## Theoretical and Computational Spin Dynamics Group

### Research interests

- Quantum dynamics of large electron and nuclear spin systems
- Fundamental theories of magnetic resonance spectroscopy and imaging
- Quantum mechanical modelling of magnetic properties and materials
- Deep neural network processing of magnetic resonance data
- Chemical and biological effects of weak magnetic fields
- Optimal control algorithms for large quantum systems
- Quantum mechanical simulations of magnetic resonance imaging
- Magnetic resonance software engineering and data formats

### Recent publications

#### Neural network interpretation using descrambler groups

J.L. Amey, J. Keeley, T. Choudhury, I. Kuprov, *Proc. Natl. Acad. Sci.,* 2021 118 (5) e2016917118

*Artificial neural networks are famously opaque — it is often unclear how they work. In this communication, we propose a group-theoretical way of finding out. It reveals considerable internal sophistication, even in simple neural networks: our nets apparently invented an elegant digital filter, a regularized integral transform, and even Chebyshev polynomials. This is a step toward saving reductionism. For centuries, the philosophical approach to science has been to find fundamental laws that govern reality, to test those laws, and to use their predictive power. Black-box neural networks amount to blasphemy within that school, but they are irresistible because they “just work.” Explaining how they work is a notoriously difficult problem, to which this paper offers a partial solution.*

#### Quantum mechanical MRI simulations: solving the matrix dimension problem

A.J. Allami, M.G. Concilio, P. Lally, I. Kuprov, *Science Advances,* 5 (2019) eaaw8962

*We propose a solution to the matrix dimension problem in quantum mechanical simulations of MRI (magnetic resonance imaging) experiments on complex molecules. This problem is very old; it arises when Kronecker products of spin operators and spatial dynamics generators are taken – the resulting matrices are far too large for any current or future computer. However, spin and spatial operators individually have manageable dimensions, and we note here that the action by their Kronecker products on any vector may be computed without opening those products. This eliminates large matrices from the simulation process. MRI simulations for coupled spin systems of complex metabolites in three dimensions with diffusion, flow, chemical kinetics, and quantum mechanical treatment of spin relaxation are now possible.*

#### Deep neural network processing of DEER data

S.G. Worswick, J.A. Spencer, G. Jeschke, I. Kuprov, *Science Advances,* 4 (2018) eaat5218

*The established model-free methods for the processing of two-electron dipolar spectroscopy data (DEER, PELDOR, DQ-EPR, RIDME, etc.) use regularised fitting. In this communication, we describe an attempt to process DEER data using artificial neural networks trained on large databases of simulated data. Accuracy and reliability of neural network outputs from real experimental data were found to be unexpectedly high. The networks are also able to reject exchange interactions and to return a measure of uncertainty in the resulting distance distributions. This paper describes the design of the training databases, discusses the training process, and rationalises the observed performance. Neural networks produced in this work are incorporated as options into Spinach and DeerAnalysis packages.*