Physics-informed Kriging for Nonlinear Systems Forecasting

A.D. Carnerero, D.R. Ramirez, T. Hatanaka, T. Alamo

In this paper, we present a novel prediction technique based on Kriging methods. Here, instead of assuming that the dynamics of the system are completely unknown and build a complete black-box model of the system, we opt to inject previous knowledge of the system into the black-box model in order to improve the performance of the obtained predictor. This can be easily done by adding new constraints to the Kriging predictor. These can be added in a hard-constraint or a soft-constraint manner, obtaining different results depending on this choice. Also, embedding physics-based conditions into the predictor is compatible with both the local-data based Kriging and the kernel-based Kriging technique, allowing for a flexible modeling depending on the application. Finally, the proposed predictors were tested against their state-of-the-art versions to show their effectiveness in a numerical example.