ABSTRACT: 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.