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Making progress in studying the interplay between disorder and fluctuationsis challenged by the complexity of extracting robust insights from experimentsaffected by noise and finite resolution. This has hindered observations of theBragg glass phase, which is predicted to occur in vortex lattices and chargedensity wave systems in the presence of disorder. Despite its sharp theoreticaldefinition in terms of diverging correlation lengths, establishing theexistence of the Bragg glass phase in a charge density wave system has beenchallenging. Here, we present the first bulk probe evidence of a Bragg glassphase in the systematically disordered CDW material Pd$_x$ErTe$_3$ usingcomprehensive x-ray data and a novel machine learning data analysis tool, X-rayTemperature Clustering (X-TEC). Using data from 20,000 Brillouin zones readilyanalyzed using X-TEC, we establish a diverging correlation length in sampleswith moderate intercalation over a wide temperature range. To enable suchcomprehensive analysis, we introduced a new high-throughput measure of inversecorrelation length: "peak-spread". The detection of Bragg glass order and theresulting phase diagram significantly advance our understanding of the complexinterplay between disorder and fluctuations. Moreover, using X-TEC to targetfluctuations through a high-throughput measure of "peak spread" canrevolutionize how the fluctuations are studied in scattering experiments.

Bragg glass signatures in Pd$_x$ErTe$_3$ with X-ray diffraction Temperature Clustering (X-TEC)