Transferable SCF-Acceleration through Solver-Aligned Initialization Learning

The cost of Kohn-Sham density functional theory (KS-DFT) calculations scales with the number of solver iterations, which depends on the quality of the initial guess. 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 self-consistent field (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, which contains molecules up to 4$\times$ larger than the training distribution, SAIL reduces ERIC by 37\% (PBE), 33\% (SCAN), and 28\% (B3LYP), more than doubling the previous state-of-the-art reduction on B3LYP. On QMugs molecules 10$\times$ larger than the training set, SAIL delivers a 1.35$\times$ wall-time speedup at the hybrid level of theory, extending ML SCF acceleration to large drug-like molecules.