Linearly constrained Gaussian processes
This work addresses the need for reliable constraint handling in Gaussian processes for applications like physics-based modeling, though it is incremental as it builds on existing methods.
The paper tackles the problem of incorporating known linear constraints into Gaussian processes by modifying the covariance function, ensuring that all predictions and samples satisfy the constraints, and demonstrates this on simulated and real-data examples.
We consider a modification of the covariance function in Gaussian processes to correctly account for known linear constraints. By modelling the target function as a transformation of an underlying function, the constraints are explicitly incorporated in the model such that they are guaranteed to be fulfilled by any sample drawn or prediction made. We also propose a constructive procedure for designing the transformation operator and illustrate the result on both simulated and real-data examples.