  Computer algebra can answer various questions about partial differential
equations using symbolic algorithms. However, the inclusion of data into
equations is rare in computer algebra. Therefore, recently, computer algebra
models have been combined with Gaussian processes, a regression model in
machine learning, to describe the behavior of certain differential equations
under data. While it was possible to describe polynomial boundary conditions in
this context, we extend these models to analytic boundary conditions.
Additionally, we describe the necessary algorithms for Gr\"obner and Janet
bases of Weyl algebras with certain analytic coefficients. Using these
algorithms, we provide examples of divergence-free flow in domains bounded by
analytic functions and adapted to observations.
