Understanding Short-Range Order (SRO) in alloys is essential in atomistic materials science, as it reveals the underlying mechanisms that drive their mechanical behavior. A precise description of local atomic environments plays a central role in characterizing and simulating complex alloys at the atomic scale. This study proposes a complementary method to the traditional SRO characterization methods by leveraging high-dimensional representations of atomic structures. These representations, commonly used as internal feature vectors, known as descriptors, in machine learning potentials, have matured significantly in recent years. We investigate how local chemical, geometric, and combined atomic effects influence the mechanical properties of medium- and high-entropy alloys (HEAs), and propose a method to identify regions with similar structural and chemical features in the multidimensional space defined by these invariant descriptors. Using the widely adopted bispectrum projection, we capture the short-range order factors—geometry and chemistry—and apply various techniques to explore the structure of the resulting high-dimensional space: (i) statistical distance analysis, which reveals the non-Gaussian nature of descriptor distribution associated with studied HEA systems, (ii) traditional Bayesian Gaussian mixture model, and (iii) a novel iterative scheme combining both approaches and a descriptor embedding. We demonstrate the efficiency of both methods on two alloys, NiCoCr (a medium-entropy alloy) and CoCuFeNiPd (a high-entropy alloy), making a priori predictions of zones of interest, called Gaussian ordered states. Finally, we show the influence of short-range order under tensile stress, opening new possibilities for predicting mechanical behavior based on these Gaussian ordered states.

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• Alloys
• Machine learning models
• Molecular dynamics
• Monte Carlo methods