The massive data that modern facilities generate spanning 3D reciprocal space volumes include 𝒪(10^{4}) Brillouin zones (BZ) at rates of 𝒪(10^{2}) gigabytes per hour. The sheer quantity of data presents a major challenge in searching for unknown order parameters and their fluctuations.

When the temperature 𝑇 is lowered below a certain threshold, the system can give way to an ordered state. Hence the temperature evolution of the X-ray diffraction (XRD) intensity for reciprocal space points **q**: *I*(**q**,*T*) must be qualitatively different if the given reciprocal space point **q** reflects order parameters or their fluctuations. Tracking the temperature evolution of thousands of Brillouin zones to identify systematic trends and correlations in a comprehensive manner is impossible to achieve manually without selection bias.

**XTEC is an unsupervised and interpretable ML algorithm that can identify the order parameters from the voluminous data by clustering the temperature series associated with a given q, I(q,T), according to qualitative features in the temperature dependence. **

At the core of XTEC is a Gaussian Mixture Model (GMM) clustering to identify distinct temperature trajectories. The figure below shows a simplified illustration of GMM clustering behind XTEC.

To cluster distinct *I*(*g*) trajectories, given the collection of series {*I*(*g*0), *I*(*g*1), … ,*I*(*g**N*-1)} (*N*=2 in the above figure), the raw trajectories (in panel (a)) can be mapped to a simple Gaussian Mixture Model (GMM) clustering problem on a *N*-dimensional space (panel (b)). In the above figure, GMM clustering identifies three distinct clusters color-coded as red, blue and green. From the GMM cluster mean and variance (panel (b)), we get the distinct trajectories of *I*(*g*) and their variance (panel (c)).

Note that *g* can be any parameter like temperature, time, energy *etc*. Hence apart from temperature series data, you can adapt XTEC to analyze any other parametric dependence like time or energy series data.

The following contains a summary of the steps involved in a typical *X-TEC* analysis. You can follow the steps listed in a Jupyter notebook tutorial (XTEC_Tutorial.ipynb) in the X-TEC Github repository.