AI Cuts Quantum Material Simulations from Years to Minutes

Scientists are tackling a major bottleneck in simulating the behaviour of nanoscale devices, namely the computationally intensive process of constructing the Hamiltonian matrix. Chen Hao Xia, Manasa Kaniselvan, and Mathieu Luisier, all from the Integrated Systems Laboratory ETH Zurich, alongside Marko Mladenoivić, present a novel machine-learning approach to directly predict this matrix, bypassing the need for exhaustive density-functional theory (DFT) calculations. This research is significant because it enables accurate modelling of large, aperiodic systems, such as those found in valence change memory (VCM) cells, which are currently beyond the reach of conventional DFT methods, achieving a mean absolute error of only 3.39 to 3.58 meV when predicting the Hamiltonian of 5,000-atom systems and successfully reproducing key device characteristics.

Predicting Hamiltonian matrices in disordered materials using machine learning is a challenging but promising endeavor

Researchers have developed a new machine-learning approach to predict the Hamiltonian matrix of large material structures with unprecedented accuracy, potentially overcoming a significant bottleneck in ab-initio device simulations. Constructing the Hamiltonian matrix is a computationally intensive step in density-functional theory (DFT) calculations, particularly for amorphous or defective materials lacking the simplifying periodicity of crystalline structures.

This work addresses this challenge by directly predicting the Hamiltonian matrix using equivariant graph neural networks and a technique called augmented partitioning training. The team demonstrated the effectiveness of their method by modelling valence change memory (VCM) cells, achieving a Mean Absolute Error (MAE) of 3.39 to 3.58 meV when predicting the Hamiltonian matrix entries of systems containing approximately 5,000 atoms, as compared to DFT.

This level of accuracy is crucial for simulating complex material behaviour without the prohibitive computational cost of traditional DFT methods. By replacing DFT-computed Hamiltonians with these machine-learned predictions, researchers were able to compute the energy-resolved transmission function of the VCMs using a quantum transport tool, obtaining qualitatively good agreement with DFT results.

This breakthrough enables the study of large-scale devices beyond the current capabilities of ab-initio calculations. The research focuses on overcoming the memory and computational limits of DFT, paving the way for more detailed and efficient simulations of advanced materials and devices. Specifically, the work centres on simulating a VCM cell comprised of a TiN-HfO2-Ti/TiN stack containing 5,268 atoms, where the conductance is modulated by oxygen vacancy distribution.

The model learns complex features, including non-regular lattices and atomic interactions, through an equivariant graph neural network trained on a limited number of VCM configurations. The developed equivariant graph neural network incorporates rotational covariance as a physical constraint, ensuring accurate predictions even with complex atomic arrangements.

The network’s architecture employs strict locality and multi-headed attention to effectively handle the intricacies of the VCM structures. This approach allows for the prediction of Hamiltonian matrices for systems with unseen vacancy distributions and filament morphologies, opening new avenues for materials discovery and device optimisation.

EGNN Architecture and Training for Hamiltonian Matrix Prediction offers a novel approach

Equivariant graph neural networks formed the core of this research, enabling accurate prediction of Hamiltonian matrices for large systems. The work addressed a critical limitation of density-functional theory (DFT) calculations, which become computationally expensive when modelling amorphous or defective materials requiring domains of thousands of atoms.

Researchers employed an EGNN architecture, detailed in Figure 2 of the published study, to learn and directly predict these matrices, bypassing the need for extensive DFT computations. This network consists of a single message passing layer, utilising node and edge embeddings to represent atoms and their interactions.

To facilitate large-scale Hamiltonian predictions, strict locality was enforced within the network, alongside multi-headed attention mechanisms to discern complex atomic environments. The model was trained on valence change memory (VCM) cells, specifically TiN-HfO2-Ti/TiN structures, generated through kinetic Monte Carlo simulations.

Two device structures with uniformly distributed vacancies were used for training, with Hamiltonians produced using the CP2K DFT package and a localized Gaussian-type orbital basis set. Crucially, the training data differed significantly from the test set, which comprised VCM configurations with clustered, physically realistic vacancy distributions, ensuring a rigorous assessment of the model’s generalizability.

Augmented partitioning was implemented during training to divide large structures into slices, fitting them into GPU memory while maintaining atomic connectivity between partitions. This partitioning occurred longitudinally to capture interfaces between materials within the VCM stack. The trained EGNN then predicted the Hamiltonian matrix for full device structures, which were subsequently used in an in-house quantum transport simulator employing the non-equilibrium Green’s function (NEGF) formalism. This methodology yielded a Mean Absolute Error (MAE) of 3.39 to 3.58 meV when predicting Hamiltonian matrix entries for systems containing approximately 5,000 atoms.

Accurate Hamiltonian matrix prediction using equivariant graph neural networks for large disordered systems is a challenging yet crucial task

Scientists achieved a Mean Absolute Error (MAE) of 3.39 to 3.58 meV when predicting the Hamiltonian matrix entries of systems containing approximately 5,000 atoms, as compared to density-functional theory (DFT) calculations. This work addresses a critical computational bottleneck in \textit{ab-initio} device modelling, particularly for amorphous or defective materials where traditional methods struggle.

The research demonstrates the potential to overcome memory and computational limits currently hindering the study of large-scale devices. The study utilized an equivariant graph neural network (EGNN) trained on valence change memory (VCM) cells to directly predict the Hamiltonian matrix of large structures.

Predictions were consistently accurate across different VCM configurations, with node errors ranging from 1.54 to 1.82 meV and edge errors around 0.12 meV. These results indicate the model’s ability to generalize and accurately predict Hamiltonian entries even with unseen vacancy distributions and filament morphologies.

The predicted Hamiltonian matrices were then used in a quantum transport simulator to compute the energy-resolved transmission function. A qualitatively good agreement was obtained between the transmission functions calculated using the machine learning-predicted Hamiltonian and those computed directly with DFT.

Total errors, averaged over all Hamiltonian entries, were measured between 0.339 and 0.358 meV, demonstrating high fidelity in the prediction process. This workflow involved augmented partitioning to enable the processing of large structures within GPU memory while preserving atomic connectivity. The model was trained on structures with uniformly distributed vacancies and then tested on more complex, physically realistic vacancy configurations generated through kinetic Monte Carlo simulations. The consistent performance across these disparate datasets highlights the robustness and potential of this approach for materials science applications.

Predicting Hamiltonian matrices accelerates large-scale electronic structure calculations significantly

A new machine learning approach circumvents computational limitations in density-functional theory (DFT), enabling the study of larger and more complex atomic structures than previously possible. This work introduces a method for directly predicting the Hamiltonian matrix of large systems using equivariant graph neural networks and augmented partitioning training, offering a pathway to overcome the memory and computational bottlenecks of traditional DFT calculations.

The researchers demonstrated their approach by modelling valence change memory (VCM) cells, achieving a Mean Absolute Error (MAE) of 3.39 to 3.58 meV when predicting the Hamiltonian matrix entries of systems containing approximately 5,000 atoms. Replacing DFT-computed Hamiltonians with these predictions in transport simulations yielded qualitatively good agreement with results obtained using conventional methods.

The authors acknowledge that further improvements in model accuracy are needed, particularly through the incorporation of more training data and more expressive network architectures. Future research will focus on extending this framework to other applications, such as phase-change memories, and exploring devices with evolving morphologies.

This advancement facilitates the investigation of devices with sizes beyond current \textit{ab-initio} capabilities, potentially accelerating materials discovery and device design. While the current model requires further refinement to enhance prediction accuracy, the demonstrated ability to rapidly construct Hamiltonian matrices, with a training cost of under 40 node hours, represents a significant step towards large-scale, first-principles device simulations.

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