Analysis of pulsed gradient nuclear magnetic resonance experiments using feedforward neural networks

Analysis of the data yielded by the pulsed-field-gradient nuclear magnetic resonance (NMR) experiment, which is used to measure self-diffusion coefficients of molecules, is problematic when the diffusion of the probe molecule is restricted by structural barriers. The solution of the diffusion equation for the particular arrangement of barriers and/or boundaries, in terms of the magnetization phase that is measured in the NMR experiment, is generally only achieved by judiciously employing approximations to simplify the solution. Many of these diffusion processes can, however, be simulated using tandem-walk methods. We present here a method in which the results of random-walk simulations of diffusion are used to train a feedforward neural network to predict the interpore-spacing and percentage porosity in cubic-packed spheres. We used stopped training and a resampling technique, which resulted in an ensemble of networks, in order to overcome the overfitting problems associated with limited training data, and to provide estimates of confidence levels for the evaluated parameters.