Optimal control, quantification and machine learning in spin dynamics

Abstract

Control and simulation of spin dynamics face two persistent bottlenecks: instrument-induced distortions that warp optimised pulses, and the near universal piecewise-constant approximation of the Hamiltonian. The latter is the lowest order Lie-solver that degrades under fast timing and realistic hardware responses. This thesis addresses both.

From first principles, piecewise-linear and piecewise-quadratic propagators that evolve on the Lie-group manifold are derived. In simulation, these higher-order Lie-solvers achieve higher trajectory accuracy with fewer time intervals. The GRadient Ascent Pulse Engineering (GRAPE) algorithm is extended to a piecewise-linear formulation (LGRAPE). The exact analytical gradients are computed via auxiliary matrix methods, delivering higher fidelities under tight timing constraints.

When significant, distortions are treated explicitly by embedding cascades of transfer functions and ensemble parameters directly into the optimisation. The resulting Response-Aware GRAPE (RAW-GRAPE) requires only the transfer functions and their Jacobians (via automatic differentiation when needed), compensating for linear/non-linear effects without brittle deconvolution. Single-pole and single-zero blocks are supplied that act as basis elements for arbitrary linear responses. When combined with non-linear elements, the framework can, in principle, incorporate any distortion cascade. Across diverse simulated experiments with representative hardware artefacts, RAW-GRAPE demonstrates higher robustness and target fidelity compared to conventional GRAPE.

As machine learning use expands, well-labelled experimental datasets remain scarce. We therefore build a forward-modelled simulation pipeline that mirrors real experiments and injects hardware artefacts on the fly. The 3D data volume bottleneck is addressed by retaining Kronecker factorisations, avoiding explicit tensor expansion. Hundreds of thousands of spectra are generated in hours to train neural networks for automated protein-backbone assignment. The pipeline integrates with CcpNmr and yields accurate end-to-end predictions on proteins up to 40 kDa. All methods are implemented in Spinach with reproducible workflows.

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Identifiers

ORCID for Uluk Rasulov: orcid.org/0009-0003-7634-4176

ORCID for Ilya Kuprov: orcid.org/0000-0003-0430-2682

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