Non-Intrusive POD–RBF Reduced OrderModeling for Parametric and Transient MantleConvection

Mantle convection plays a fundamental role in governing the thermal and dynamical
evolution of terrestrial planets, yet its numerical simulation remains computationally ex-
pensive due to strong nonlinearities, high Rayleigh numbers, and the presence of thin
thermal boundary layers. In this work, we present a non-intrusive reduced-order modeling
(ROM) framework for two-dimensional mantle convection based on Proper Orthogonal
Decomposition combined with Radial Basis Function interpolation (POD–RBF).
High-fidelity full-order model (FOM) simulations are first performed using a finite-
volume discretization of the incompressible Boussinesq equations under the infinite-Prandtl-
number approximation. The FOM is carefully validated across a wide range of Rayleigh
numbers. Particular attention is devoted to high-Rayleigh-number regimes, where mesh
refinement studies are conducted to improve accuracy and ensure reliable reference solu-
tions.
The ROM is constructed from snapshot data of velocity and temperature fields. POD
analysis reveals a rapid decay of singular values, indicating a low-dimensional structure
of the solution manifold. The parametric dependence of the reduced coefficients is recon-
structed using RBF interpolation, yielding a fully data-driven and non-intrusive ROM.
To rigorously assess predictive capability, the ROM is validated using test points ex-
cluded from the training dataset. Leave-One-Out cross-validation demonstrates that the
ROM accurately predicts unseen solutions across the parameter space, with low relative
L2 errors for both velocity and temperature fields. Field-level comparisons confirm that
the dominant flow structures and thermal patterns are faithfully reproduced.
The framework is further extended to transient simulations, where both time and
Rayleigh number are treated as parameters. This two-dimensional parametric unsteady
ROM successfully captures time-dependent dynamics while providing significant compu-
tational speed-up. The proposed approach offers a robust and efficient tool for parametric
mantle convection modeling and provides a solid basis for future extensions toward three-
dimensional configurations and uncertainty quantification.