In the context of industrial digitalization and real-time monitoring, accessing 3D fields (velocity, viscosity, turbulence, concentration, etc.) in real time can be crucial, as local sensor networks are sometimes insufficient to provide a comprehensive view of the system's dynamics. This PhD project aims to investigate a methodology for the real-time reconstruction of fields within an instrumented industrial tank equipped with a mixing system. The proposed approach relies on finite element modeling of the relevant physics within the tank (e.g., fluid dynamics, thermal processes) and model reduction techniques such as physics-based Machine Learning (virtual sensor approach). A key focus of this thesis will also be the development of the tank instrumentation and its associated acquisition chain, both to validate the models and to generate a database for applying the proposed methodology.