Journal of Magnetic Resonance Open (Jun 2024)

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

  • Nicholas Hindley,
  • Stephen J. DeVience,
  • Ella Zhang,
  • Leo L. Cheng,
  • Matthew S. Rosen

Journal volume & issue
Vol. 19
p. 100151

Abstract

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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 nuclear magnetic resonance spectra acquired on a novel low-field instrument 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 for fast exchange. Nonetheless, where a discoverable relationship between indirect measurements and emergent dynamics exists, we demonstrate the possibility of approximating it in an efficient, data-driven manner.

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