[Paper Review] Graph Convolutional Neural Networks for (QM)ML/MM Molecular Dynamics Simulations

Albert Hofstetter, Lennard Böselt+1 more|arXiv (Cornell University)|Jun 29, 2022

Machine Learning in Materials Science61 references32 citations

TL;DR

This paper proposes a graph convolutional neural network (GCNN) with ∆-learning to enable accurate, efficient (QM)ML/MM molecular dynamics simulations of condensed-phase systems. By combining DFTB as a baseline with a GCNN that captures long-range interactions through message passing, the method achieves chemical accuracy in energy and force predictions, outperforming baseline models in stability and generalization across diverse solvated systems.

ABSTRACT

To accurately study chemical reactions in the condensed phase or within enzymes, both a quantum-mechanical description and sufficient configurational sampling is required to reach converged estimates. Here, quantum mechanics/molecular mechanics (QM/MM) molecular dynamics (MD) simulations play an important role, providing QM accuracy for the region of interest at a decreased computational cost. However, QM/MM simulations are still too expensive to study large systems on longer time scales. Recently, machine learning (ML) models have been proposed to replace the QM description. The main limitation of these models lies in the accurate description of long-range interactions present in condensed-phase systems. To overcome this issue, a recent workflow has been introduced combining a semi-empirical method (i.e. density functional tight binding (DFTB)) and a high-dimensional neural network potential (HDNNP) in a $\Delta$-learning scheme. This approach has been shown to be capable of correctly incorporating long-range interactions within a cutoff of 1.4 nm. One of the promising alternative approaches to efficiently take long-range effects into account is the development of graph convolutional neural networks (GCNN) for the prediction of the potential-energy surface. In this work, we investigate the use of GCNN models -- with and without a $\Delta$-learning scheme -- for (QM)ML/MM MD simulations. We show that the $\Delta$-learning approach using a GCNN and DFTB and as baseline achieves competitive performance on our benchmarking set of solutes and chemical reactions in water. The method is additionally validated by performing prospective (QM)ML/MM MD simulations of retinoic acid in water and S-adenoslymethioniat interacting with cytosine in water. The results indicate that the $\Delta$-learning GCNN model is a valuable alternative for (QM)ML/MM MD simulations of condensed-phase systems.

Motivation & Objective

• To develop a machine learning potential based on graph convolutional neural networks (GCNNs) for (QM)ML/MM molecular dynamics simulations.
• To assess whether GCNNs can accurately model long-range interactions and non-local charge transfer in condensed-phase systems.
• To compare the performance of GCNNs with and without ∆-learning against established high-dimensional neural network potentials (HDNNPs).
• To evaluate the impact of training data ordering, loss function weighting, and neighborhood reduction on model generalization and computational cost.
• To determine the suitability of GCNN-based ∆-learning for systems with high elemental diversity, such as metalloenzymes or organometallic catalysts.

Proposed method

• A graph convolutional neural network (GCNN) is trained to predict the potential-energy surface (PES) of QM zones in (QM)ML/MM simulations.
• The GCNN uses message passing operations with dense layers to propagate information across atomic graphs, enabling non-local electronic structure effects.
• A ∆-learning scheme is employed, where the GCNN predicts the energy and force correction relative to a DFTB baseline, improving accuracy for long-range interactions.
• The loss function includes weighted contributions for total energy (wE = 1), QM forces (wFQM = 0.1), and MM forces (wFMM = 10), optimizing generalization.
• Neighborhood reduction schemes are tested to reduce computational cost, though they degrade force prediction accuracy.
• Training data is split into time-ordered and randomly shuffled sets to assess the impact of data ordering on convergence and performance.

Experimental results

Research questions

• RQ1 Can GCNNs with ∆-learning achieve comparable or better accuracy than HDNNPs in (QM)ML/MM MD simulations of solvated molecules?
• RQ2 How does the inclusion of QM and MM force gradients in the loss function affect model generalization and prediction accuracy?
• RQ3 Does data ordering (time-based vs. random) influence training convergence and model performance in GCNN-based (QM)ML/MM simulations?
• RQ4 To what extent do neighborhood reduction schemes reduce computational cost without sacrificing force accuracy in MD simulations?
• RQ5 How do GCNNs scale with increasing elemental diversity compared to HDNNPs in complex condensed-phase systems?

Key findings

• The ∆-learning GCNN model achieved lower mean absolute error (MAE) in energy and force predictions than the baseline DFTB for all five test systems, including retinoic acid and SAM/cyt in water.
• The GCNN with ∆-learning showed stable (QM)ML/MM MD simulations over 110,000 steps, even with a relatively small initial QM training set of 7,000 steps.
• Optimal loss weighting (wE = 1, wFQM = 0.1, wFMM = 10) improved generalization, while higher QM force weights led to overfitting and reduced performance.
• Randomly shuffled training data converged faster than time-ordered data, reducing training time without compromising model accuracy.
• Neighborhood reduction schemes reduced computational cost but significantly degraded force prediction accuracy, making them unsuitable for MD simulations.
• The GCNN-based ∆-learning approach scales more favorably with increasing elemental diversity than HDNNPs, which suffer from exponential scaling of symmetry functions.