MALOQ Accelerates Quantum Transport Operator Learning.

Machine-learned (ML) operator models hold significant promise for accelerating electronic-structure calculations, particularly by predicting density functional theory (DFT) Hamiltonian and density matrices at a fraction of the traditional computational cost. This advancement allows for extending these calculations to scales previously considered unfeasible. Introducing MALOQ (Massively Accelerated Learning of Operators for Quantum Transport), a new application designed to train on and predict electronic-structure matrices for systems ranging from a few atoms up to 100,000 atoms, encompassing a wide array of atomic elements and large basis sets. MALOQ is built upon a state-of-the-art, SO(2)-equivariant backbone architecture. Key innovations include custom data-processing kernels tailored for high-rank Hamiltonian matrix data and a scalable edge-wise distribution of atomic graphs. These features enable MALOQ to reduce time-per-epoch by over 30% compared to molecule-wise distributed frameworks and facilitate inference on material graphs of any size. Demonstrations on the Alps supercomputer showed scalable training and inference for systems with 3,000 to 12,000 atoms, utilizing up to 192 and 256 GPUs, respectively.