Physics-Informed Deep Learning and Bayesian Inference for Inverse Problems in 1D ¹H NMR Analysis

by Nicolas Schmid (ZHAW)

Wednesday 28 Oct 2026, 15:00 → 16:00 Europe/Zurich

OVGA/200

Nuclear Magnetic Resonance (NMR) spectroscopy probes local magnetic environments to characterize molecular structures, serving as a standard experimental tool across chemistry and materials research. However, extracting underlying physical parameters from experimental 1D ¹H spectra behaves as an ill-posed inverse problem. Signal overlap, experimental artefacts, and quantum-mechanical strong coupling pose persistent challenges. When scalar couplings approach the magnitude of chemical-shift differences, off-diagonal Hamiltonian terms mix spin states, shifting transition frequencies and redistributing intensities in ways that cannot be determined by simple linear first-order rules.

Much like forward-modelling workflows in condensed-matter physics and electronic structure theory, forward simulations from a spin Hamiltonian can be carried out reliably, but the corresponding inverse mapping tends to be non-unique and numerically challenging. We present a hierarchical framework that addresses these difficulties by combining physics-informed deep learning, quantum spin dynamics, and Bayesian inference across three complementary stages:

• Physics-Informed Deconvolution (MLdecon): Rather than fitting unconstrained peak profiles, a convolutional neural network trained on synthetic spectra generated from physical line models learns to decompose congested envelopes into peak positions, widths, and intensities. In benchmark tests, this model shows competitive performance against standard optimization routines and has been integrated into Bruker TopSpin for laboratory workflows.
• Direct Hamiltonian Parameter Detection (MolDETR): To move beyond local peak fitting, we adapted a set-based detection transformer to estimate spin-system descriptors directly from 1D ¹H spectra. Trained on synthetic data generated through quantum-mechanical spin-dynamics simulations with artefact augmentation, MolDETR predicts unordered sets of chemical shifts, scalar coupling constants, and proton counts without requiring a known chemical graph. On experimental test sets, it achieves median errors typically below 1 Hz for chemical shifts and around 0.2 Hz for scalar couplings.
• Bayesian Refinement with Explicit Quantum Hamiltonians: Empirical priors (such as HOSE codes or standard DFT estimates) can be broad and occasionally misguide non-linear solvers. Using MolDETR predictions as concentrated, spectrum-conditioned priors helps constrain Bayesian total line-shape analysis under an explicit quantum spin Hamiltonian. Sequential Monte Carlo and Hamiltonian Monte Carlo sampling explore the resulting parameter spaces, offering posterior distributions with physically calibrated uncertainty estimates.

By coupling synthetic spin simulations with transformer-based inference and Bayesian sampling, this workflow highlights a practical strategy for handling complex inverse problems and parameter estimation in experimental spectroscopy.