In the quest to understand how structure and dynamics are connected in glasses, a number of machine learning based methods have been developed that predict dynamics in supercooled liquids. These methods include both increasingly complex machine learning techniques and increasingly sophisticated descriptors used to describe the environment around particles. In many cases, both the chosen machine learning technique and choice of structural descriptors are varied simultaneously, making it hard to quantitatively compare the performance of different machine learning approaches. Here, we use three different machine learning algorithms—linear regression, neural networks, and graph neural networks—to predict the dynamic propensity of a glassy binary hard-sphere mixture using as structural input a recursive set of order parameters recently introduced by Boattini et al. [Phys. Rev. Lett. 127, 088007 (2021)]. As we show, when these advanced descriptors are used, all three methods predict the dynamics with nearly equal accuracy. However, the linear regression is orders of magnitude faster to train, making it by far the method of choice.

1.
L.
Berthier
and
G.
Biroli
, “
Theoretical perspective on the glass transition and amorphous materials
,”
Rev. Mod. Phys.
83
,
587
(
2011
).
2.
C. P.
Royall
and
S. R.
Williams
, “
The role of local structure in dynamical arrest
,”
Phys. Rep.
560
,
1
(
2015
).
3.
H.
Tanaka
,
H.
Tong
,
R.
Shi
, and
J.
Russo
, “
Revealing key structural features hidden in liquids and glasses
,”
Nat. Rev. Phys.
1
,
333
348
(
2019
).
4.
E. D.
Cubuk
,
S. S.
Schoenholz
,
J. M.
Rieser
,
B. D.
Malone
,
J.
Rottler
,
D. J.
Durian
,
E.
Kaxiras
, and
A. J.
Liu
, “
Identifying structural flow defects in disordered solids using machine-learning methods
,”
Phys. Rev. Lett.
114
,
108001
(
2015
).
5.
V.
Bapst
,
T.
Keck
,
A.
Grabska-Barwińska
,
C.
Donner
,
E. D.
Cubuk
,
S. S.
Schoenholz
,
A.
Obika
,
A. W. R.
Nelson
,
T.
Back
,
D.
Hassabis
, and
P.
Kohli
, “
Unveiling the predictive power of static structure in glassy systems
,”
Nat. Phys.
16
,
448
(
2020
).
6.
E.
Boattini
,
S.
Marín-Aguilar
,
S.
Mitra
,
G.
Foffi
,
F.
Smallenburg
, and
L.
Filion
, “
Autonomously revealing hidden local structures in supercooled liquids
,”
Nat. Commun.
11
,
5479
(
2020
).
7.
J.
Paret
,
R. L.
Jack
, and
D.
Coslovich
, “
Assessing the structural heterogeneity of supercooled liquids through community inference
,”
J. Chem. Phys.
152
,
144502
(
2020
).
8.
E.
Boattini
,
F.
Smallenburg
, and
L.
Filion
, “
Averaging local structure to predict the dynamic propensity in supercooled liquids
,”
Phys. Rev. Lett.
127
,
088007
(
2021
).
9.
S. S.
Schoenholz
,
E. D.
Cubuk
,
D. M.
Sussman
,
E.
Kaxiras
, and
A. J.
Liu
, “
A structural approach to relaxation in glassy liquids
,”
Nat. Phys.
12
,
469
(
2016
).
10.
D.
Richard
,
M.
Ozawa
,
S.
Patinet
,
E.
Stanifer
,
B.
Shang
,
S. A.
Ridout
,
B.
Xu
,
G.
Zhang
,
P. K.
Morse
,
J.-L.
Barrat
 et al, “
Predicting plasticity in disordered solids from structural indicators
,”
Phys. Rev. Mater.
4
,
113609
(
2020
).
11.
S.
Marín-Aguilar
,
H. H.
Wensink
,
G.
Foffi
, and
F.
Smallenburg
, “
Tetrahedrality dictates dynamics in hard sphere mixtures
,”
Phys. Rev. Lett.
124
,
208005
(
2020
).
12.
D. C.
Rapaport
, “
The event-driven approach to N-body simulation
,”
Prog. Theor. Phys. Suppl.
178
,
5
14
(
2009
).
13.
A.
Widmer-Cooper
,
P.
Harrowell
, and
H.
Fynewever
, “
How reproducible are dynamic heterogeneities in a supercooled liquid?
,”
Phys. Rev. Lett.
93
,
135701
(
2004
).
14.
A.
Widmer-Cooper
and
P.
Harrowell
, “
On the study of collective dynamics in supercooled liquids through the statistics of the isoconfigurational ensemble
,”
J. Chem. Phys.
126
,
154503
(
2007
).
15.
W.
Lechner
and
C.
Dellago
, “
Accurate determination of crystal structures based on averaged local bond order parameters
,”
J. Chem. Phys.
129
,
114707
(
2008
).
16.
P. J.
Steinhardt
,
D. R.
Nelson
, and
M.
Ronchetti
, “
Bond-orientational order in liquids and glasses
,”
Phys. Rev. B
28
,
784
(
1983
).
17.
C. M.
Bishop
,
Pattern Recognition and Machine Learning (Information Science and Statistics)
(
Springer-Verlag
,
2006
).
18.
A.
Paszke
,
S.
Gross
,
F.
Massa
,
A.
Lerer
,
J.
Bradbury
,
G.
Chanan
,
T.
Killeen
,
Z.
Lin
,
N.
Gimelshein
,
L.
Antiga
 et al, “
PyTorch: An imperative style, high-performance deep learning library
,”
Advances in Neural Information Processing Systems
(
Curran Associates
,
2019
), Vol. 32, p.
8026
.
19.
D. P.
Kingma
and
J.
Ba
, “
Adam: A method for stochastic optimization
,” arXiv:1412.6980 (
2014
).
20.
N.
Srivastava
,
G.
Hinton
,
A.
Krizhevsky
,
I.
Sutskever
, and
R.
Salakhutdinov
, “
Dropout: A simple way to prevent neural networks from overfitting
,”
J. Mach. Learn. Res.
15
,
1929
(
2014
); available at http://jmlr.org/papers/v15/srivastava14a.html.
21.
P. W.
Battaglia
,
J. B. C.
Hamrick
,
V.
Bapst
,
A.
Sanchez-Gonzalez
,
V.
Zambaldi
,
M.
Malinowski
,
A.
Tacchetti
,
D.
Raposo
,
A.
Santoro
,
R.
Faulkner
,
C.
Gulcehre
,
F.
Song
,
A.
Ballard
,
J.
Gilmer
,
G. E.
Dahl
,
A.
Vaswani
,
K.
Allen
,
C.
Nash
,
V. J.
Langston
,
C.
Dyer
,
N.
Heess
,
D.
Wierstra
,
P.
Kohli
,
M.
Botvinick
,
O.
Vinyals
,
Y.
Li
, and
R.
Pascanu
, “
Relational inductive biases, beep learning, and graph networks
,” arXiv:1806.01261 (
2018
).
22.
P.
Battaglia
,
R.
Pascanu
,
M.
Lai
,
D.
Jimenez Rezende
 et al, “
Interaction networks for learning about objects, relations and physics
,”
Advances in Neural Information Processing Systems
(
Curran Associates
,
2016
), Vol. 29, p.
4502
.
23.
F.
Scarselli
,
M.
Gori
,
A. C.
Tsoi
,
M.
Hagenbuchner
, and
G.
Monfardini
, “
The graph neural network model
,”
IEEE Trans. Neural Networks
20
,
61
(
2009
).
24.
U.
Buchenau
, “
Thermodynamics and dynamics of the inherent states at the glass transition
,”
J. Non-Cryst. Solids
407
,
179
(
2015
).
25.
D. A.
Stariolo
,
J. J.
Arenzon
, and
G.
Fabricius
, “
Inherent structures dynamics in glasses: A comparative study
,”
Physica A
340
,
316
(
2004
).
26.
F. H.
Stillinger
and
T. A.
Weber
, “
Hidden structure in liquids
,”
Phys. Rev. A
25
,
978
(
1982
).
27.
A. J.
Dunleavy
,
K.
Wiesner
,
R.
Yamamoto
, and
C. P.
Royall
, “
Mutual information reveals multiple structural relaxation mechanisms in a model glass former
,”
Nat. Commun.
6
,
6089
6098
(
2015
).
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