Neural Network Method for Diffusion-Ordered NMR Spectroscopy

Two-Dimensional Laplace NMR Reconstruction through Deep Learning Enhancement

Laplace NMR is a powerful tool for studying molecular dynamics and spin interactions, providing diffusion and relaxation information that complements Fourier NMR used for composition determination and structure elucidation. However, Laplace NMR demands sophisticated signal processing algorithms such as inverse Laplace transform (ILT). Due to the inherently ill-posed nature of ILT problems, it is generally challenging to perform satisfactory Laplace NMR processing and reconstruction, particularly for two-dimensional Laplace NMR. Herein, we propose a proof-of-concept approach that blends a physics-informed strategy with data-driven deep learning for two-dimensional Laplace NMR reconstruction. This approach integrates prior knowledge of mathematical and physical laws governing multidimensional decay signals by constructing a forward process model to simulate relationships among different decay factors. Benefiting from a noniterative neural network algorithm that automatically acquires prior information from synthetic data during training, this approach avoids tedious parameter tuning and enhances user friendliness. Experimental results demonstrate the practical effectiveness of this approach. As an advanced and impactful technique, this approach brings a fresh perspective to multidimensional Laplace NMR inversion.

SCREENES: Enhancing non-uniform sampling reconstruction for symmetrical NMR spectroscopy

BACKGROUND

Symmetrical NMR spectroscopy, such as Total Correlation Spectroscopy (TOCSY) and other homonuclear spectroscopy, displays symmetry in chemical shift but are generally not symmetrical in terms of intensity, which constitutes a pivotal branch of multidimensional NMR spectroscopy and offers a robust tool for elucidating the structures and dynamics of complex samples, particularly in the context of biological macromolecules. Non-Uniform Sampling (NUS) stands as a critical technique for accelerating multidimensional NMR experiments. However, symmetrical NMR spectroscopy inherently presents dynamic peak intensities, where cross peaks tend to be substantially weaker compared to diagonal peaks. Recovering these weaker cross peaks from NUS data poses a significant challenge, often resulting in compromised data quality.

RESULTS

We enhance the reconstruction quality of NUS symmetrical NMR spectroscopy based on the assumption that the asymmetry in intensity is mild. Regarding the sampling schedule, we employ the symmetrical sampling structure integrated with Poisson sampling schedule to enhance the efficiency of data acquisition. In term of the reconstruction algorithm, we propose the new method by incorporating hard and soft symmetrical constraints into our recently developed L1-norm-based Compressed Sensing (CS) method known as Sparse Complex-valued REconstruction Enabled by Newton method (SCREEN). Additionally, we propose a two-step reconstruction strategy that separately addresses diagonal and cross peaks. In this two-step strategy, cross peaks are effectively reconstructed by excluding the stronger diagonal peaks. Extensive experimental results validate the effectiveness of our proposed methodology.

SIGNIFICANCE

This method enhances the overall quality of the reconstructed NUS symmetrical NMR spectra, especially in terms of cross peaks, thereby enriching the interpretation of spectral information. Furthermore, it boosts the robustness towards regularization parameters, facilitating a user-friendly experience.

Mixtures Recomposition by Neural Nets: A Multidisciplinary Overview

Artificial Neural Networks (ANNs) are transforming how we understand chemical mixtures, providing an expressive view of the chemical space and multiscale processes. Their hybridization with physical knowledge can bridge the gap between predictivity and understanding of the underlying processes. This overview explores recent progress in ANNs, particularly their potential in the 'recomposition' of chemical mixtures. Graph-based representations reveal patterns among mixture components, and deep learning models excel in capturing complexity and symmetries when compared to traditional Quantitative Structure-Property Relationship models. Key components, such as Hamiltonian networks and convolution operations, play a central role in representing multiscale mixtures. The integration of ANNs with Chemical Reaction Networks and Physics-Informed Neural Networks for inverse chemical kinetic problems is also examined. The combination of sensors with ANNs shows promise in optical and biomimetic applications. A common ground is identified in the context of statistical physics, where ANN-based methods iteratively adapt their models by blending their initial states with training data. The concept of mixture recomposition unveils a reciprocal inspiration between ANNs and reactive mixtures, highlighting learning behaviors influenced by the training environment.

Infrared Diffusion-Ordered Spectroscopy Reveals Molecular Size and Structure

Inspired by ideas from NMR, we have developed Infrared Diffusion-Ordered Spectroscopy (IR-DOSY), which simultaneously characterizes molecular structure and size. We rely on the fact that the diffusion coefficient of a molecule is determined by its size through the Stokes-Einstein relation, and achieve sensitivity to the diffusion coefficient by creating a concentration gradient and tracking its equilibration in an IR-frequency resolved manner. Analogous to NMR-DOSY, a two-dimensional IR-DOSY spectrum has IR frequency along one axis and diffusion coefficient (or equivalently, size) along the other, so the chemical structure and the size of a compound are characterized simultaneously. In an IR-DOSY spectrum of a mixture, molecules with different sizes are nicely separated into distinct sets of IR peaks. Extending this idea to higher dimensions, we also perform 3D-IR-DOSY, in which we combine the conformation sensitivity of femtosecond multi-dimensional IR spectroscopy with size sensitivity.

A study on multi-exponential inversion of nuclear magnetic resonance relaxation data using deep learning

Nuclear magnetic resonance (NMR) is a powerful tool for formation evaluation in the oil industry to determine parameters, such as pore structure, fluid saturation, and permeability of porous materials, which are critical to reservoir engineering. The inversion of the measured relaxation data is an ill-posed problem and may lead to deviations of inversion results, which may degrade the accuracy of further data analysis and evaluation. This paper proposes a deep learning method for multi-exponential inversion of NMR relaxation data to improve accuracy. Simulated NMR data are first constructed using a priori knowledge based on the signal parameters and Gaussian distribution. These data are then used to train the neural network designed to consider noise characteristics, signal decay characteristics, signal energy variations, and non-negative features of the T₂ spectra. With the validation from simulated data, the models introduced by multi-scale convolutional neural network (CNN) and attention mechanism outperform other approaches in terms of denoising and T₂ inversion. Finally, NMR measurements of rock cores are used to compare the effectiveness of the attention multi-scale convolutional neural network (ATT-CNN) model in practical applications. The results demonstrate that the proposed method based on deep learning has better performance than the regularization method.