Algorithmic Linearly Constrained Gaussian Processes
This work addresses the challenge of incorporating precise algebraic constraints into Gaussian processes for applications in physics, geomathematics, and control, representing a novel integration of fields rather than an incremental improvement.
The authors tackled the problem of constructing multi-output Gaussian process priors that satisfy linear differential equations by using Gröbner bases for parameterization, resulting in a method that combines stochastic learning with computer algebra to handle examples like Maxwell's equations.
We algorithmically construct multi-output Gaussian process priors which satisfy linear differential equations. Our approach attempts to parametrize all solutions of the equations using Gröbner bases. If successful, a push forward Gaussian process along the paramerization is the desired prior. We consider several examples from physics, geomathematics and control, among them the full inhomogeneous system of Maxwell's equations. By bringing together stochastic learning and computer algebra in a novel way, we combine noisy observations with precise algebraic computations.