Gaussian process (GP) regression is a flexible non-parametric approach to approximate complex models.In many cases,these models correspond to processes with bounded physical properties.Standard GP regression typically results in a proxy model which is unbounded for all temporal or spacial points,and thus leaves the possibility of taking on infeasible values.We propose an approach to enforce the physical constraints in a probabilistic way under the GP regression framework.In addition,this new approach reduces the variance in the resulting GP model.