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Atomistic simulations such as molecular dynamics (MD) are a cornerstone of computational material science. MD is a powerful tool that can generate fully-resolved, (classically) dynamically correct trajectories based only on a description of the energetics of the interactions between atoms. A longstanding challenge in MD is the development of approximations to the exact quantum potential energy surface that are computationally affordable and scalable, therefore enabling simulations of much larger systems over much longer times than are possible using direct solutions to Schrödinger’s equation.
Until recently, the functional form of these so-called interatomic potentials was largely based on physical considerations. In the past years, machine learning approaches thoroughly reshaped the field through the introduction of numerical methods which require less prior knowledge, lead to lower regression errors, and better transferability. While machine learning has shown great promise, developments are often still guided by ad hoc heuristics, which slows down further progress. This calls for a rigorous study of the modeling and numerical errors involved in the representation of forces and energies obtained from quantum mechanics by models of classical mechanics, through both a priori or a posteriori error estimates, of uncertainty quantification for detecting which parameters influence most the results, of the influence of the training database or how it should be augmented to minimize prediction errors.
This workshop aims to explore mathematical challenges of this kind and to discuss how fundamental insights can be translated into practical improvements in the cost/accuracy tradeoff of the next generation of data-driven interatomic potentials, enabling robust large-scale simulations at unprecedented accuracies and spatio-temporal scales.