Transferable SCF-Acceleration through Solver-Aligned Initialization Learning
Authors: Eike S. Eberhard, Viktor Kotsev, Timm Güthle, Stephan Günnemann
Organizations: 1Technical University of Munich (TUM) · 2Munich Data Science Institute (MDSI) · 3Munich Center for Machine Learning (MCML)
Abstract
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× 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× larger than the training set, SAIL delivers a 1.35× wall-time speedup at the hybrid level of theory, extending ML SCF acceleration to large drug-like molecules.
We present \textsc{dm-PhiSNet}, a physically constrained \textsc{PhiSNet}-based equivariant model that predicts one-electron reduced density matrices (1-RDMs) directly from molecular geometries in an atomic-orbital (AO) basis for accelerated self-consistent field (SCF) workflows. Training follows a two-stage schedule with progressively introduced physically motivated objectives, and the resulting predictions are refined by a lightweight analytic block. This block enforces electron-number conservation, drives the 1-RDM toward generalized idempotency in the AO metric, and regularizes the occupation spectrum of the Löwdin-orthogonalized density. Across six closed-shell systems -- H2O, CH4, NH3, HF, ethanol, and NO3− -- the refined 1-RDMs provide SCF initial guesses that substantially reduce iteration steps by 49--81% relative to standard initializations. Beyond SCF acceleration, the learned 1-RDMs yield accurate one-shot total energies and Hellmann--Feynman atomic forces without force supervision, indicating that the model captures chemically meaningful electronic structure. These results demonstrate that combining equivariant learning with analytic constraint enforcement provides a simple, general route to solver-ready density-matrix initializations and accelerated SCF workflows.
Zuriel Y. Yescas-Ramos, Andrés Álvarez-García, Huziel E. Sauceda
Machine-learned (ML) operator models can be trained to predict density functional theory (DFT) Hamiltonian/density matrices at significantly reduced computational cost, thus extending electronic-structure calculations to previously unfeasible scales. Here, we introduce MALOQ (Massively Accelerated Learning of Operators for Quantum Transport), an application built to train on and predict electronic-structure matrices for systems made of few to 100k atoms, described by large basis sets, and covering a wide range of atomic elements. Based on a state-of-the-art, SO(2)-equivariant backbone architecture, MALOQ provides (i) custom data-processing kernels to handle high-rank Hamiltonian matrix data and (ii) a scalable edge-wise distribution of atomic graph(s). Trained on the largest molecular Hamiltonian datasets available today, it reduces time-per-epoch by over 30% compared to a molecule-wise-distributed framework, and enables inference on material graphs of arbitrary size. We demonstrate scalable training and inference for 3,000-12,000 atoms on the Alps supercomputer, up to 192 GPUs and 256 GPUs, respectively.
Manasa Kaniselvan, Alexander Maeder, Denghui Lu +2
Machine learning interatomic potentials (MLIPs) have become a hallmark of AI for scientific simulation. While efforts on new architectures and datasets have led to increasingly accurate and general models, the choice of optimizer for training has largely remained unexplored, defaulting to Adam and its variants in the community. Here, we implement and systematically compare a class of recently proposed matrix-structured optimizers, including Muon, SOAP, and the hybrid SOAP-Muon, for training NequIP and Allegro MLIP models. We find that these optimizers can substantially outperform Adam in both convergence speed and final accuracy. SOAP and SOAP-Muon emerge as robust and consistently strong methods, while Muon only provides partial gains relative to Adam. The improvements are particularly pronounced under partial force supervision. Our results indicate that optimizer choice is an overlooked yet impactful design axis for MLIPs.
Gil Harari, Yoel Zimmermann, Ola Tangen Kulseng +4