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A popular way to accelerate the sampling of rare events in molecular dynamicssimulations is to introduce a potential that increases the fluctuations ofselected collective variables. For this strategy to be successful, it iscritical to choose appropriate variables. Here we review some recentdevelopments in the data-driven design of collective variables, with a focus onthe combination of Fisher's discriminant analysis and neural networks. Thisapproach allows to compress the fluctuations of metastable states into alow-dimensional representation. We illustrate through several examples theeffectiveness of this method in accelerating the sampling, while alsoidentifying the physical descriptors that undergo the most significant changesin the process.

Training collective variables for enhanced sampling via neural networks based discriminant analysis