Data-Completion and Model Correction by Means of Evanescent Regularization

Abstract

System components are often regarded as part of a whole system, especially when it comes to data-driven modeling. Thus, subsystem modeling is disregarded in general when building a data-driven response, especially since multiple subsystem outputs are never measured in real applications. However, subsystem knowledge and accurate modeling are of utmost importance when aiming to repair, tune or troubleshoot a system. This work proposes a holistic modeling of subsystems in an embedded system setting. A hybrid modeling starting from the physics-based model is proposed in this work, correcting or enhancing the model, and predicting output variables, even when a measurement is never available for some of those variables. The process relies on the variables’ history, and employs an adjoint-free neural ordinary differential equation technique, along with evanescent regularization to enhance the convergence on the unmeasurable variables. The updated model converges to the exact measurements, for both the measurable and the unmeasurable variables. Multiple examples are presented using synthetic data, to allow an easy evaluation of the hidden or unmeasurable variables. The relative error offered by the updated model is around 0.001% for the measurable quantities and 0.1% for the unmeasurable ones.