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 at 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.