Hybrid twins based on optimal transport

Abstract

Nowadays data is acquiring an indisputable importance in every field including engineering. In the past, experimental data was used to calibrate state-of-the art models. Once the model was optimally calibrated, numerical simulations were run. However, data can offer much more, playing a more important role than calibration or statistical analysis in the modeling/simulation process. Indeed, today data is gathered and used to train models able to replace complex engineering systems. The more and better the training data, the more accurate the model is. However, in engineering experimental data use to be the best data but also the most expensive in time and computing effort. Therefore, numerical simulations, cheaper and faster, are used instead but, even if they are closed to reality, they always present an error related to the ignorance of the engineer over the complex real system. It seems thus coherent to take advantage of each approach. This leads to the “hybrid twin” rationale. On the one hand, numerical simulations are computed as primary data source, assuming their inherent error. On the other hand, some experimental data is gathered to train a machine learning correction model which fills the prediction-measurement gap. However, learning this ignorance gap becomes difficult in some fields such as fluids dynamics, where a regression over the localized solutions can lead to non physical interpolated solutions. Therefore, the “hybrid twin” methodology proposed in this article relies on Optimal Transport theory, which provides a mathematical framework to measure distances between general objects and a completely different interpolation approach between functions.