Institute Quantum Phenomena in Novel Materials

Data Analysis using Artificial Intelligence

Here we present a new approach to eliminate measurement artifacts and evaluate neutron scattering data using artificial intelligence to determine physical parameters.

• Scientific Challenge
• Measurement and Training Data
• AI Approach
• ANNtoolbox

Scientific Challenge

We investigate novel magnetism that typically occurs in quantum spin systems and frustrated systems. While identifying, synthesizing and characterizing potential magnetic materials, our goal is to determine the magnetic Hamiltonian by inelastic neutron scattering.

An essential part of determining the exact magnetic Hamiltonian of a specimen is fitting the experimental inelastic neutron scattering (INS) data sets to theoretical simulations based on pre-assumed Hamiltonians. This approach works very well when the assumed Hamiltonian is approximately equal to the real one. However, for some magnets where quantum effects dominate, any small perturbation of the Hamiltonian can radically affect the inelastic excitation spectra, making the traditional fitting approach very time-consuming. Therefore, we would like to leverage machine learning models that can find the best-fitting Hamiltonian for a given experimental dataset.

Another potential application area of ​​machine learning algorithms concerns the quality of the experimental INS data. In general, INS data has problems with systematic or non-reproducible artifacts and noise caused by the measurement environment and/or additional sample-dependent characteristics. Currently, most of these artifacts are removed manually, which is often time-consuming and inaccurate. Therefore, an intelligent algorithm is needed to process the experimental data and automatically remove artifacts and other noise that is different for each measurement. We combine both aspects.

Measurement and Training Data

Determination of magnetic Hamiltonian of a system requires the measurement of complete excitation spectra. This is typically measured as a structure factor S(Q,ω) in inelastic neutron scattering experiments where Q (Q_x, Q_y, Q_z) is the momentum transfer and ω is the energy transfer. We perform these measurements at so called large-scale neutron facilities such as  ILL (Grenoble, France) and ISIS (Didcot, United Kingdom) and the large 4-dimensional S(Q,ω) dataset can be as big as 250 GB for a single system.

The measurement data to be evaluated are either measurements on powder (uniform statistical directional distribution) or single crystal measurements. For single crystals, INS experiments can usually record sections in three-dimensional reciprocal space. The fourth dimension is then the energy transfer. By making a prior selection, meaningful symmetry axes can be selected and sections can be placed along these so that the dimensions can be reduced to two. The scattering intensity is determined for each point in space and for each energy transfer. The number of these layers can be combined so that 4D data can also be evaluated.

Calculations with SpinW

SpinW (spin-double-u) is a Matlab library that can optimize magnetic structures using mean field theory and calculate spin wave dispersion and spin-spin correlation function for complex crystal and magnetic structures.

We use this package to calculate inelastic neutron scattering distributions as basic concept.

Spin Wave spectra S(Q',ω') in Yb₂Ti₂O₇ simulated from SpinW package for a random combination of the magnetic interactions J₁ to J₄ in a magnetic field of 0T, 2T and 5T.

HZB has supported this project from the beginning.

For details check https://www.spinw.org

Balz, C., Lake, B., Reuther, J. et al. Physical realization of a quantum spin liquid based on a complex frustration mechanism. Nature Phys 12, 942–949 (2016). https://doi.org/10.1038/nphys3826

Random Field

After a model has been developed using SpinW and the parameter range has been set, the generation of theoretical scatter distributions can begin. A Monte Carlo approach is chosen in which a random parameter set is continuously generated from which the scatter pattern is calculated. The result will be saved as a HDF5 file.

Training data generation

The data that is necessary to train an ANN must now be divided into the three groups:  Training, validation and testing dataset. The theoretical data must be converted to simulate measurement data with the usual measurement errors by adding gaps, noise, other peaks, background effects and/or different scale values.

AI Approach

The basic idea is to read the high-dimensional data sets into an artificial neural network and to receive a set of descriptive interaction parameters as a response. Python with Tensorflow and the Keras library are used for the implementation.

Various neural networks were tested, starting with a fully connected network, then CNN, algorithmically optimized CNN and finally an approach using a Bayesian neural network.

A full connected neural network as a first test system.

Investigations

Two IT topics were assigned for a bachelor's and a master's thesis at the Hunboldt University of Berlin.

• "Optimizing a Neural Network Analysis Approach for Simulated Neutron Measurement Data of Polycrystalline Samples", Humboldt Universität Berlin, bachelor thesis, Tim Schuster, 2023
• "Predicting Spin - Interaction Parameters of the Hamiltonian from Simulated INS Data of Single Crystals", Humboldt Universität Berlin, master thesis, Eduard Gette, 2023

ANNtoolbox

The ANNtoolbox software package, which is currently under development, combines the two concepts of the thesis publications mentioned in the previous section. In it, it is possible to configure the software according to the specifications via files or by setting variables and to search for the best ANN from different approaches. Corresponding functions are available for reading in data, creating simulation measurement data and for training and validation.

An example of the result of training with BaNi₂V₂O₈ powder data sets.