Metastable austenitic steels may undergo a phase transformation from austenite to {\epsilon}- and/or {\alpha}- martensite due to stress or plastic deformation. This phase transformation is similar to the two-way effect observed in shape memory alloys, except that it is irreversible upon unloading, resulting in a stable martensitic phase, at least when {\alpha}-martensite is formed. The objective of this work is to demonstrate how a data-driven model for the phase transformation in metastable austenitic steels can be built. We investigate a broad class of descriptors that encode the topological information of three-dimensional microstructures in a compact data format suitable for use as an input vector in supervised machine learning (ML). The primary criterion for these descriptors is that they can be used to characterize both experimental and simulated microstructures in order to generate time-dependent data sets of the dynamical evolution of microstructures under various mechanical loads. In a subsequent step, the correlations of these microstructure descriptors with physical parameters describing the thermodynamic phase stability and mechanical loading are investigated. It is demonstrated that hybrid data sets from experimental and numerical modeling data can be generated that serve as the basis for the supervised training of a suitable ML algorithm. The trained ML model will be examined in terms of accuracy, robustness, and numerical efficiency in its description of deformation-induced phase transformations in metastable austenite.