Machine Learning Potentials for Metal-Organic Frameworks using an Incremental Learning Approach

Computational modeling of physical processes in metal-organic frameworks (MOFs) is highly challenging. The intrinsic length and time scales often stretch far beyond the nanometer and picosecond range due to e.g. large spatial heterogeneities or complex phase transitions. Machine learning potentials (MLPs) can extend the applicability of density functional theory (DFT) towards such challenging systems, but the generation of a representative training set of atomic configurations still poses a major challenge. In this work, we present an incremental learning scheme that constructs accurate and transferable MLPs based on a minimal number of DFT evaluations. Key to the approach is a combination of an active learning scheme that generates systematically improved MLPs with efficient and parallelized enhanced sampling protocols that explore increasingly larger portions of the phase space and learn physical interactions on-the-fly. The method requires a single atomic structure and a collective variable as input, after which the incremental learning approach constructs accurate interatomic potentials based on as few as 1000 single point DFT evaluations, even for flexible frameworks with multiple structurally different phases. The accuracy of the obtained potentials is extensively validated in terms of structural and mechanical properties across a wide range of thermodynamic conditions, yielding thermodynamically transferable MLPs. Finally, it is demonstrated how the incremental learning approach shows great potential to train universal MLPs for a larger set of materials. A proof of principle based on 10 well-known aluminum- and zirconium-based MOFs is shown. The proposed incremental learning approach is universally applicable and may induce a paradigm shift in both the accuracy as well as the time and length scale of computational models for framework materials.