Infusing Self-Consistency into Density Functional Theory Hamiltonian Prediction via Deep Equilibrium Models

TL;DR

This paper presents the DEQH model, a neural network architecture that integrates Deep Equilibrium Models to predict DFT Hamiltonians, capturing self-consistency without requiring DFT calculations during training, thus improving accuracy and efficiency.

Contribution

The paper introduces a novel DEQ-based framework for Hamiltonian prediction that inherently models self-consistency, reducing computational costs and enhancing accuracy over traditional methods.

Findings

DEQHNet outperforms existing models on benchmark datasets.

The model effectively captures self-consistency in Hamiltonian prediction.

Ablation studies confirm the importance of DEQ integration.

Abstract

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. We open source our implementation at https://github.com/Zun-Wang/DEQHNet.