Machine learning can predict the major regio-, site-, and diastereoselective outcomes of Diels-Alder reactions better than standardq uantum-mechanical methods and with accuracies exceeding 90 %provided that i) the diene/dienophile substrates are represented by "physical-organic" descriptors reflecting the electronic and steric characteristics of their substituents and ii)t he positions of such substituents relative to the reaction core are encoded ("vectorized") in an informative way.
A good deal of molecular dynamics simulations aims at predicting and quantifying rare events, such as the folding of a protein or a phase transition. Simulating rare events is often prohibitive, especially if the equations of motion are high-dimensional, as is the case in molecular dynamics. Various algorithms have been proposed for efficiently computing mean first passage times, transition rates or reaction pathways. This article surveys and discusses recent developments in the field of rare event simulation and outlines a new approach that combines ideas from optimal control and statistical mechanics. The optimal control approach described in detail resembles the use of Jarzynski's equality for free energy calculations, but with an optimized protocol that speeds up the sampling, while (theoretically) giving variance-free estimators of the rare events statistics. We illustrate the new approach with two numerical examples and discuss its relation to existing methods.
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