doi.org/10.26434/chemrxiv.12271289.v1
Machine Learning for Accurate Force Calculations in Molecular
Dynamics Simulations
Punyaslok Pattnaik, Shampa Raghunathan, Tarun Kalluri, Prabhakar Bhimalapuram, C. V. Jawahar, U. Deva
Priyakumar
Submitted date: 08/05/2020 • Posted date: 08/05/2020
Licence: CC BY-NC-ND 4.0
Citation information: Pattnaik, Punyaslok; Raghunathan, Shampa; Kalluri, Tarun; Bhimalapuram, Prabhakar;
Jawahar, C. V.; Priyakumar, U. Deva (2020): Machine Learning for Accurate Force Calculations in Molecular
Dynamics Simulations. ChemRxiv. Preprint. https://doi.org/10.26434/chemrxiv.12271289.v1
The computationally expensive nature of ab initio molecular dynamics simulations severely limits its ability to
simulate large system sizes and long time scales, both of which are necessary to imitate experimental
conditions. In this work, we explore an approach to make use of the data obtained using the quantum
mechanical density functional theory (DFT) on small systems and use deep learning to subsequently simulate
large systems by taking liquid argon as a test case. A suitable vector representation was chosen to represent
the surrounding environment of each Ar atom, and a DNetFF machine learning model where, the neural
network was trained to predict the difference in resultant forces obtained by DFT and classical force fields was
introduced. Molecular dynamics simulations were then performed using forces from the neural network for
various system sizes and time scales depending on the properties we calculated. A comparison of properties
obtained from the classical force field and the neural network model was presented alongside available
experimental data to validate the proposed method.
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Machine Learning for Accurate Force
Calculations in Molecular Dynamics Simulations
Punyaslok Pattnaik,
†
Shampa Raghunathan,
†
Tarun Kalluri,
‡
Prabhakar
Bhimalapuram,
†
C. V. Jawahar ,
‡
and U. Deva Priyakumar
⇤,†
†Center for Computational Natural Sciences and Bioinformatics, International Institute of
Information Technology, Hyderabad 500 032, India
‡Center for Visual Information Technology, KCIS, International Institute of Information
Technology, Hyderabad 500 032, India
E-mail: deva@iiit.ac.in
Abstract
The computationally expensive nature of ab initio molecular dynamics simulations
severely limits its ability to simulate large system s i zes and long time scales, both of
which are necessary to imitate experimental conditions. In this work, we explore an
approach to make use of the data obtained using the quantum mechanical density func-
tional theory (DFT) on small systems and use deep learning to subsequently simulate
large systems by taking liquid argon as a test case. A suitable vector representation
was chosen to represent the surroundi ng environment of each Ar atom, and a -NetFF
machine learning model where, the neural network was trained to predict the di↵erence
in result ant forces obtained by DFT and classical force fields was introduced. Molec-
ular dynamics simulations were then performed using forces from the neural network
for various system sizes and time scales depending on the properties we calculated. A
comparison of properties obtained from the classical force field and t h e neural networ k
1
model was presented alongside available experimental data to validate the prop os ed
method.
Introduction
The modeling of a condensed phase system involving chemical pro ce sses s p an n i ng multiple
time and length scales is particularly challenging. Ab initio molecular dynamics ( AIMD )
which explicitly treats elect r on ic degrees of freedom is n at u r al ly the first method of choice,
however computati o n al l y deman d i n g , thus prohibiting its application to large molecular
systems.
1,2
Classical molecular dynamics (MD) simulati on s employing for ce fields can do a
proper sampling of the phase space of large systems (up to million atoms),
3,4
but underlying
interatomic potentials are often not accurate enough to obtain quantitavely accurate results.
Their transferability to situations that were not originally used in the paramet er i za t i on is
questionable, which further limits their accuracy.
The need to construct a multiscale model (considering electronic, nuclear dynamics
5–7
and their coupl i n g to slower, cooperative motions of the system) to capture accurate dy-
namics of chemical processes cannot be overstated.
8–10
The fundamental question is: Can
one quantify the relevance of atomistic models to electronic interactions employing any nu-
merical formalism and how corresponding MD errors reflect emergent features in ab initio
driving forces? One of the most successful approaches relies on quantum mechanical (QM)
calculations on gas-phase (sometimes considering the imp l i cit sol vent model) cluster s to pa-
rameterize a model meant for bulk phase simulations. Another empirical procedure is based
on the minimization of a “loss function” or “objective function” between simulated and
experimental physical properties.
With th e increasing availability of computational resou r ces and d a t a, machine learning
(ML) techniques have been popularly applied to predict quantum mechanical properties.
11–17
AplethoraofsophisticatedMLapproachesexist:Forpredictinggroundstateenergies,ap-
2
proaches, such as, b oosted regression tree algorithms,
18
high-dimensional neural network
potential energy surfaces using symmetry functions,
11
continuous-filter convolutional lay-
ers
17
and single-atom atomic environment vectors (AEV)
13
have been used. Atomization
energies for molecul es have been predicted based on nuclear charges and atomic positions
only.
19
Multiple electronic, ground , an d excited-state properties have also been predicted
simultaneously using Coulomb matrices in conjunction with deep multi-task artificial neural
networks.
14,20
The bag-of-bonds model was used to predict accurate electronic properties
of molecules, such as, their polarizability and molecular frontier orbital energies.
21,22
Using
artificial neural networks (ANNs), energies of molecules have also been predicted as a sum
of intrinsic bond energies, while also providing valuable insight into the relative strengths
of bonds as a function of their molecular environment.
16
ANNs have also been used al on g
with genetic algorithm ( GA) optimization to discover unconventio n a l spin-crossover com-
plexes, which emphasizes their power for discovering new inorganic materials.
23
Recently
an ML model was proposed where a novel molecular descriptor inspired by classical force
fields ter m s – bonds, angles, non-bonded interactions a n d dihedrals to perform geometry
optimizations along with predicting their energies.
24
This model employs feed-forward fully
connected deep neural networks. Graph neural networks were used to predict solvent-solute
interaction map
25
for studying solvation fr ee energies of dru g-l ike m ol ecu les/sol u te. Instead
of applying ML techniques to directly compute prop erties of new molecules through inter-
polation in chemical compound space, recently, ML of force field parameters was performed
for semi-empi r i ca l modeling.
26
In the r ecent years, machine learni n g (ML) has emerged as a potential technique for de-
veloping a new generation of highly accurate force fields (FFs) for simulations of molecules
and materials. Ramprasad and coworkers
27–29
have developed ML-based atomistic force
fields for MD simulations. They have mainly focused on bul k solid-state materials. Another
approach, on-the-fly ML of QM forces in MD simulations was recently reported by Li and
coworkers
30
on bulk Si. The sm ooth overlap of atom i c positions (S OAP) metric has been
3
used to construct potential energy surfaces, and its performance was evaluated for small
silicon clusters.
15
Gaussian ap p r oximation potentials have been used to generate trajectories
for water di mer s, energetics path for a migrating vacancy and the transformation of rhomb o-
hedral graphite to diamond.
31
Another popularly used class of ML-FFs based on Gaussian
process (GP) regression was developed for stduyin g 19-atom Ni nanocluster
32
as well as
adsorption energies of small molecules on NiGa and RhAu nanoclusters.
33,34
Interatomic
potentials for metallic aluminium, carbon and dimer potentials for noble gases have been
reconstructed using neural networks.
35
The e↵ect s of such fitted potentials on the calculation
of physical properties obtained from their trajectories, at di↵erent physical conditions, such
as, temperature and pr es su r e, n e ed to be studied to further reinforce on their fu t u r e applica-
tions. Machine learning is also being successfully used to analyze longtime scale simulation
data on large systems.
36,37
As the area of development of ML-FFs for MD si mulations is expand i n g towards assessing
and improving the accuracy and transferability of the model, learning and predicting atomic
forces have b een receiving notable successes. Because, atomic forces can be seen as true QM
observation within the BO-approximation to abide by the Hellmann-Feynman theorem.
38
The energy of a m ol ecu l ar system would then be recovered through appropriate integration
of the force-field kernel. ML models are often trained on reference data obtained from QM-
based methods, such as, density functional theory (D FT) within the Kohn-Sham formalism.
DFT cont i nues to exist as one of the most popular and widely used QM-t ar g et from molecular
regime
14,19,21,27,39–42
to condensed matter and materials informatics.
11,15,20,31,43–48
In this a r t i cl e, we explore an approach in which DFT calculations for smaller systems can
be used, in conjunction with machine learning to simulate larger systems at a computational
e↵ort comparable to cl a ssi ca l force fields, while being able to predict forces sim i l a r to DFT.
A -NetFF model that uses the di↵erence in forces obtained fr o m t h e molecular mechanical
force field and the quantum mechan i ca l DFT app r oa ches to train the NN was introduced
for const r u ct in g the force field for MD simulations. The predictive power of the present ML
4
