Transferable SCF-Acceleration through Solver-Aligned Initialization Learning

Machine learning methods that predict initial guesses from molecular geometry can reduce this cost, but matrix-prediction models fail when extrapolating to larger molecules, degrading rather than accelerating convergence [Liu et al. 2025]. We show that this failure is a supervision problem, not an extrapolation problem: models trained on ground-state targets fit those targets well out of distribution, yet produce initial guesses that slow convergence. Solver-Aligned Initialization Learning (SAIL) resolves this for both Hamiltonian and density matrix models by differentiating through the SCF solver end-to-end. We introduce the Effective Relative Iteration Count (ERIC), a correction to the commonly used RIC that accounts for hidden Fock-build overhead. On QM40, containing molecules up to 4$\times$ larger than the training distribution, SAIL reduces ERIC by 37% (PBE), 33% (SCAN), and 27% (B3LYP), more than doubling the previous state-of-the-art reduction on B3LYP (10%). On QMugs molecules 10$\times$ the training size, SAIL delivers a 1.25$\times$ wall-time speedup at the hybrid level of theory, extending ML SCF acceleration to large drug-like molecules.