Atomic-scale modelling makes it possible to predict from first principles the properties
of materials and molecules. More often than not, however, one has to strike a balance between accuracy and efficiency -- be it in the form of approximate descriptions of the electronic structure or in the form of accelerated sampling protocols that disrupt the natural time evolution of the system. Here I will present two examples of how one can remedy to these shortcomings. First, I will present examples of how Gaussian process regression can bridge the gap between different levels of theory, and even identify the portions of a molecules that are most affected by a given approximation. Second, I will discuss how the dynamical perturcation introduced by (generalized) Langevin sampling, used to improve sampling efficiency, can be predicted and corrected for.
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