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

Laplace-related techniques in nuclear magnetic resonance (NMR), including both standalone Laplace NMR and combined Laplace-Fourier NMR, provide detailed insights into molecular dynamics and spin interactions through the measurement of relaxation and diffusion parameters, offering complementary chemical resolution to Fourier NMR. Spectrum reconstruction with accurate diffusion coefficients or relaxation time is essential for the Laplace-related NMR experiments, but existing processing methods generally yield varying results because of the ill-posed nature of inverse Laplace transform, making it challenging to assess the accuracy and reliability of estimations without ideal references. To address this, we developed a deep learning–based method that not only recovers parameter distributions from exponential signals with improved accuracy but also provides an uncertainty estimation for each reconstruction result. This additional insight allows the user to assess the confidence across spectral regions, providing a clearer and more reliable framework for Laplace-related data interpretation, thus facilitating broader applications in fields such as chemistry and materials science.