An application of artificial intelligence to a linear inverse problem in dipolar spectroscopy

Abstract

Double Electron-Electron Resonance (DEER) Spectroscopy plays a pivotal role in analysing molecular distances at the nanoscale, a crucial factor in understanding the structure and dynamics of biological macromolecules. However, the challenge lies in extracting distance distributions from DEER data due to the inherently ill-conditioned nature of the inverse problem. Traditional solutions, such as regularisation, introduce bias through operator selection based on prior assumptions like smoothness.

Recent applications of neural networks in this field provide a promising, data-driven alternative. Nevertheless, concerns regarding the perceived ’black box’ nature of these networks raise questions about their trustworthiness. Trust, though often nebulous, can be clarified by comparing it to the trust we place in human experts. Human experts are considered trustworthy when:



1. They possess recognised expertise, demonstrated through a history of high-quality publications.

2. They accurately assess and communicate their confidence level in their judgements, avoiding unwarranted overconfidence.

3. They readily admit when a problem or question falls outside their area of expertise, avoiding speculation in unfamiliar domains.

4. They effectively articulate their reasoning and thought process, ensuring transparency in their decision-making.

Translating these criteria to neural networks yields explicit expectations:

1. Demonstrated high predictive accuracy, validated through rigorous testing and consistent performance.

2. The ability to quantify uncertainty in predictions.

3. The capability to detect when a query falls outside its training distribution.

4. An explainable decision-making process.

This thesis delves into enhancing predictive accuracy in DEER spectroscopy by addressing the “vanishing gradient problem” in neural networks. It explores uncertainty quantification through ensemble techniques and out-of-distribution detection via model fitting. Lastly, it introduces “descrambling”, an innovative post-hoc explainability method based on equivalence transforms, aimed at elucidating the internal processes of the neural network.

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Identifiers

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

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