Optimal Transport in Particle Physics

Progress in science and engineering increasingly depends on the ability to extract reliable information from large, noisy datasets and from simulations of systems across many scales. In particle physics, noisy measurements of proton-proton collisions at the Large Hadron Collider must be corrected before they can be compared with theoretical predictions. Likewise, understanding how quantum field theories change across scales is important in the study of the strong force. Closely related challenges also arise in quantum information science, including the correction of quantum computer readout noise. Although these challenges arise in a wide range of scientific applications, fundamental mathematical questions remain poorly understood. These include: How can we recover the true signal from a noisy measurement, and how confident can we be in the recovery? How can computers efficiently simulate systems across scales, and can we guarantee that the simulations will accurately approximate the systems they are meant to represent? To answer these questions, the investigator will use tools from optimal transport theory to develop methods that are computationally efficient and supported by rigorous guarantees. This research will be integrated with training opportunities for undergraduate students, graduate students, and postdoctoral scholars. The research program has two main components. In the first component, the investigator will study data unfolding, a fundamental problem in which one removes noise or artifacts from data so that the denoised data can be compared with the output of other experiments, numerical simulations, and theoretical predictions. The investigator will use optimal transport to develop alternatives to classical, grid-based methods and apply them to jet substructure unfolding of Large Hadron Collider measurements. In the second component of the research program, the investigator will study the exact renormalization group equations, which describe how theoretical predictions change depending on the scale at which a system is observed. The investigator will formulate these equations on the lattice as time-dependent Wasserstein gradient flows, analyzing convergence as the lattice discretization is refined and developing new numerical methods for their simulation. 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.