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

Abstract

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.

Operando Modeling of Zeolite-Catalyzed Reactions Using First-Principles Molecular Dynamics Simulations

“…It was recently shown that a data-generation scheme relying on underlying DFT-based MD techniques is not very efficient. 283 During a regular MD run, subsequent structures are very much correlated, and thus, a strategy where training data are derived from underlying DFT-based MD simulations is not very efficient. In this case a lot of quantum-mechanical evaluations are performed which do not give substantial new information to train the MLP.…”

“…To circumvent this caveat, we proposed an active learning scheme in which an iterative procedure is used to train the MLP. 283 A first-generation MLP is trained based on a small set of underlying training data and then used in enhancedsampling MD simulations. When new portions of phase space are encountered which have not yet been seen, new DFT evaluations are performed to train the next iteration of the MLP.…”

Machine learning transferable atomic forces for large systems from underconverged molecular fragments

“…Consequently, theoretical studies are of high interest for the analysis and prediction of MOF properties 59 , and reliable and accurate interatomic potentials are urgently needed 60,61 . Accordingly, several MLPs for MOFs have been reported in the literature to date 33,62,63 . For our benchmark study, two types of HDNNPs are constructed based on either converged fragments providing bulk-like DFT reference forces, or making use of smaller fragments of about half this diameter yielding forces strongly differing from the bulk material.…”

“…61,62 Accordingly, several MLPs for MOFs have been reported in the literature to date. 33,63,64 For our benchmark study, two types of HDNNPs are constructed based on either converged fragments providing bulklike DFT reference forces, or making use of smaller fragments of about half this diameter yielding forces strongly differing from the bulk material. We show that in both cases HDNNPs of comparable quality can be obtained predicting reliable forces suitable for simulations of large systems.…”

Reducing the cost of neural network potential generation for reactive molecular systems

“…However, the trajectory is highly correlated in time and thus most of the expensive AIMD data does not contribute useful information for the training of the model. This selection has been approached in different ways from random sampling and manual selection to more data-driven procedures, 25,27,[34][35][36][37][38][39][40][41] with QbC being a particularly efficient method. QbC considers a set of candidate structures, in this case the whole AIMD trajectory, and iteratively builds up the training set.…”