Optimal design of experiments in the context of machine-learning inter-atomic potentials: improving the efficiency and transferability of kernel based methods

Data-driven, machine learning (ML) models of atomistic interactions are often based on flexible and non-physical functions that can relate nuanced aspects of atomic arrangements into predictions of energies and forces. As a result, these potentials are as good as the training data (usually results of so-called ab initio simulations) and we need to make sure that we have enough information for a model to become sufficiently accurate, reliable and transferable. The main challenge stems from the fact that descriptors of chemical environments are often sparse high-dimensional objects without a well-defined continuous metric. Therefore, it is rather unlikely that any ad hoc method of choosing training examples will be indiscriminate, and it will be easy to fall into the trap of confirmation bias, where the same narrow and biased sampling is used to generate train- and test- sets. We will demonstrate that classical concepts of statistical planning of experiments and optimal design can help to mitigate such problems at a relatively low computational cost. The key feature of the method we will investigate is that they allow us to assess the informativeness of data (how much we can improve the model by adding/swapping a training example) and verify if the training is feasible with the current set before obtaining any reference energies and forces -- a so-called off-line approach. In other words, we are focusing on an approach that is easy to implement and doesn't require sophisticated frameworks that involve automated access to high-performance computational (HPC).