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Unveiling the predictive power of static structure in glassy systems

Nature Physics volume 16, pages 448–454 (2020)Cite this article

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An Author Correction to this article was published on 16 April 2020

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Abstract

Despite decades of theoretical studies, the nature of the glass transition remains elusive and debated, while the existence of structural predictors of its dynamics is a major open question. Recent approaches propose inferring predictors from a variety of human-defined features using machine learning. Here we determine the long-time evolution of a glassy system solely from the initial particle positions and without any handcrafted features, using graph neural networks as a powerful model. We show that this method outperforms current state-of-the-art methods, generalizing over a wide range of temperatures, pressures and densities. In shear experiments, it predicts the locations of rearranging particles. The structural predictors learned by our network exhibit a correlation length that increases with larger timescales to reach the size of our system. Beyond glasses, our method could apply to many other physical systems that map to a graph of local interaction.

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Fig. 1: Simulations.
Fig. 2: Model architecture.
Fig. 3: Thermal experiments results.
Fig. 4: Shear-stress experiment results.
Fig. 5: Analysis of the graph network at T = 0.44.

Data availability

The data represented in Figs. 1, 3a–d, 4a and 5, and Extended Data Figs. 1, 3 and 7 are available as Source Data. Training data at all four temperatures studied in the text are available at https://github.com/deepmind/deepmind-research/tree/master/glassy_dynamics. All other data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

Code availability

Source code for training and evaluating our graph network is available at https://github.com/deepmind/deepmind-research/tree/master/glassy_dynamics.

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Acknowledgements

We thank F. Zamponi for critical input on this work, and our colleagues A. Ballard, P. Battaglia, J. Jumper, J. Kirkpatrick, N. Rabinowitz, A. Sanchez-Gonzalez, A. Senior and P. Wirnsberger for many useful discussions.

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Author notes

  1. These authors contributed equally: V. Bapst and T. Keck.

Authors and Affiliations

  1. DeepMind, London, UK

    V. Bapst, T. Keck, A. Grabska-Barwińska, C. Donner, A. Obika, A. W. R. Nelson, T. Back, D. Hassabis & P. Kohli

  2. Google Brain, Mountain View, CA, USA

    E. D. Cubuk & S. S. Schoenholz

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Contributions

V.B. conceived and led the overall study. V.B., T.K., A.G.-B. and C.D. created the data, trained the machine learning models and analysed the results. V.B., T.K., A.G.-B. and C.D. wrote the paper with contributions from E.D.C., S.S.S., T.B. and P.K. and comments from all other authors. E.D.C. and S.S.S. provided advice on the physics of the system. A.O., A.W.R.N., T.B., D.H. and P.K. managed and coordinated the overall project.

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Correspondence to V. Bapst.

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The authors declare no competing interests.

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Peer review information Nature Physics thanks Giulio Biroli and Vincenzo Vitelli for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data

Extended Data Fig. 1 Ablation of the dataset size.

Pearson correlation coefficient (left) and accuracy metric (right) for the graph neural network trained on different number of training examples. Each training example is augmented by applying the 24 symmetries of the box.

Extended Data Fig. 2 Effects of the edge thresholds and number of recurrences on the graph network’s performance.

Pearson correlation coefficient for the ‘none’ network (no features, top) and the default network (distance and type features, bottom) for the ballistic, glassy and diffusive timescales (from left to right). Each point shows the median value of 3-10 independently trained networks. While in the first case there are some sharp peaks upon varying the edge threshold, in the second case the prediction monotonously increases with the edge threshold. Note that the prediction’s quality always increases with the number of recurrences.

Extended Data Fig. 3 Correlation coefficients for all temperatures and timescales.

Pearson correlation coefficients for the machine learning methods and physics baselines, for the 4 different temperatures considered for training. The glassy timescale is indicated by a dashed line on each plot. Each point and its error bars shows the median, best and worst of ten independently-trained models.

Extended Data Fig. 4 GNN samples.

Qualitative results for the first 10 test-data configurations (columns) at the 10 investigated times-scales (rows) for T = 0.44. Linear interpolation of the propensity predicted by the GNN and the 10 % most mobile particles (black) in a two-dimensional slice through the simulation box.

Extended Data Fig. 5 Soft modes samples.

Qualitative results for the first 10 test-data configurations (columns) at the 10 investigated times-scales (rows) for T = 0.44. Linear interpolation of the propensity predicted by the SM baseline and the 10 % most mobile particles (black) in a two-dimensional slice through the simulation box.

Extended Data Fig. 6 Ground truth samples.

Qualitative results for the first 10 test-data configurations (columns) at the 10 investigated times-scales (rows) for T = 0.44. Linear interpolation of the ground truth and the 10 % most mobile particles (black) in a two-dimensional slice through the simulation box.

Extended Data Fig. 7 Propensity distributions.

Propensity distribution of type A particles for different state points at \(\tau_{\textrm{g}}\): a) the mean expected displacement and b) the predicted displacements. With decreasing temperature, the tails of the distributions become more pronounced.

Extended Data Fig. 8 Shell ablation experiment.

Shell ablation experiments for different temperatures. Ten models are shown per condition, their median is represented with the thick dashed line. For the ballistic regime, two shells are enough for the correct prediction. Only in the coolest regime (T=0.44), an extra shell improves the result. As the temperature cools, the number of shells required for the correct prediction grows from about three for T=0.56 to five at T=0.44. The diffusive regime seems to require fewer shells.

Extended Data Fig. 9 Shell perturbation experiment.

Edge perturbation experiments for all temperatures examined, as in Fig. 5c, ten models shown per condition. Note that the number of edges goes down at higher temperatures due to the changing box size.

Extended Data Fig. 10 Linear propensity prediction.

Linear regression on the number of neighbouring particles within a sphere of a given size (x-axis). Results are shown for different S(q,t) values, and different temperatures (colour). Linear prediction gets easier with time and lower temperature. Nearest neighbours matter most for the ballistic regime, whereas for glassy and diffusive regime, best discrimination is achieved for larger spheres. There, wavy pattern shifts with temperature. The shift gets removed by re-scaling the x-axis to match the box size of all four conditions.

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Source Data Fig. 5

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Source Data Extended Data Fig. 1

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Source Data Extended Data Fig. 7

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Bapst, V., Keck, T., Grabska-Barwińska, A. et al. Unveiling the predictive power of static structure in glassy systems. Nat. Phys. 16, 448–454 (2020). https://doi.org/10.1038/s41567-020-0842-8

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