Classifying the age of a glass based on structural properties: A machine learning approach

Giulia Janzen, Casper Smit, Samantha Visbeek, Vincent E. Debets, Chengjie Luo, Cornelis Storm, Simone Ciarella, and Liesbeth M. C. Janssen

Phys. Rev. Materials 8, 025602 – Published 21 February 2024

Abstract

It is well established that physical aging of amorphous solids is governed by a marked change in dynamical properties as the material becomes older. Conversely, structural properties such as the radial distribution function exhibit only a very weak age dependence, usually deemed negligible with respect to the numerical noise. Here we demonstrate that the extremely weak age-dependent changes in structure are, in fact, sufficient to reliably assess the age of a glass with the support of machine learning. We employ a supervised learning method to predict the age of a glass based on the system's instantaneous radial distribution function. Specifically, we train a multilayer perceptron for a model glass former quenched to different temperatures and find that this neural network can accurately classify the age of our system across at least 4 orders of magnitude in time. Our analysis also reveals which structural features encode the most useful information. Overall, this work shows that through the aid of machine learning, a simple structure-dynamics link can, indeed, be established for physically aged glasses.

Received 1 March 2023
Accepted 8 January 2024

DOI:https://doi.org/10.1103/PhysRevMaterials.8.025602

Physics Subject Headings (PhySH)

Aging

Glasses

Machine learning

Statistical Physics & ThermodynamicsPolymers & Soft Matter

Authors & Affiliations

Giulia Janzen ^1,2, Casper Smit ^1,3,*, Samantha Visbeek ^1,3,*, Vincent E. Debets^1,2, Chengjie Luo^1,2, Cornelis Storm^1,2, Simone Ciarella ^1,2,4,5,†, and Liesbeth M. C. Janssen ^1,2,‡

¹Department of Applied Physics, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
²Institute for Complex Molecular Systems, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
³Institute of Physics, University of Amsterdam, Science Park 904, Amsterdam 1098 XH, The Netherlands
⁴Laboratoire de Physique de l'Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, 75005 Paris, France
⁵Netherlands eScience Center, Amsterdam 1098 XG, The Netherlands

^*These authors contributed equally to this work.
^†simoneciarella@gmail.com
^‡l.m.c.janssen@tue.nl

Article Text (Subscription Required)

Click to Expand

Supplemental Material (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 8, Iss. 2 — February 2024

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Age dependence in structural and dynamical properties. Snapshots after a temperature quench for waiting times (a) $t_{w} = 1$ and (b) $t_{w} = 1000$ . (c) Radial distribution function for A particles $g_{A A} (r)$ and (d) mean-square displacement $〈 δ r^{2} (t_{w}, t + t_{w}) 〉$ at fixed quenching temperature $T_{q} = 0.375$ for waiting times $t_{w} = 1, 10, 100, 1000$ .
Reuse & Permissions
Figure 2
The F1 score as a function of the number of features $N_{f}$ used in the machine learning model. The blue dashed line corresponds to the F1 score shown in Table 2 obtained with the full dataset (120 features). The orange squares represent the F1 score obtained with the principal components selected by PCA, the pink dots correspond to the F1 score obtained with the most important features selected with a SHAP analysis, and the light blue triangles represent the F1 score gained using the features that change the most on average. (a) Quenching temperature $T_{q} = 0.1$ . The SHAP analysis shows that the six most important features are $g_{A A} (1.05)$ , $g_{A A} (1.65)$ , $g_{A B} (1.35)$ , $g_{A A} (1.80)$ , $g_{A A} (1.75)$ , and $g_{A B} (1.30)$ . The six features that change the most on average are $g_{A A} (1.00)$ , $g_{B B} (2.00)$ , $g_{A B} (1.25)$ , $g_{B B} (2.05)$ , $g_{A A} (1.60)$ , and $g_{A B} (1.40)$ . (b) Quenching temperature $T_{q} = 0.25$ . The SHAP analysis shows that the six most important features are $g_{A A} (1.00)$ , $g_{A A} (1.65)$ , $g_{A B} (1.60)$ , $g_{A B} (1.55)$ , $g_{B B} (1.80)$ , and $g_{A A} (1.05)$ . The six features that change the most on average are $g_{A A} (1.00)$ , $g_{A B} (1.55)$ , $g_{B B} (1.00)$ , $g_{B B} (2.25)$ , $g_{A B} (1.40)$ , and $g_{B B} (1.05)$ . (c) Quenching temperature $T_{q} = 0.375$ . The SHAP analysis shows that the six most important features are $g_{B B} (1.50)$ , $g_{A A} (1.00)$ , $g_{A A} (2.45)$ , $g_{A B} (1.60)$ , $g_{B B} (1.55)$ , and $g_{B B} (1.45)$ . The six features that change the most on average are $g_{B B} (1.00)$ , $g_{B B} (1.55)$ , $g_{B B} (1.05)$ , $g_{B B} (1.50)$ , $g_{B B} (2.35)$ , and $g_{B B} (2.30)$ .
Reuse & Permissions
Figure 3
Variation of the radial distribution function $〈 δ g_{i} (t_{w}, r) 〉$ as a function of age $t_{w}$ . The symbols represent the six features that change the most on average for a system at $T_{q} = 0.1$ . In the inset the red diamonds show the feature that changes the most, $〈 δ g_{A A} (1.00) 〉$ , with its corresponding standard deviation, and the blue dots correspond to the most important feature according to the SHAP analysis, $〈 δ g_{A A} (1.05) 〉$ , and its standard deviation.
Reuse & Permissions
Figure 4
The F1 score as a function of the quenching temperature used to test the model $T_{q_{test}}$ . The purple line shows the neural network $M$ trained with $T_{q_{train}} = 0.1, 0.15, 0.2, 0.25, 0.35, 0.375$ , the red line represents $M_{high}$ trained with $T_{q_{train}} = 0.25, 0.35, 0.375$ , and the blue line indicates $M_{low}$ trained for $T_{q_{train}} = 0.1, 0.15, 0.2$ . Each dot corresponds to the F1 score obtained in the test set when $T_{q_{test}} \neq T_{q_{train}}$ . The temperatures used in the test set are $T_{q_{test}} = 0.1, 0.11, 0.12, 0.15, 0.17, 0.2, 0.23, 0.25, 0.27, 0.3, 0.32$ . The inset shows the F1 score when the networks $M$ , $M_{high}$ , and $M_{low}$ are tested with $T_{q_{test}} = T_{q_{train}}$ .
Reuse & Permissions
Figure 5
SHAP-based interpretation of the multilayer perceptron predictions. Here we analyze a neural network $M$ with 12 hidden layers that has $T_{q}$ and ${\hat{g}}_{i} (r)$ as input and is trained with $T_{q_{train}} = 0.1, 0.15, 0.2, 0.25, 0.35, 0.375$ . (a) SHAP beeswarm plot that shows how the most important features impact the model's output. The $x$ position of the dots is determined by the SHAP values of the features, and color is used to display the original value of the features. Partial dependence plot for (b) $T_{q}$ and (c) ${\hat{g}}_{A A} (1.65)$ . The $x$ axis is the value of the feature, and the $y$ axis is the average value of the model output when we fix $T_{q}$ or ${\hat{g}}_{A A} (1.65)$ to a given value. Each class has a label that goes from 0, young glass with $t_{w} = 0$ , to 4, old glass with $10^{3} \leq t_{w} \leq 10^{4}$ . The inset in (c) shows the waiting time $t_{w}$ as a function of ${\hat{g}}_{A A} (1.65)$ . Here we show the actual data for a passive system quenched at $T_{q} = 0.35$ .
Reuse & Permissions

Physical Review Materials