Coupling of reduced mathematical models and data for assimilation and the development of digital twins
The digitisation in all its aspects and the dematerialisation of most acts have brought us into the worlds of digital technology, of simulation, of artificial intelligence and of massive data. The idea of retrieving, acquiring and using this data to make digital twins (of complex machines, but also why not of all or part of ourselves) is truly fascinating (but can of course frighten). The reality is nevertheless more complex because the data are often partial, even oriented, flawed and sometimes also costly.Mathematical modelling of the phenomena that govern these data often exists, based on physical laws and proven in many situations. These models are also approximate, but they provide knowledge that is useful to combine with data to gain accuracy for the design of numerical twins: ie use data to correct model bias and use the model to correct measurement bias. We will present the basics of this approach together with the associated theory and we will illustrate through a few examples the progress and achievements in this area and will draw some perspectives.