Accelerating Excited-State Calculations of Large Systems with Restricted Boltzmann Machines

Accurate excited-state electronic-structure calculations for large systems remain challenging due to the prohibitive cost of constructing and screening the configuration space in conventional linear-response approaches. Here, we present a generative machine-learning-accelerated simplified Tamm-Dancoff approximation (gML-sTDA) method that enables efficient excited-state calculations for large systems. The key idea is to use restricted Boltzmann machines (RBM) as generative models to learn the distribution of important singly excited Slater determinants (SSDs) from previously calculated excited-state solutions and to propose new relevant SSDs in an iterative way to avoid exhaustively evaluating matrix elements over the huge configuration space. Benchmarks on finite single-walled carbon nanotube models up to 1114 atoms (16,424 basis functions) show that gML-sTDA reproduces sTDA reference excitation energies with mean absolute errors of ∼0.007-0.011 eV and yields essentially identical absorption spectra while providing substantial speedups. In particular, relative to the tight-threshold sTDA reference protocol, the overall acceleration ratio approaches ∼40× for the largest nanotube and remains close to ∼9× compared with the default-threshold sTDA-cut workflow. Additional applications to a silicon quantum dot, a large black-phosphorus supercell, and a rubrene cluster demonstrate consistent performance, with speedup factors of 7.4, 4.5, and 9.8, respectively, compared to those of the sTDA-cut. These results establish gML-sTDA as a practical and scalable route to excited-state electronic structure calculations in large-scale systems and provide an efficient starting point for applications requiring repeated excited-state evaluations.