A new approach to combine physics-based and data-driven models using a localised trustworthiness metric

                                
==Abstract==

Artificial Neural Networks (ANNs) can solve many (un)supervised learning tasks by virtue of the universal approximation theorem. In the context of on-line process control for manufacturing processes, ANNs are an ideal approach for e.g., on-line monitoring or prediction tasks. However, since they are trained on experimental input-output pairs, the governing physical relations are only implicitly included. This, for instance, can cause inaccuracies when extrapolating to out-of-sample data-points [1]. On the other hand, the numerical approximation of the governing physical laws via numerical methods holds strong potential for the accurate simulation of physical phenomena that occur during manufacturing processes. However, the corresponding computational effort is an impediment that arises with the need for numerous simulations [2]. This makes the application of such numerical schemes computationally intractable within an on-line monitoring context. As such, it is clear that ANNs and numerical simulation models have strong potential, but are fundamentally different models. However, their combination serves as a potentially efficient and accurate aggregated predictor, the so called grey-box model. Such grey-box model is based on highly efficient machine learning algorithms, the black-box member, and backed by validated data with respect to physics generated by the numerical model, the white-box member. A grey-box model capable of defining a trustworthy prediction, including a measurement of uncertainty on the estimator, remains challenging.