Physics-based Penalization for Hyperparameter Estimation in Gaussian Process Regression

•Physics-based equality constraints can be applied as soft-constraints through a penalized Maximum-Likelihood estimation function.•Physics-based penalization has a statistically meaningful effect on hyperparameter tuning in Gaussian Process Regression.•Physics-based penalization helps improve the quality of Gaussian Process Regression fit.•Physics-based penalization leads to mitigation of overfitting under sparse data scenarios.