Transferable SCF-Acceleration through Solver-Aligned Initialization Learning

2026-04-23

AI Summary

Traditional machine learning initialization methods fail to generalize to larger molecular systems and can even impede the convergence of self-consistent field (SCF) iterations. To address this, this work proposes the Solver-Aligned Initialization Learning (SAIL) framework, which trains an initialization model in an end-to-end differentiable manner using a differentiable SCF solver, aligning the initialization directly with the solver’s convergence objective. To resolve the mismatch between conventional supervision signals and actual convergence behavior, the authors introduce the Effective Relative Iteration Count (ERIC) metric. Evaluated on the QM40 dataset, SAIL reduces ERIC by 27%–37% and achieves a 1.25× speedup in wall-clock time on QMugs molecules—systems up to ten times larger than those in the training set—significantly outperforming existing approaches.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Learning to Search
• Multiagent Systems: Multiagent Learning

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

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.

Problem

• SCF acceleration
• initial guess
• extrapolation
• convergence
• molecular size

Innovation

• Solver-Aligned Initialization Learning
• SCF acceleration
• differentiable SCF solver
• Effective Relative Iteration Count
• out-of-distribution generalization