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Graph Dynamical Networks for Unsupervised Learning of Atomic Scale Dynamics in Materials

Tian Xie, Arthur France-Lanord, Yanming Wang, Yang Shao-Horn, Jeffrey C. Grossman

arXiv:1902.06836v2cond-mat.mtrl-scics.LGphysics.chem-ph

TL;DR

Atomic-scale dynamics in complex material environments are difficult to extract from MD data, and a general approach across condensed phases is lacking. GDyNets combines Koopman analysis and graph convolution to learn local atomic dynamics; a toy system and applications to interfaces and polymer electrolytes indicate its potential across material systems.

  • Problem

    A general method for understanding atomic-scale dynamics across solid, liquid, and amorphous materials is lacking, while those dynamics matter to material performance and are difficult to extract in complex environments.

    Source: INTRODUCTION · p. 2

  • Method

    GDyNets combines Koopman analysis with graph convolutional neural networks to learn local atomic dynamics while sharing information across similar environments.

    Source: INTRODUCTION · p. 3

  • Results

    Learning local dynamics is exponentially easier than global dynamics in a toy lattice, and applications to solid-liquid interfaces and polymer electrolytes indicate potential across material systems.

    Source: DISCUSSION · p. 11

  • Takeaways & Limitations

    The approach could help uncover physical insights from atomic-scale dynamics that may otherwise be overlooked in materials research.

    Source: INTRODUCTION · p. 3

    The local Markov assumption is approximate when the state includes only neighboring atoms, though exact when it includes all system atoms.

    Source: RESULTS · p. 3

Abstract

from arXiv · show

Understanding the dynamical processes that govern the performance of functional materials is essential for the design of next generation materials to tackle global energy and environmental challenges. Many of these processes involve the dynamics of individual atoms or small molecules in condensed phases, e.g. lithium ions in electrolytes, water molecules in membranes, molten atoms at interfaces, etc., which are difficult to understand due to the complexity of local environments. In this work, we develop graph dynamical networks, an unsupervised learning approach for understanding atomic scale dynamics in arbitrary phases and environments from molecular dynamics simulations. We show that important dynamical information can be learned for various multi-component amorphous material systems, which is difficult to obtain otherwise. With the large amounts of molecular dynamics data generated everyday in nearly every aspect of materials design, this approach provides a broadly useful, automated tool to understand atomic scale dynamics in material systems.

INTRODUCTION

A general approach for learning atomic-scale dynamics across condensed phases is lacking, despite the importance of atom and molecule motion to material performance. GDyNets combines Koopman analysis with graph convolution to learn local dynamics and is demonstrated on complex material systems.

INTRODUCTION

  • Atomic-scale dynamics in complex, multicomponent materials are difficult to extract from large MD datasets, and a general approach across solid, liquid, and amorphous phases is lacking.Existing approaches typically use system-specific coordination descriptions or average atomic behavior.Source: INTRODUCTION · p. 2
  • GDyNets combines Koopman analysis with graph convolutional neural networks to learn individual atoms’ dynamics while sharing knowledge across similar local environments.Its variational loss learns a linear model for atomic dynamics.Source: INTRODUCTION · p. 3
  • Modeling local rather than global dynamics improves sampling because many atoms occupy structurally similar but distinct local environments, and global dynamics can be exponentially more complex in a toy system.Source: INTRODUCTION · p. 3
  • The method is applied to silicon dynamics at solid-liquid interfaces and lithium-ion transport in amorphous polymer electrolytes, with potential to uncover overlooked physical insights.Source: INTRODUCTION · p. 3

RESULTS

GDyNets models local atomic dynamics from molecular-dynamics trajectories and identifies informative states and transitions across toy, interfacial, and polymer-electrolyte systems. Its results connect local environments with relaxation processes and lithium-ion conduction.

Koopman analysis of atomic scale dynamics

  • The local-configuration model assumes Markovian dynamics and shared dynamics across target-atom sets; Markovianity is exact with all atoms but approximate with neighbor-only configurations.Source: RESULTS · p. 3

Learning feature map function with graph dynamical networks

  • GDyNets uses graph convolutional networks to encode local environments and a VAMP loss to learn linear dynamics for target atoms.Its GCN encodes time-varying local graphs and is invariant to permutation, rotation, and reflection.Source: RESULTS · pp. 4–5

Local and global dynamics in the toy system

  • GDyNets identified the two-site lithium transition at 42.3 ps, whereas the global VAMPnet learned a 236 ps transition and performed worse in the CK test.The global model treated spatially distinct but equivalent octahedral sites as different states; the authors note that slower global transitions proliferate exponentially with system size, making atomic-scale dynamics impractical to discover within reasonable simulation time.Source: RESULTS · p. 7

Silicon dynamics in solid-liquid interface

  • GDyNets identified four Si interface states, including distinct interfacial liquid and solid states that the q3 order parameter does not provide.The authors report that the learned states are more robust to accidental order in the liquid; q3 is specific to diamond-like structures, while GDyNets can potentially apply to any material given MD data.Source: RESULTS · p. 8
  • 538 ns solid–liquid transition relaxation was identified from a 12.5 ns trajectory, alongside 73.2 ns solid-interface and 2.26 ns liquid-interface processes.The authors attribute identification of rare events to the ensemble of independent Si-atom trajectories and report strong CK-test performance.Source: RESULTS · pp. 7–8

Lithium ion dynamics in polymer electrolytes

  • In PEO/LiTFSI, a four-state model resolved distinct Li-ion solvation environments, with the most populated state at 50.6 ± 0.8%.The other state populations were 27.3 ± 0.4%, 15.1 ± 0.4%, and 7.0 ± 0.9%.Source: RESULTS · p. 9
  • The slowest Li-ion relaxation involves transport into and out of a PEO-coordinated environment, while faster processes include hydroxyl-group movement and transitions from state 0 to states 2 and 3.The model performs well in CK tests.Source: RESULTS · p. 9

Implications to lithium ion conduction

  • At τ = 0.8 ns, same-state transitions account for most Li-ion conduction, while diffusion of negatively charged state 2 contributes ∼40% and explains observed negative transference at high salt concentration.Source: RESULTS · p. 10

DISCUSSION

GDyNets applies Koopman models and graph convolutional networks to learn local atomic dynamics from materials MD data. The discussion highlights its potential scope, the role of symmetry-aware local representations, and current limitations.

DISCUSSION

  • The authors identify potential applications in systems including battery electrolytes, desalination membranes, and metal-organic frameworks, while noting that global dynamics could be learned with pooling.Hierarchical pooling may be needed for global dynamics in large biological systems.Source: DISCUSSION · pp. 10–11
  • Graph convolution enables parameter sharing and symmetry-invariant local representations, helping identify similar environments and learn local rather than exponentially more complicated global dynamics.The built-in invariances can also cause the model to ignore dynamics between symmetrically equivalent structures, such as ammonia flips.Source: DISCUSSION · p. 11
  • GDyNets currently lacks a generative component for directly generating future structures; a graph decoder is suggested as a possible addition.Transfer learning on graph embeddings may also reduce the number of MD trajectories needed.Source: DISCUSSION · p. 11
  • Toy and materials examples support GDyNets as a general approach for learning atomic-scale dynamics, with local dynamics potentially easier to learn than global dynamics in systems with representative local structures.The discussion notes that Koopman models have seen limited use for learning materials dynamics from MD, and that the learned model is linear.Source: DISCUSSION · pp. 10–11

METHODS

The methods construct trajectory graphs, learn local atomic features, and use Koopman-based analyses to characterize timescales, state structure, and lithium-ion conduction.

METHODS

  • Each trajectory frame becomes a graph of atoms connected to M nearest neighbors, with M set to 12 for the toy system and 20 for the Si-Au and PEO/LiTFSI systems.Neighbor distances are represented using radial basis functions with μ_t = t·0.2 Å and σ = 0.2 Å under periodic boundary conditions.Source: METHODS · p. 12
  • The graph convolution uses attention over neighboring atom and edge embeddings, followed by a nonlinear node embedding and average pooling over target atoms.The attention layer reweights neighbor contributions; the pooled embeddings represent the target-atom set.Source: METHODS · p. 12
  • Eigenvalues of the transition matrix yield relaxation timescales, and the smallest lag time τ* at which they become constant is selected for the Markovian model.The timescales are evaluated across lag times and remain constant for τ > τ*.Source: METHODS · pp. 12–13
  • State-weighted radial distribution functions are calculated by weighting neighbor counts according to the reference particle’s probability of occupying each state.The state-specific density is also used in the calculation.Source: METHODS · p. 13
  • For lithium conduction, the method estimates transition-specific mean-square displacement and diffusion, then uses the Koopman matrix and cluster Nernst–Einstein equation to calculate transition contributions.The state charges and stationary state distribution enter the contribution calculation.Source: METHODS · pp. 13–14
  • The toy-system MD used a 200 ns trajectory at 64 K, while the Si-Au interface simulations ran for 25 ns at the eutectic point of 629 K and 23.4% Si.The toy system froze sulfur atoms; atomic positions were sampled every 0.1 ps for the toy system and every 20 ps for Si-Au.Source: METHODS · p. 14
  • The algorithm scales as O(NMK), where N is the atom count, M the number of neighbors, and K the neural-network depth.The trajectories and implementation code are identified as available online.Source: METHODS · pp. 14–15

SUPPLEMENTARY NOTES

The supplementary notes describe how the graph architecture handles complex local environments, how local transitions inform global dynamics, and how state charges are estimated.

SUPPLEMENTARY NOTES

  • A gated attention layer reweights nearest-neighbor connections, allowing simple nearest-neighbor graphs to represent local environments that include non-covalent interactions.The neighbor count is chosen large enough to include those interactions, and the learned weights relate to bond length and atom types.Source: SUPPLEMENTARY NOTES · p. 27
  • The FCC toy-system global transition matrix is constructed from local octahedral- and tetrahedral-site stay probabilities, but its comparison with observed global dynamics is limited by trajectory size and approximate transition assumptions.The model treats same-type neighboring-site transition probabilities as zero even though they are not strictly zero at a given lag time.Source: SUPPLEMENTARY NOTES · pp. 27–28
  • State charge in PEO/LiTFSI is estimated by integrating charge density within the first solvation shell, whose boundary is set from a Gaussian fit to the state-weighted nitrogen distribution.The shell edge is defined as the Gaussian mean plus three standard deviations.Source: SUPPLEMENTARY NOTES · p. 28

SUPPLEMENTARY TABLES

The supplementary tables cover state-level charge and transition-level diffusion coefficients in PEO/LiTFSI.

SUPPLEMENTARY TABLES

  • Supplementary Table 1 reports the charge carried by each state in PEO/LiTFSI.Source: Table 1 · p. 29
  • Supplementary Table 2 reports diffusion coefficients for each PEO/LiTFSI state transition at a stated lag time.Source: Table 2 · p. 29

SUPPLEMENTARY FIGURES

The supplementary figures concern lithium relaxation in an FCC lattice, silicon-state order parameters at an interface, and state-weighted local structure in a polymer electrolyte.

SUPPLEMENTARY FIGURES

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