Machine Learning (ML) has become essential in several industries. In Computational Science and Engineering (CSE), the complexity of the ML lifecycle comes from the large variety of data, scientists' expertise, tools, and workflows. If data are not tracked properly during the lifecycle, it becomes unfeasible to recreate a ML model from scratch or to explain to stackholders how it was created. The main limitation of provenance tracking solutions is that they cannot cope with provenance capture and integration of domain and ML data processed in the multiple workflows in the lifecycle, while keeping the provenance capture overhead low. To handle this problem, in this paper we contribute with a detailed characterization of provenance data in the ML lifecycle in CSE; a new provenance data representation, called PROV-ML, built on top of W3C PROV and ML Schema; and extensions to a system that tracks provenance from multiple workflows to address the characteristics of ML and CSE, and to allow for provenance queries with a standard vocabulary. We show a practical use in a real case in the O&G industry, along with its evaluation using 239,616 CUDA cores in parallel.