Rapid high-fidelity quantum simulations using multi-step nonlinear autoregression and graph embeddings

The design and high-throughput screening of materials using machine-learning assisted quantum-mechanical simulations typically requires the existence of a very large data set, often generated from simulations at a high level of theory or fidelity. A single simulation at high fidelity can take on the order of days for a complex molecule. Thus, although machine learning surrogate simulations seem promising at first glance, generation of the training data can defeat the original purpose. For this reason, the use of machine learning to screen or design materials remains elusive for many important applications. In this paper we introduce a new multi-fidelity approach based on a dual graph embedding to extract features that are placed inside a nonlinear multi-step autoregressive model. Experiments on five benchmark problems, with 14 different quantities and 27 different levels of theory, demonstrate the generalizability and high accuracy of the approach. It typically requires a few 10s to a few 1000’s of high-fidelity training points, which is several orders of magnitude lower than direct ML methods, and can be up to two orders of magnitude lower than other multi-fidelity methods. Furthermore, we develop a new benchmark data set for 860 benzoquinone molecules with up to 14 atoms, containing energy, HOMO, LUMO and dipole moment values at four levels of theory, up to coupled cluster with singles and doubles.