Towards Ultimate NMR Resolution with Deep Learning

In multidimensional NMR spectroscopy, practical resolution is defined as the ability to distinguish and accurately determine signal positions against a background of overlapping peaks, thermal noise, and spectral artifacts. In the pursuit of ultimate resolution, we introduce Peak Probability Presentations ($P^3$)- a statistical spectral representation that assigns a probability to each spectral point, indicating the likelihood of a peak maximum occurring at that location. The mapping between the spectrum and $P^3$ is achieved using MR-Ai, a physics-inspired deep learning neural network architecture, designed to handle multidimensional NMR spectra. Furthermore, we demonstrate that MR-Ai enables coprocessing of multiple spectra, facilitating direct information exchange between datasets. This feature significantly enhances spectral quality, particularly in cases of highly sparse sampling. Performance of MR-Ai and high value of the $P^3$ are demonstrated on the synthetic data and spectra of Tau, MATL1, Calmodulin, and several other proteins.