High-confidence reconstruction for Laplace inversion in NMR based on uncertainty-informed deep learning

Area of Science:

• Nuclear Magnetic Resonance (NMR) Spectroscopy
• Computational Chemistry
• Data Science

Background:

• Laplace-related NMR techniques offer insights into molecular dynamics and spin interactions by measuring relaxation and diffusion parameters.
• Accurate spectrum reconstruction is crucial for Laplace-NMR, but traditional methods struggle due to the ill-posed nature of the inverse Laplace transform, leading to unreliable estimations.
• Current methods lack a reliable way to assess the accuracy and confidence of parameter estimations without ideal references.

Purpose of the Study:

• To develop a robust deep learning-based method for accurate spectrum reconstruction in Laplace-related NMR experiments.
• To provide uncertainty estimations alongside parameter distributions for improved data interpretation.
• To enhance the reliability and applicability of Laplace-NMR techniques in scientific research.

Main Methods:

• A deep learning model was developed to recover parameter distributions from exponential signals.
• The method incorporates uncertainty quantification for each reconstruction result.
• The approach was validated for its accuracy in recovering diffusion coefficients and relaxation times.

Main Results:

• The deep learning method achieved improved accuracy in recovering parameter distributions compared to existing techniques.
• The generated uncertainty estimations allow users to assess confidence levels across spectral regions.
• The method demonstrated reliable performance in spectrum reconstruction for Laplace-NMR data.

Conclusions:

• The developed deep learning method offers a more accurate and reliable framework for interpreting Laplace-related NMR data.
• Uncertainty estimation provides crucial insights into the confidence of spectral reconstructions.
• This advancement facilitates broader applications of Laplace-NMR in chemistry, materials science, and other fields.