materials science. These calculations can provide atomic level detail of physical phenomena and chemical reactions that can help to understand experimental observations. With modern computing advances, computationally intensive simulations using quantum mechanical methods such as hybrid density-functional theory (DFT), Møller-Plesset second-order perturbation theory (MP2), or coupled-cluster approaches can be performed to provide accurate descriptions of electronic and vibrational states, as well as thermodynamic quantities for a diverse set of systems. The high computational expense of these approaches, however, generally limits their application to static gas-phase clusters or small, sub-nanometer systems sizes. This can be far below the spatial scales of most experimental studies, which frequently probe nanometers or beyond and involve dynamic measurements. For example, the "gold standard" CCSD(T) (coupled-cluster considering single, double, and perturbative triple excitations) method scales as O(N 7 ), where N is the number of basis functions involved in the calculation. Consequently, it is generally only applicable to systems with tens of atoms or less, precluding its use for larger biomolecules or condensed phases. Neural network (NN) approaches can be used to completely parameterize the quantum mechanical interactions, 1-3 bypassing the need for direct electronic state calculation and thus yielding improved scaling and efficiency. However, NNs tend to require extremely large training sets and can perform poorly outside of their training regime. This need for large data sets, in particular, makes such approaches challenging to implement and use effectively. Therefore, there is a widespread need for the development of computational methods that can maintain the accuracy of high level approaches while yielding substantial gains in training set size, computational costs, and scaling.