A statistical learning framework for mapping indirect measurements of ergodic systems to emergent properties

TL;DR

This paper introduces a statistical learning approach that maps indirect measurements to emergent properties in ergodic systems without requiring detailed system descriptions, validated through NMR spectra and exchange rates.

Contribution

It presents a novel framework using neural networks and Monte Carlo simulations to relate measurements to system dynamics without analytic models.

Findings

Neural networks achieved <1% error for exchange rates <150 s-1

Performance declined for higher exchange rates due to measurement indistinguishability

Framework enables understanding of system properties without detailed theoretical models

Abstract

The discovery of novel experimental techniques often lags behind contemporary theoretical understanding. In particular, it can be difficult to establish appropriate measurement protocols without analytic descriptions of the underlying system-of-interest. Here we propose a statistical learning framework that avoids the need for such descriptions for ergodic systems. We validate this framework by using Monte Carlo simulation and deep neural networks to learn a mapping between low-field nuclear magnetic resonance spectra and proton exchange rates in ethanol-water mixtures. We found that trained networks exhibited normalized-root-mean-square errors of less than 1% for exchange rates under 150 s-1 but performed poorly for rates above this range. This differential performance occurred because low-field measurements are indistinguishable from one another at fast exchange. Nonetheless, where a discoverable relationship between indirect measurements and emergent dynamics exists, we demonstrate the possibility of approximating it without the need for precise analytic descriptions, allowing experimental science to flourish in the midst of ongoing theoretical work