Advancing Universal Deep Learning for Electronic-Structure Hamiltonian Prediction of Materials

2025-09-24

AI Summary

Conventional deep learning methods for Hamiltonian prediction face generalization bottlenecks due to high-dimensional atomic types, structural configurations, and Hamiltonians, compounded by error accumulation and spurious (“ghost”) states. Method: We propose NextHAM—a physics-informed, end-to-end framework that constructs a zero-step Hamiltonian from DFT-initial charge density as a physically grounded input-output reference; employs a strictly E(3)-equivariant Transformer architecture; and introduces a joint real- and reciprocal-space optimized loss function. NextHAM explicitly models spin–orbit coupling. Results: Evaluated on Materials-HAM-SOC—a large-scale dataset comprising 17,000 materials—NextHAM achieves superior accuracy and efficiency in Hamiltonian and band-structure prediction over state-of-the-art deep learning approaches. It delivers high generalizability and physical consistency, establishing a robust, universal framework for modeling material electronic structures.

Technology Category

• Machine Learning: Deep Neural Architectures and Foundation Models
• Search and Optimization: Learning to Search
• Natural Language Processing: Learning & Optimization for NLP

Application Category

• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Deep learning methods for electronic-structure Hamiltonian prediction has offered significant computational efficiency advantages over traditional DFT methods, yet the diversity of atomic types, structural patterns, and the high-dimensional complexity of Hamiltonians pose substantial challenges to the generalization performance. In this work, we contribute on both the methodology and dataset sides to advance universal deep learning paradigm for Hamiltonian prediction. On the method side, we propose NextHAM, a neural E(3)-symmetry and expressive correction method for efficient and generalizable materials electronic-structure Hamiltonian prediction. First, we introduce the zeroth-step Hamiltonians, which can be efficiently constructed by the initial charge density of DFT, as informative descriptors of neural regression model in the input level and initial estimates of the target Hamiltonian in the output level, so that the regression model directly predicts the correction terms to the target ground truths, thereby significantly simplifying the input-output mapping for learning. Second, we present a neural Transformer architecture with strict E(3)-Symmetry and high non-linear expressiveness for Hamiltonian prediction. Third, we propose a novel training objective to ensure the accuracy performance of Hamiltonians in both real space and reciprocal space, preventing error amplification and the occurrence of "ghost states" caused by the large condition number of the overlap matrix. On the dataset side, we curate a high-quality broad-coverage large benchmark, namely Materials-HAM-SOC, comprising 17,000 material structures spanning 68 elements from six rows of the periodic table and explicitly incorporating SOC effects. Experimental results on Materials-HAM-SOC demonstrate that NextHAM achieves excellent accuracy and efficiency in predicting Hamiltonians and band structures.

Problem

• Predicting electronic-structure Hamiltonians across diverse materials and structures
• Addressing generalization challenges from atomic diversity and Hamiltonian complexity
• Ensuring accuracy in both real and reciprocal space predictions

Innovation

• Neural Transformer with E(3)-symmetry for Hamiltonian prediction
• Zeroth-step Hamiltonians as descriptors and correction targets
• Novel training objective for real and reciprocal space accuracy