Computer simulations based on statistical methods have emerged as a powerful tool for studying structure-property relationships at the atomistic level. However, to provide reliable insights into materials in realistic conditions, it is essential to accurately describe their behaviour at finite temperatures. While ab initio calculations offer the flexibility to study any stoichiometry and chemical complexity, their scalability and computer resource requirements limit their application to large systems and timescales. Machine learning interatomic potentials (MLIP) overcome this limitation by approximating quantum mechanical (QM) potential energy surfaces at a fraction of the cost. Despite their advantages, ML methods based on atom-centred density have been constrained to systems with 4-5 chemical elements.

This thesis aims to address these challenges by focusing on two aspects: 1) accurately describing finite temperature effects, and 2) enabling ML models based on atom densities representations to describe systems with a large number of chemical elements. To address finite temperature effects, we employ a combination of machine learning and statistical sampling methods, using elemental nickel as a prototypical material with a wide application temperature range. Our framework covers bulk, interfacial, and defect properties from 100 to 2500 K and models nuclear quantum fluctuations and electronic entropy when necessary. The presented framework is versatile and, when paired with an appropriate potential, can be readily applied to complex alloys and various material classes.

Another problem we tackle in this thesis is how to describe different chemistries with ML. We generate a dataset covering a wide range of concentrations of 25 d-block transition metals and apply a scheme to compress chemical information in lower-dimensional space. The resulting model demonstrates semi-quantitative accuracy for prototypical alloys and is stable for extrapolation. We use this model to study element segregation in an equimolar 25-element alloy, reproducing in a computational setting Cantor et al.'s experiments. Our observations are used to define data-driven Hume-Rothery rules for alloy design guidance. Furthermore, we investigate three prototypical alloys (CoCrFeMnNi, CoCrFeMoNi, and IrPdPtRhRu), determining their stability and short-range order behaviour of their constituents.