**Supervised learning and the finite-temperature string method for
computing committor functions and reaction rates**

MR Hasyim and CH Batton and KK Mandadapu, JOURNAL OF CHEMICAL PHYSICS, 157, 184111 (2022).

DOI: 10.1063/5.0102423

A central object in the computational studies of rare events is the
committor function. Though costly to compute, the committor function
encodes complete mechanistic information of the processes involving rare
events, including reaction rates and transition-state ensembles. Under
the framework of transition path theory, Rotskoff et al. **Proceedings of
the 2nd Mathematical and Scientific Machine Learning Conference,
Proceedings of Machine Learning Research (PLMR, 2022), Vol. 145, pp.
757-780** proposes an algorithm where a feedback loop couples a neural
network that models the committor function with importance sampling,
mainly umbrella sampling, which collects data needed for adaptive
training. In this work, we show additional modifications are needed to
improve the accuracy of the algorithm. The first modification adds
elements of supervised learning, which allows the neural network to
improve its prediction by fitting to sample-mean estimates of committor
values obtained from short molecular dynamics trajectories. The second
modification replaces the committor-based umbrella sampling with the
finite-temperature string (FTS) method, which enables homogeneous
sampling in regions where transition pathways are located. We test our
modifications on low-dimensional systems with non-convex potential
energy where reference solutions can be found via analytical or finite
element methods, and show how combining supervised learning and the FTS
method yields accurate computation of committor functions and reaction
rates. We also provide an error analysis for algorithms that use the FTS
method, using which reaction rates can be accurately estimated during
training with a small number of samples. The methods are then applied to
a molecular system in which no reference solution is known, where
accurate computations of committor functions and reaction rates can
still be obtained. Published under an exclusive license by AIP
Publishing.

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