In this work, we revisit our recent iterative machine learning (ML)–molecular dynamics (MD) technique “Reweighted autoencoded variational Bayes for enhanced sampling” [J. M. L. Ribeiro et al., J. Chem. Phys. 149, 072301 (2018) and Y. Wang, J. M. L. Ribeiro, and P. Tiwary, Nat. Commun. 10, 3573 (2019)] and analyze and formalize some of its approximations. These include (a) the choice of a predictive time-delay, or how far into the future should the ML try to predict the state of a given system output from MD, and (b) that for short time-delays, how much of an error is made in approximating the biased propagator for the dynamics as the unbiased propagator. We demonstrate through a master equation framework as to why the exact choice of time-delay is irrelevant as long as a small non-zero value is adopted. We also derive a correction to reweight the biased propagator, and somewhat to our dissatisfaction but also to our reassurance, we find that it barely makes a difference to the intuitive picture we had previously derived and used.

1.
J. M. L.
Ribeiro
,
P.
Bravo
,
Y.
Wang
, and
P.
Tiwary
,
J. Chem. Phys.
149
,
072301
(
2018
).
2.
J. M. L.
Ribeiro
and
P.
Tiwary
,
J. Chem. Theory Comput.
15
,
708
(
2019
).
3.
Y.
Wang
,
J. M. L.
Ribeiro
, and
P.
Tiwary
,
Nat. Commun.
10
,
3573
(
2019
).
4.
Y.
Wang
,
J. M. L.
Ribeiro
, and
P.
Tiwary
,
Curr. Opin. Struct. Biol.
61
,
139
(
2020
).
5.
A. A.
Alemi
,
I.
Fischer
,
J. V.
Dillon
, and
K.
Murphy
, arXiv:1612.00410 (
2016
).
6.
P. G.
Bolhuis
,
D.
Chandler
,
C.
Dellago
, and
P. L.
Geissler
,
Annu. Rev. Phys. Chem.
53
,
291
(
2002
).
7.
F.
Noé
and
C.
Clementi
,
Curr. Opin. Struct. Biol.
43
,
141
(
2017
).
8.
B.
Peters
,
Annu. Rev. Phys. Chem.
67
,
669
(
2016
).
9.
Z.
Ghahramani
and
M. J.
Beai
,
Advances in Neural Information Processing Systems
(
MIT Press
,
2000
), p.
449
.
10.
C. X.
Hernández
,
H. K.
Wayment-Steele
,
M. M.
Sultan
,
B. E.
Husic
, and
V. S.
Pande
,
Phys. Rev. E
97
,
062412
(
2018
).
11.
C.
Wehmeyer
and
F.
Noé
,
J. Chem. Phys.
148
,
241703
(
2018
).
12.
S.
Still
,
Entropy
16
,
968
989
(
2014
).
13.
D. J.
Bicout
and
A.
Szabo
,
J. Chem. Phys.
109
,
2325
(
1998
).
14.
P.
Tiwary
and
B. J.
Berne
,
J. Chem. Phys.
147
,
152701
(
2017
).
15.
E.
Rosta
and
G.
Hummer
,
J. Chem. Theory Comput.
11
,
276
(
2015
).
16.
G.
Bussi
and
M.
Parrinello
,
Phys. Rev. E
75
,
056707
(
2007
).
17.
W.
Chen
,
H.
Sidky
, and
A. L.
Ferguson
,
J. Chem. Phys.
151
,
064123
(
2019
).
18.
S.
Kieninger
,
L.
Donati
, and
B. G.
Keller
,
Curr. Opin. Struct. Biol.
61
,
124
(
2020
).

Supplementary Material

You do not currently have access to this content.