Deep regression with ensembles enables fast, first-order shimming in low-field NMR.

Shimming in the context of nuclear magnetic resonance aims to achieve a uniform magnetic field distribution, as perfect as possible, and is crucial for useful spectroscopy and imaging. Currently, shimming precedes most acquisition procedures in the laboratory, and this mostly semi-automatic procedure often needs to be repeated, which can be cumbersome and time-consuming. The paper investigates the feasibility of completely automating and accelerating the shimming procedure by applying deep learning (DL). We show that DL can relate measured spectral shape to shim current specifications and thus rapidly predict three shim currents simultaneously, given only four input spectra. Due to the lack of accessible data for developing shimming algorithms, we also introduce a database that served as our DL training set, and allows inference of changes to 1H NMR signals depending on shim offsets. In situ experiments of deep regression with ensembles demonstrate a high success rate in spectral quality improvement for random shim distortions over different neural architectures and chemical substances. This paper presents a proof-of-concept that machine learning can simplify and accelerate the shimming problem, either as a stand-alone method, or in combination with traditional shimming methods. Our database and code are publicly available.

Role of critical points of the skin friction field in formation of plumes in thermal convection.

The dynamics in the thin boundary layers of temperature and velocity is the key to a deeper understanding of turbulent transport of heat and momentum in thermal convection. The velocity gradient at the hot and cold plates of a Rayleigh-Bénard convection cell forms the two-dimensional skin friction field and is related to the formation of thermal plumes in the respective boundary layers. Our analysis is based on a direct numerical simulation of Rayleigh-Bénard convection in a closed cylindrical cell of aspect ratio Γ=1 and focused on the critical points of the skin friction field. We identify triplets of critical points, which are composed of two unstable nodes and a saddle between them, as the characteristic building block of the skin friction field. Isolated triplets as well as networks of triplets are detected. The majority of the ridges of linelike thermal plumes coincide with the unstable manifolds of the saddles. From a dynamical Lagrangian perspective, thermal plumes are formed together with an attractive hyperbolic Lagrangian coherent structure of the skin friction field. We also discuss the differences from the skin friction field in turbulent channel flows from the perspective of the Poincaré-Hopf index theorem for two-dimensional vector fields.