Reproduce “Transferable SCF-Acceleration through Solver-Aligned Initialization Learning” on OpenResearch

About this paper

Eike S. Eberhard, Viktor Kotsev, Timm Güthle, Stephan Günnemann

Solver-Aligned Initialization Learning (SAIL), a fine-tuning strategy differentiating through the self-consistent field (SCF) solver, resolves the size-extrapolation failure of machine learning-based initial guesses for Kohn-Sham Density Functional Theory. This approach enables robust acceleration for matrix-based methods on molecules up to ten times larger than the training data and enhances performance for meta-GGA and hybrid functionals, leading to substantial reductions in effective iteration counts and wall-time speedups (e.g., 1.35x for B3LYP on QMugs).

Key insights

• The observed size-extrapolation failure in matrix-based ML models is identified as a "supervision problem" where ground-state-aligned training does not optimize for SCF convergence, rather than an inherent architectural limitation.
• Direct optimization of the SCF solver's dynamics allows the model to learn "unphysical" initial guesses that are more effective at accelerating convergence, often even when they increase the ground-state error.
• SAIL significantly improves coefficient-based models for meta-GGA and hybrid functionals by allowing them to learn density distortions that compensate for systematic errors from necessary approximations in Fock construction.

Summary by alphaXiv.