CAREER: Microscopic Transport, Machine Learning, and Bayesian Analysis for Extracting the Dense Nuclear Matter Equation of State from Heavy-Ion Collisions at RHIC and FRIB

The strong force governs interactions between quarks and gluons, the elementary constituents of matter. It binds quarks and gluons into protons, neutrons, and other hadrons, binds protons and neutrons in atomic nuclei, and determines properties of neutron stars and their mergers. This project focuses on nuclear matter – many-body systems interacting through the strong force – and its thermodynamics, which describes how the pressure or energy change with density or temperature. This behavior is summarized in a function called the equation of state. Constraining the equation of state is a prominent goal in nuclear physics, answering key open questions: How hard is it to squeeze nuclear matter? At what density and temperature do protons and neutrons “melt” into their constituent particles? What is the pressure in neutron-star cores? In the laboratory, this is studied using experiments that collide heavy nuclei at large speeds, momentarily creating dense and hot nuclear matter. The strong interaction governs how dense and hot these systems become, how they expand and cool, and how this affects the final speeds and directions of particles recorded in detectors. The central challenge is to translate these final particle measurements into information about the hot and dense matter that produced them. This project addresses this challenge by comparing experimental measurements with dynamical simulations to constrain the equation of state of nuclear matter. This comparison is made possible by advancing state-of-the-art simulations of heavy-ion collisions, employing machine learning to overcome otherwise insurmountable computational barriers, and performing Bayesian analysis of simulation results and experimental measurements. The first goal of this project addresses the development and implementation of necessary improvements to the heavy-ion simulation framework SMASH, including more flexible single-particle potentials that capture the momentum dependence of nuclear interactions. This enables accounting for the effects of momentum-dependent interactions on collective particle motion, one of the key experimental signatures of the nuclear matter equation of state. The second goal focuses on constructing an accurate SMASH emulator: a surrogate, less computationally-demanding model of the full simulation. This emulator, constructed with support of machine learning techniques, enables otherwise prohibitively computationally-expensive comparisons of model and experimental data. The third goal employs Bayesian analysis – a statistical method for combining simulations, measurements, and their uncertainties – to extract robust constraints on the nuclear matter equation of state from comparisons of simulations and heavy-ion collision measurements, including those performed at the Relativistic Heavy Ion Collider and the Facility for Rare Isotope Beams. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.