Magnetorheological elastomers (MREs) are composite materials comprised of elastomer matrix and magnetic inclusions [1]. In periodic structures, the magneto-mechanical response can be exploited to induce buckling-type structural instabilities that give rise to an abrupt change in their microscopic morphology [4]. The detection of the related instability points together with the resulting buckling patterns is an elaborate and time-consuming process. It is thus our goal to create a surrogate model that can predict the associated effects in an accelerated manner and with a reduced footprint concerning direct computational resources. We study the macroscopic bifurcation behavior of MRE microstructures [4] as a starting point. We present a general spline-based computational approach for the prediction of physical phenomena that integrates quantitative (discrete, data-based) and qualitative (axiomatic, feature-based) evidence and information. For this approach, a new software-package for flexible spline-based regression is proposed: It enables to complement the available data by constraining the ansatz space by physical conditions. While the former are obtained from observation and given quantitatively (but potentially subjected to uncertainty and noise), the latter can be incorporated qualitatively through explicit function and parameter constraints, wiggle-constraints [2] or general non-linear constraints. Our general approach and software-package are then used to generate analytical expressions of instability landscapes [4] by least-squares minimization [5] taking into account both numerically obtained datasets of instability points and a-priori known physical features to rely on much scarcer datasets. [1] Danas, K., Kankanala, S. V., Triantafyllidis, N. Experiments and modeling of iron- particle-filled magnetorheological elastomers. Journal of the Mechanics and Physics of Solids 60, pp. 120–138. 2012 [2] Duchon, J. Splines minimizing rotation-invariant semi-norms in Sobolev spaces. Lecture Notes in Mathematics 571, pp. 85–100, 1977. [3] Kullback, S. and Leibler, R.A. On Information and Sufficiency. The Annals of Mathematical Statistics 22, pp. 79–86, 1951. [4] Polukhov, E. and Keip, M.-A. Multiscale stability analysis of periodic magnetorheological elastomers. Mechanics of Materials 159, 103699, 2021. [5] Wahba, G. Spline models for observational data. Society for Industrial and Applied Mathematics, 1990.