Machine Learning of Experimental Observables

First principles simulation methods such as Density functional theory (DFT) allow for the calculation of a variety of different experimentally measurable quantities such as mechanical, magnetic, or spectroscopic properties [1]. However, first principle methods are limited in their applicability for larger time and length scales (c.f. Multiscale Modeling Methodology) of the model system. We are actively working on developing machine learning (ML) approaches to learn the relationship between the atomistic structure and the observable properties. The increased computational efficiency of ML models extends the computationally accessible range of time and length scales of our simulations, which is indispensable to approach the structural and dynamic complexity of experimental samples and methods. While experiments often study macroscopic samples at extended time scales, they also offer the unique opportunity to validate theoretical models and methods.

One experimental technology, for which we apply ML to learn experimental observables, is nuclear magnetic resonance (NMR) spectroscopy, which addresses the nuclear spins of the sample to elucidate local structure and atomistic dynamics. A lot of spectroscopic properties are scalar quantities, which are usually derived from tensors describing the physical interaction. Scalar observables can be described with rotationally invariant ML model, since the quantity of interest does not change upon rotation of the system. In contrast, experimental observables which depend explicitly on the tensorial nature of the probed spectroscopic interaction, such as the tensor orientation, require rotationally equivariant ML models adopting the rotation of the system for the tensor. However, even the predictive accuracy for scalar observables improves notably upon application of tensor ML models. [2]

Comparing experiments with first principle results is not only challenging because of the limited model system size for theoretical simulations but also due to the neglect of dynamic effects. The computational efficiency of ML models makes it possible to combine the simulation of observables with multiscale modeling methods such as molecular dynamics and kinetic Monte Carlo (c.f. Kinetic Monte Carlo) to incorporate thermodynamic sampling of the observable as well as simulating dynamic effects. We are ultimately aiming at reproducing the spectroscopic experiment in silico. [3]

Machine Learning of Experimental Observables

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