Exploring mesoscopic physical phenomena has always been a challenge for brute-force all-atom molecular dynamics simulations. Although recent advances in computing hardware have improved the accessible length scales, reaching mesoscopic timescales is still a significant bottleneck. Coarse-graining of all-atom models allows robust investigation of mesoscale physics with a reduced spatial and temporal resolution but preserves desired structural features of molecules, unlike continuum-based methods. Here, we present a hybrid bond-order coarse-grained forcefield (HyCG) for modeling mesoscale aggregation phenomena in liquid–liquid mixtures. The intuitive hybrid functional form of the potential offers interpretability to our model, unlike many machine learning based interatomic potentials. We parameterize the potential with the continuous action Monte Carlo Tree Search (cMCTS) algorithm, a reinforcement learning (RL) based global optimizing scheme, using training data from all-atom simulations. The resulting RL-HyCG correctly describes mesoscale critical fluctuations in binary liquid–liquid extraction systems. cMCTS, the RL algorithm, accurately captures the mean behavior of various geometrical properties of the molecule of interest, which were excluded from the training set. The developed potential model along with the RL-based training workflow could be applied to explore a variety of other mesoscale physical phenomena that are typically inaccessible to all-atom molecular dynamics simulations.

1.
Y.
Shibuta
,
S.
Sakane
,
E.
Miyoshi
,
S.
Okita
,
T.
Takaki
, and
M.
Ohno
, “
Heterogeneity in homogeneous nucleation from billion-atom molecular dynamics simulation of solidification of pure metal
,”
Nat. Commun.
8
,
10
(
2017
).
2.
J.
Jung
,
W.
Nishima
,
M.
Daniels
,
G.
Bascom
,
C.
Kobayashi
,
A.
Adedoyin
,
M.
Wall
,
A.
Lappala
,
D.
Phillips
,
W.
Fischer
et al, “
Scaling molecular dynamics beyond 100,000 processor cores for large-scale biophysical simulations
,”
J. Comput. Chem.
40
,
1919
1930
(
2019
).
3.
F.
Noé
, “
Machine learning for molecular dynamics on long timescales
,” in
Machine Learning Meets Quantum Physics
(
Springer
,
2020
), pp.
331
372
; available at https://link.springer.com/chapter/10.1007/978-3-030-40245-7_16.
4.
A.
Chandra
,
P.
Keblinski
,
O.
Sahni
, and
A. A.
Oberai
, “
A continuum framework for modeling liquid-vapor interfaces out of local thermal equilibrium
,”
Int. J. Heat Mass Transfer
144
,
118597
(
2019
).
5.
A.
Chandra
,
Z.
Liang
,
A. A.
Oberai
,
O.
Sahni
, and
P.
Keblinski
, “
On the applicability of continuum scale models for ultrafast nanoscale liquid-vapor phase change
,”
Int. J. Multiphase Flow
135
,
103508
(
2021
).
6.
A.
Chandra
,
Interfacial Relations in Liquid-Vapor Phase Change Processes: An Atomistic and Continuum Study
(
Rensselaer Polytechnic Institute
,
2021
).
7.
H.
Talebi
,
M.
Silani
,
S. P. A.
Bordas
,
P.
Kerfriden
, and
T.
Rabczuk
, “
A computational library for multiscale modeling of material failure
,”
Comput. Mech.
53
,
1047
1071
(
2014
).
8.
R. E.
Rudd
and
J. Q.
Broughton
, “
Coarse-grained molecular dynamics and the atomic limit of finite elements
,”
Phys. Rev. B
58
,
R5893
(
1998
).
9.
S. Y.
Joshi
and
S. A.
Deshmukh
, “
A review of advancements in coarse-grained molecular dynamics simulations
,”
Mol. Simul.
47
,
786
803
(
2021
).
10.
W.
Peng
,
A.
Chandra
,
P.
Keblinski
, and
J. L.
Moran
, “
Thermal transport dynamics in active heat transfer fluids (AHTF)
,”
J. Appl. Phys.
129
,
174702
(
2021
).
11.
D. S.
Sholl
and
R. P.
Lively
, “
Seven chemical separations to change the world
,”
Nature
532
,
435
(
2016
).
12.
T.
Cheisson
and
E. J.
Schelter
, “
Rare earth elements: Mendeleev’s bane, modern marvels
,”
Science
363
,
489
493
(
2019
).
13.
T.
Liu
,
K. R.
Johnson
,
S.
Jansone-Popova
, and
D.-e.
Jiang
, “
Advancing rare-earth separation by machine learning
,”
JACS Au
2
,
1428
1434
(
2022
).
14.
R. J.
Ellis
,
Y.
Meridiano
,
J.
Muller
,
L.
Berthon
,
P.
Guilbaud
,
N.
Zorz
,
M. R.
Antonio
,
T.
Demars
, and
T.
Zemb
, “
Complexation-induced supramolecular assembly drives metal-ion extraction
,”
Chem. - Eur. J.
20
,
12796
12807
(
2014
).
15.
A. G.
Baldwin
,
A. S.
Ivanov
,
N. J.
Williams
,
R. J.
Ellis
,
B. A.
Moyer
,
V. S.
Bryantsev
, and
J. C.
Shafer
, “
Outer-sphere water clusters tune the lanthanide selectivity of diglycolamides
,”
ACS Cent. Sci.
4
,
739
747
(
2018
).
16.
R. J.
Ellis
and
M. R.
Antonio
, “
Coordination structures and supramolecular architectures in a cerium (iii)–malonamide solvent extraction system
,”
Langmuir
28
,
5987
5998
(
2012
).
17.
Z.
Lu
,
S.
Dourdain
, and
S.
Pellet-Rostaing
, “
Understanding the effect of the phase modifier n-octanol on extraction, aggregation, and third-phase appearance in solvent extraction
,”
Langmuir
36
,
12121
12129
(
2020
).
18.
D.
Sheyfer
,
Q.
Zhang
,
J.
Lal
,
T.
Loeffler
,
E. M.
Dufresne
,
A. R.
Sandy
,
S.
Narayanan
,
S. K. R. S.
Sankaranarayanan
,
R.
Szczygiel
,
P.
Maj
et al, “
Nanoscale critical phenomena in a complex fluid studied by x-ray photon correlation spectroscopy
,”
Phys. Rev. Lett.
125
,
125504
(
2020
).
19.
D.
Sheyfer
,
M. J.
Servis
,
Q.
Zhang
,
J.
Lal
,
T.
Loeffler
,
E. M.
Dufresne
,
A. R.
Sandy
,
S.
Narayanan
,
S. K. R. S.
Sankaranarayanan
,
R.
Szczygiel
et al, “
Advancing chemical separations: Unraveling the structure and dynamics of phase splitting in liquid–liquid extraction
,”
J. Phys. Chem. B
126
,
2420
2429
(
2022
).
20.
M. J.
Servis
and
G. B.
Stephenson
, “
Mesostructuring in liquid–liquid extraction organic phases originating from critical points
,”
J. Phys. Chem. Lett.
12
,
5807
5812
(
2021
).
21.
B. L.
Bonnett
,
D.
Sheyfer
,
P.
Wimalasiri
,
S.
Nayak
,
J.
Lal
,
Q.
Zhang
,
S.
Seifer
,
G. B.
Stephenson
, and
M. J.
Servis
,
Phys. Chem. Chem. Phys.
25
,
16389
16403
(
2023
).
22.
M. G.
Martin
and
J. I.
Siepmann
, “
Transferable potentials for phase equilibria. 1. United-atom description of n-alkanes
,”
J. Phys. Chem. B
102
,
2569
2577
(
1998
).
23.
P.
Bai
,
M.
Tsapatsis
, and
J. I.
Siepmann
, “
Trappe-zeo: Transferable potentials for phase equilibria force field for all-silica zeolites
,”
J. Phys. Chem. C
117
,
24375
24387
(
2013
).
24.
S. J.
Marrink
,
H. J.
Risselada
,
S.
Yefimov
,
D. P.
Tieleman
, and
A. H.
De Vries
, “
The MARTINI force field: Coarse grained model for biomolecular simulations
,”
J. Phys. Chem. B
111
,
7812
7824
(
2007
).
25.
P. C. T.
Souza
,
S.
Thallmair
,
P.
Conflitti
,
C.
Ramírez-Palacios
,
R.
Alessandri
,
S.
Raniolo
,
V.
Limongelli
, and
S. J.
Marrink
, “
Protein–ligand binding with the coarse-grained martini model
,”
Nat. Commun.
11
,
3714
(
2020
).
26.
A.
Ganesan
,
M. L.
Coote
, and
K.
Barakat
, “
Molecular dynamics-driven drug discovery: Leaping forward with confidence
,”
Drug Discovery Today
22
,
249
269
(
2017
).
27.
X.
Liu
,
D.
Shi
,
S.
Zhou
,
H.
Liu
,
H.
Liu
, and
X.
Yao
, “
Molecular dynamics simulations and novel drug discovery
,”
Expert Opin. Drug Discovery
13
,
23
37
(
2018
).
28.
S.
Ahmad
,
B. F.
Johnston
,
S. P.
Mackay
,
A. G.
Schatzlein
,
P.
Gellert
,
D.
Sengupta
, and
I. F.
Uchegbu
, “
In silico modelling of drug–polymer interactions for pharmaceutical formulations
,”
J. R. Soc., Interface
7
,
S423
S433
(
2010
).
29.
S.
Kmiecik
,
D.
Gront
,
M.
Kolinski
,
L.
Wieteska
,
A. E.
Dawid
, and
A.
Kolinski
, “
Coarse-grained protein models and their applications
,”
Chem. Rev.
116
,
7898
7936
(
2016
).
30.
L.
Monticelli
,
S. K.
Kandasamy
,
X.
Periole
,
R. G.
Larson
,
D. P.
Tieleman
, and
S.-J.
Marrink
, “
The MARTINI coarse-grained force field: Extension to proteins
,”
J. Chem. Theory Comput.
4
,
819
834
(
2008
).
31.
P. C. T.
Souza
,
R.
Alessandri
,
J.
Barnoud
,
S.
Thallmair
,
I.
Faustino
,
F.
Grünewald
,
I.
Patmanidis
,
H.
Abdizadeh
,
B. M. H.
Bruininks
,
T. A.
Wassenaar
et al, “
Martini 3: A general purpose force field for coarse-grained molecular dynamics
,”
Nat. Methods
18
,
382
388
(
2021
).
32.
P.
Español
and
P. B.
Warren
, “
Perspective: Dissipative particle dynamics
,”
J. Chem. Phys.
146
,
150901
(
2017
).
33.
R. D.
Groot
and
P. B.
Warren
, “
Dissipative particle dynamics: Bridging the gap between atomistic and mesoscopic simulation
,”
J. Chem. Phys.
107
,
4423
4435
(
1997
).
34.
P. J.
Hoogerbrugge
and
J. M. V. A.
Koelman
, “
Simulating microscopic hydrodynamic phenomena with dissipative particle dynamics
,”
Europhys. Lett.
19
,
155
(
1992
).
35.
W.
Wang
and
R.
Gómez-Bombarelli
, “
Coarse-graining auto-encoders for molecular dynamics
,”
npj Comput. Mater.
5
,
125
(
2019
).
36.
J.
Tersoff
, “
New empirical approach for the structure and energy of covalent systems
,”
Phys. Rev. B
37
,
6991
7000
(
1988
).
37.
H.
Chan
,
M. J.
Cherukara
,
B.
Narayanan
,
T. D.
Loeffler
,
C.
Benmore
,
S. K.
Gray
, and
S. K. R. S.
Sankaranarayanan
, “
Machine learning coarse grained models for water
,”
Nat. Commun.
10
,
379
(
2019
).
38.
S.
Manna
,
T. D.
Loeffler
,
R.
Batra
,
S.
Banik
,
H.
Chan
,
B.
Varughese
,
K.
Sasikumar
,
M.
Sternberg
,
T.
Peterka
,
M. J.
Cherukara
et al, “
Learning in continuous action space for developing high dimensional potential energy models
,”
Nat. Commun.
13
,
368
(
2022
).
39.
S.
Banik
,
T. D.
Loeffler
,
R.
Batra
,
H.
Singh
,
M. J.
Cherukara
, and
S. K. R. S.
Sankaranarayanan
, “
Learning with delayed rewards—A case study on inverse defect design in 2D materials
,”
ACS Appl. Mater. Interfaces
13
,
36455
36464
(
2021
).
40.
H.
Chan
,
B.
Narayanan
,
M.
Cherukara
,
T. D.
Loeffler
,
M. G.
Sternberg
,
A.
Avarca
, and
S. K. R. S.
Sankaranarayanan
, “
BLAST: Bridging length/timescales via atomistic simulation toolkit
,”
MRS Adv.
6
,
21
31
(
2021
).
41.
C. B.
Browne
,
E.
Powley
,
D.
Whitehouse
,
S. M.
Lucas
,
P. I.
Cowling
,
P.
Rohlfshagen
,
S.
Tavener
,
D.
Perez
,
S.
Samothrakis
, and
S.
Colton
, “
A survey of Monte Carlo tree search methods
,”
IEEE Trans. Comput. Intell. AI Games
4
,
1
43
(
2012
).
42.
G.
Chaslot
,
S.
Bakkes
,
I.
Szita
, and
P.
Spronck
, “
Monte-Carlo tree search: A new framework for game AI
,” in
Proceedings of the AAAI Conference onArtificial Intelligence and Interactive Digital Entertainment, 2008;
available at
https://ojs.aaai.org/index.php/AIIDE/article/view/18700/18475.
43.
M.
Świechowski
,
K.
Godlewski
,
B.
Sawicki
, and
J.
Mańdziuk
, “
Monte Carlo tree search: A review of recent modifications and applications
,”
Artif. Intell. Rev.
56
,
2497
2562
(
2023
).
44.
T. M.
Dieb
,
S.
Ju
,
K.
Yoshizoe
,
Z.
Hou
,
J.
Shiomi
, and
K.
Tsuda
, “
MDTS: Automatic complex materials design using Monte Carlo tree search
,”
Sci. Technol. Adv. Mater.
18
,
498
503
(
2017
).
45.
J.
Bergstra
,
D.
Yamins
, and
D.
Cox
, “
Making a science of model search: Hyperparameter optimization in hundreds of dimensions for vision architectures
,” in
International Conference on Machine Learning
(
PMLR
,
2013
), pp.
115
123
.
46.
M. J.
Servis
,
M.
Piechowicz
,
I. A.
Shkrob
,
L.
Soderholm
, and
A. E.
Clark
, “
Amphiphile organization in organic solutions: An alternative explanation for small-angle x-ray scattering features in malonamide/alkane mixtures
,”
J. Phys. Chem. B
124
,
10822
10831
(
2020
).
47.
L.
Lefrançois
,
J.-J.
Delpuech
,
M.
Hébrant
,
J.
Chrisment
, and
C.
Tondre
, “
Aggregation and protonation phenomena in third phase formation: An NMR study of the quaternary malonamide/dodecane/nitric acid/water system
,”
J. Phys. Chem. B
105
,
2551
2564
(
2001
).
48.
M. J.
Servis
,
B.
Sadhu
,
L.
Soderholm
, and
A. E.
Clark
, “
Amphiphile conformation impacts aggregate morphology and solution structure across multiple lengthscales
,”
J. Mol. Liq.
345
,
117743
(
2022
).
49.
A. P.
Thompson
,
H. M.
Aktulga
,
R.
Berger
,
D. S.
Bolintineanu
,
W. M.
Brown
,
P. S.
Crozier
,
P. J.
in’t Veld
,
A.
Kohlmeyer
,
S. G.
Moore
,
T. D.
Nguyen
,
R.
Shan
,
M. J.
Stevens
,
J.
Tranchida
,
C.
Trott
, and
S. J.
Plimpton
, “
LAMMPS—A flexible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales
,”
Comput. Phys. Commun.
271
,
108171
(
2022
).
50.
J.
Wang
et al.,
Development and testing of a general amber force field
,”
J. Comput. Chem.
25
(9)
,
1157
1174
(
2004
).

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