Here we propose the Reweighted Autoencoded Variational Bayes for Enhanced
Sampling (RAVE) method, a new iterative scheme that uses the deep learning
framework of variational autoencoders to enhance sampling in molecular
simulations. RAVE involves iterations between molecular simulations and deep
learning in order to produce an increasingly accurate probability distribution
along a low-dimensional latent space that captures the key features of the
molecular simulation trajectory. Using the Kullback-Leibler divergence between
this latent space distribution and the distribution of various trial reaction
coordinates sampled from the molecular simulation, RAVE determines an optimum,
yet nonetheless physically interpretable, reaction coordinate and optimum
probability distribution. Both then directly serve as the biasing protocol for
a new biased simulation, which is once again fed into the deep learning module
with appropriate weights accounting for the bias, the procedure continuing
until estimates of desirable thermodynamic observables are converged. Unlike
recent methods using deep learning for enhanced sampling purposes, RAVE stands
out in that (a) it naturally produces a physically interpretable reaction
coordinate, (b) is independent of existing enhanced sampling protocols to
enhance the fluctuations along the latent space identified via deep learning,
and (c) it provides the ability to easily filter out spurious solutions learned
by the deep learning procedure. The usefulness and reliability of RAVE is
demonstrated by applying it to model potentials of increasing complexity,
including computation of the binding free energy profile for a hydrophobic
ligand-substrate system in explicit water with dissociation time of more than
three minutes, in computer time at least twenty times less than that needed for
umbrella sampling or metadynamics.

提出了 RAEBV 方法，使用自编码变分贝叶斯方法来提高分子模拟的采样效率，并在计算自由能与发现关键特征空间方面具有显著优势。

重新加权自编码变分贝叶斯用于增强采样（RAVE）

Reweighted Autoencoded Variational Bayes for Enhanced Sampling (RAVE)

A Boltzmann machine is a stochastic neural network that has been extensively
used in the layers of deep architectures for modern machine learning
applications. In this paper, we develop a Boltzmann machine that is capable of
modelling thermodynamic observables for physical systems in thermal
equilibrium. Through unsupervised learning, we train the Boltzmann machine on
data sets constructed with spin configurations importance-sampled from the
partition function of an Ising Hamiltonian at different temperatures using
Monte Carlo (MC) methods. The trained Boltzmann machine is then used to
generate spin states, for which we compare thermodynamic observables to those
computed by direct MC sampling. We demonstrate that the Boltzmann machine can
faithfully reproduce the observables of the physical system. Further, we
observe that the number of neurons required to obtain accurate results
increases as the system is brought close to criticality.

通过学习物理系统中热力学量的 Boltzmann 机器，通过自发的学习机器，我们训练了 Boltzmann 机器， 并通过其生成的自旋状态检验热力学可观测量与直接 MC 采样的差距，证明了 Boltzmann 机器能够忠实地再现物理系统的可观测量，并观察到随着系统接近临界状态需要更多的神经元以获得准确的结果。