Optimal control design of NMR and dynamic nuclear polarization experiments using monotonically convergent algorithms

Area of Science:

• Physical Sciences
• Chemistry
• Spectroscopy

Background:

• Optimal control theory is increasingly used in nuclear magnetic resonance (NMR) spectroscopy for designing and optimizing pulse sequences.
• Current methods primarily rely on gradient-based numerical optimization, demanding significant computational resources and fast convergence.
• There is a need for alternative, more efficient numerical approaches for NMR experiment design.

Purpose of the Study:

• To introduce and evaluate an alternative optimal control theory approach, the Krotov formulation, for numerical NMR experiment design.
• To develop an algorithm that explicitly minimizes radio frequency power consumption, addressing practical experimental limitations like sample heating.
• To demonstrate the Krotov approach's efficiency and distinct control space exploration compared to gradient-based methods.

Main Methods:

• Implementation of the Krotov formulation of optimal control theory for numerical experiment design.
• Development of an iterative algorithm that solves stationary conditions to maximize objectives while minimizing radio frequency power.
• Application of the Krotov approach to optimize nuclear magnetic resonance (NMR) and dynamic nuclear polarization (DNP) experiments.

Main Results:

• The Krotov-based method demonstrates faster convergence per iteration compared to traditional gradient-based methods.
• The algorithm successfully incorporates radio frequency power minimization as an explicit constraint.
• The Krotov approach explores different control space trajectories, offering an alternative optimization pathway.

Conclusions:

• The Krotov formulation provides a computationally efficient and practical alternative for designing optimal NMR pulse sequences.
• Minimizing radio frequency power through this method facilitates experimental implementation and reduces heating artifacts.
• This approach advances NMR and DNP experiment design, enabling the development of new, high-performance pulse sequences.