Real-space machine learning of correlation density functionals

Machine learning (ML) plays a pivotal role in extending the reach of quantum chemistry methods for both molecules and materials. However, leveraging ML to improve upon human-designed density functional approximations (DFAs), the primary workhorse for quantum simulations, remains challenging due to severely limited transferability to unseen chemical systems. Here we address this challenge through real-space ML, where energies are learned point by point via correlation energy densities per particle obtained from regularized perturbation theory. We pursue two crucial strategies that enable the construction of highly transferable DFAs, grounded in the Møller–Plesset adiabatic connection framework, for correlation energies defined with respect to the Hartree–Fock reference. First, we introduce the Local Energy Loss, whose data efficiency (expanding each system’s single energy into thousands of datapoints) dramatically enhances transferability when combined with a physically informed ML construction. Second, we construct a real-space, machine-learned, and regularized extension of Spin-Component-Scaled second-order Møller–Plesset perturbation theory, opening new avenues for developing transferable DFAs particularly suited for overcoming self-interaction errors common to traditional DFAs.