Neural network representations of fermionic ground and excited states

Artificial neural networks have proven to be flexible and effective tools for representing ground-state wave functions, yet their application to excited states remains largely unexplored. Here, we extend neural-network quantum state methods to simultaneously obtain low-lying states of fermionic systems. After imposing only minimal symmetry requirements and boundary conditions, we construct an orthogonal subspace that evolves through imaginary-time propagation, leveraging a combination of reinforcement and supervised learning techniques. I will discuss the development of this algorithm and report recent advances in neural network representations of ground states in strongly interacting fermionic systems, including ultracold Fermi gases, nuclear matter, and nuclei. These results highlight the versatility of neural networks in capturing the complex correlations that characterize these systems.