Physics-driven learning for inverse problems in quantum chromodynamics

The integration of deep learning techniques and physics-driven designs is reforming the way we address inverse problems, in which accurate physical properties are extracted from complex observations. This is particularly relevant for quantum chromodynamics (QCD) — the theory of strong interactions — with its inherent challenges in interpreting observational data and demanding computational approaches. This Perspective highlights advances of physics-driven learning methods, focusing on predictions of physical quantities towards QCD physics and drawing connections to machine learning. Physics-driven learning can extract quantities from data more efficiently in a probabilistic framework because embedding priors can reduce the optimization effort. In the application of first-principles lattice QCD calculations and QCD physics of hadrons, neutron stars and heavy-ion collisions, we focus on learning physically relevant quantities, such as perfect actions, spectral functions, hadron interactions, equations of state and nuclear structure. We also emphasize the potential of physics-driven designs of generative models beyond QCD physics. Integrating physics priors into machine learning enhances efficiency, reduces data needs and yields reliable results. This Perspective explores physics-driven learning and inverse modelling of generative models to provide solutions for inverse problem in quantum chromodynamics.