Learning local equivariant representations for quantum operators

2024-07-08

arXiv.org

AI Summary

Existing density functional theory (DFT) methods suffer from low computational efficiency, poor generalizability, and difficulty in jointly modeling multiple quantum operators (e.g., Hamiltonians and overlap matrices) for large-scale systems. To address these challenges, we propose a strictly localized equivariant message-passing graph neural network. Our method introduces the first SO(2)-group-convolutional equivariant architecture, ensuring exact rotational symmetry while supporting f- and g-orbitals; employs invariant tensor parameterization to enable multi-operator co-modeling; and captures complex many-body correlations via local message passing within a fixed receptive field. Evaluated on 2D/3D materials datasets, our approach achieves state-of-the-art accuracy with strong robustness under few-shot settings. Moreover, it reduces computational complexity significantly, enabling on-device parallel simulation of million-atom systems.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Search and Optimization: Sampling/Simulation-based Search
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

Predicting quantum operator matrices such as Hamiltonian, overlap, and density matrices in the density functional theory (DFT) framework is crucial for material science. Current methods often focus on individual operators and struggle with efficiency and scalability for large systems. Here we introduce a novel deep learning model, SLEM (strictly localized equivariant message-passing) for predicting multiple quantum operators, that achieves state-of-the-art accuracy while dramatically improving computational efficiency. SLEM's key innovation is its strict locality-based design for equivariant representations of quantum tensors while preserving physical symmetries. This enables complex many-body dependency without expanding the effective receptive field, leading to superior data efficiency and transferability. Using an innovative SO(2) convolution and invariant overlap parameterization, SLEM reduces the computational complexity of high-order tensor products and is therefore capable of handling systems requiring the $f$ and $g$ orbitals in their basis sets. We demonstrate SLEM's capabilities across diverse 2D and 3D materials, achieving high accuracy even with limited training data. SLEM's design facilitates efficient parallelization, potentially extending DFT simulations to systems with device-level sizes, opening new possibilities for large-scale quantum simulations and high-throughput materials discovery.

Problem

• Density Functional Theory
• Large Quantum Systems
• Hamiltonian Prediction

Innovation

• SLEM
• SO(2) Convolution
• Parallel Computing