Numerical simulation is widely used to study physical systems, although it can be computationally too expensive. To counter this limitation, a surrogate may be used, which is a high-performance model that replaces the main numerical model by using, e.g., a machine learning (ML) regressor that is trained on a previously generated subset of possible inputs and outputs of the numerical model. In this context, inspired by the definition of the mean squared error (MSE) metric, we introduce the pointwise MSE (PMSE) metric, which can give a better insight into the performance of such ML models over the test set, by focusing on every point that forms the physical system. To show the merits of the metric, we will create a dataset of a physics problem that will be used to train an ML surrogate, which will then be evaluated by the metrics. In our experiment, the PMSE contour demonstrates how the model learns the physics in different model regions and, in particular, the correlation between the characteristics of the numerical model and the learning progress can be observed. We therefore conclude that this simple and efficient metric can provide complementary and potentially interpretable information regarding the performance and functionality of the surrogate.
IOS Press, Inc.
6751 Tepper Drive
Clifton, VA 20124
Tel.: +1 703 830 6300
Fax: +1 703 830 2300 email@example.com
(Corporate matters and books only) IOS Press c/o Accucoms US, Inc.
For North America Sales and Customer Service
West Point Commons
Lansdale PA 19446
Tel.: +1 866 855 8967
Fax: +1 215 660 5042 firstname.lastname@example.org