In this study, we introduce a unified neural network architecture, the Deep
Equilibrium Density Functional Theory Hamiltonian (DEQH) model, which
incorporates Deep Equilibrium Models (DEQs) for predicting Density Functional
Theory (DFT) Hamiltonians. The DEQH model inherently captures the
self-consistency nature of Hamiltonian, a critical aspect often overlooked by
traditional machine learning approaches for Hamiltonian prediction. By
employing DEQ within our model architecture, we circumvent the need for DFT
calculations during the training phase to introduce the Hamiltonian's
self-consistency, thus addressing computational bottlenecks associated with
large or complex systems. We propose a versatile framework that combines DEQ
with off-the-shelf machine learning models for predicting Hamiltonians. When
benchmarked on the MD17 and QH9 datasets, DEQHNet, an instantiation of the DEQH
framework, has demonstrated a significant improvement in prediction accuracy.
Beyond a predictor, the DEQH model is a Hamiltonian solver, in the sense that
it uses the fixed-point solving capability of the deep equilibrium model to
iteratively solve for the Hamiltonian. Ablation studies of DEQHNet further
elucidate the network's effectiveness, offering insights into the potential of
DEQ-integrated networks for Hamiltonian learning.

该研究介绍了一个统一的神经网络架构，Deep Equilibrium Density Functional Theory Hamiltonian (DEQH) 模型，它结合了 Deep Equilibrium Models (DEQs) 来预测 Density Functional Theory (DFT) Hamiltonians。DEQH 模型固有地捕捉了 Hamiltonian 的自洽性质，解决了传统机器学习方法在 Hamiltonian 预测中常忽略的关键问题。在多个数据集上测试，DEQHNet 显著提高了预测准确性，除了预测器外，DEQH 模型还是一个 Hamiltonian 求解器，利用深度平衡模型的固定点求解能力迭代求解 Hamiltonian，对 DEQHNet 的消融研究进一步阐明了网络的有效性，揭示了 DEQ 集成网络在 Hamiltonian 学习中的潜力。