Machine Learning at ILL: First autonomous steps of the neutron spectrometer ThALES

This also means that for an efficient measurement, it is particularly important that this effort is well-targeted, i.e., data is taken at meaningful points, and that no time is wasted to obtain information that later turns out to be irrelevant.

A promising route lies in autonomous learning, where algorithms such as gpCAM - developed by Marcus Noack of the CAMERA team at Berkeley Lab - learn from a comparatively little amount of input data and decide themselves on the next steps to take. The main ingredients in gpCAM are a flexible Gaussian process engine and a powerful mathematical optimization, which is used to train the process but also to find the next optimal measurement points.

In the Bayesian language, gpCAM estimates the posterior mean and covariance and uses them in a function optimization to calculate the optimal next measurement point. The posterior is based on a prior Gaussian probability density function, which is repeatedly retrained on previously measured points ^[3,4].

The algorithm is known as the Kriging model in the geosciences, named after Danie G. Krige, a South African geologist, who sought to estimate the most likely distribution of gold from a few boreholes in the Witwatersrand reef complex in South Africa. Sometimes, this task resembles the situation in an experiment: the meaningful inelastic neutron scattering intensity S(Q,ω) might be distributed like gold veins defined by the momentum Q and energy hω transfer, and the experimenter does not know where to look next at. Moreover, while the gold seeker moves across a two-dimensional space (the land) when choosing a place to drill, the space defined by momentum and energy transfer is four-dimensional.

It is a surprisingly neglected practice to quantify measuring probabilities based on statistical or Bayesian methods or, simply speaking, a surprisingly neglected question, how many individual measuring points S(Qi,ωi)  are needed to either acquire sufficient information – whether it be in the agnostic case, or to confirm pre-established theoretical models.

A glance at published work suggests that the amount of meaningful data is of the order of kbytes or less, rather than Gbytes or more. The measurement time for hundreds of (meaningful) points on a TAS is of the order of hours, compared to several days in the traditional setting, which shows the optimization potential of an assisting autonomous algorithm. Already in the very first test runs, without any specific tuning of kernel definitions and acquisition functions, the algorithm demonstrated its efficiency as shown in the example below, where a conventional grid-scan on a magnetic excitation is compared to various intermediate states of the gpCAM acquisition. In addition, the results were achieved without human supervision or interaction.

The next goal is to assist gpCAM with the implementation of previously known information like crystal symmetry or even theoretical models, in order to reduce the number of points and to increase the efficiency of the measurement even further.