine learning tools to our physical system, we have to be particularly careful about fulfilling gauge-invariance. Incorporating gauge-invariance into neural networks may lead to deep learning systems with novel properties. We may learn more about the nature of neural networks and their capabilities and limitations by comparing their results to results obtained from physical simulations. Conversely, representing physical systems through neural networks, we may learn more about alternative representations of the information content. Such an approach could be regarded as a new kind of an effective field theoretic description. With our new findings, we ultimately want to enable Glasma simulations of larger system sizes and at higher collision energies that due to computational limitations are currently unfeasible.

Our research project aimed to harness the power of machine learning to enhance our understanding of complex physical systems, specifically focusing on the dynamics of heavy ion collisions studied at particle colliders such as the LHC at CERN. By exploring deep learning techniques, we sought to analyze and predict the intricate behaviors involved in these high-energy events. One of the most significant breakthroughs of our project was the development of Lattice Gauge Equivariant Convolutional Neural Networks (L-CNNs). These neural networks are designed to respect the lattice gauge symmetry, a fundamental aspect of gauge theories in physics. This allows L-CNNs to accurately model and predict the behaviors of fields of the strong force, making them powerful tools for theoretical and computational physics. We also investigated the benefits of using neural network architectures that reflect the underlying symmetries of physical problems, demonstrating that equivariant neural networks outperform traditional ones in various tasks, enhancing both performance and generalizability. Additionally, we applied machine learning to find better parametrizations of fixed point actions in SU(3) gauge theory, crucial for reducing discretization effects and lattice artifacts. Our project has laid the groundwork for future research that combines machine learning with theoretical physics for the strong nuclear force. The L-CNNs we developed can potentially be adapted and applied to a wide range of problems, including the early stages of heavy ion collisions. Our findings highlight the importance of incorporating physical symmetries into neural network designs, leading to more robust and insightful models.