Benchmarking tree-based machine learning surrogates for the coupled Luikov heat and mass transfer system

Abstract

Replacing repeated high-quality simulations with a fast surrogate is central to parametric studies, sensitivity analyses, and inverse design of coupled transport systems, yet the relative merits of tree-based ensembles for this task remain insufficiently characterized. A purely data-driven benchmark is therefore presented, in which five regressors of increasing flexibility — ridge regression, random forest, extremely randomized trees, histogram-based gradient boosting, and XGBoost — are compared as surrogates for the coupled Luikov system of heat and mass transfer, a stiff multiphysics problem whose bidirectional coupling and multi-scale behavior make repeated numerical solution costly. The surrogates map the five governing dimensionless groups (the thermal and mass Biot numbers, the Luikov number, the Kossovitch number, and the Posnov number) together with the spatio-temporal coordinates directly to the dimensionless temperature and moisture fields, with no physics embedded in the model. A dataset of 120 cases was produced with a fully implicit finite-difference solver, yielding 243,000 pointwise samples. The five candidates were then compared on a case-level 80/20 split with five-fold grouped cross-validation, so that accuracy reflects generalization to unseen parameter sets. The extremely randomized trees model attained the highest cross-validated accuracy T^*R² = 0.971, M^*R² = 0.952, with the lowest fold-to-fold variance for the temperature field and generalized to 24 held-out cases T^*R² = 0.980, M^*R² = 0.984; per-case median R² of 0.990 and 0.984). Averaged over ten independent case-level splits, the held-out R² was 0.978 ± 0.011 (T*) and 0.971 ± 0.010 (M*), the more stable estimate of generalization. Permutation importance singled out dimensionless time as the strongest predictor in both fields, with the thermal Biot number ranking next for temperature and the Luikov number and spatial position next for moisture—an ordering consistent with the underlying transport physics. Extremely randomized trees, and tree-based ensembles more broadly, thus emerged as accurate and interpretable surrogates for the coupled Luikov system that remain inexpensive to evaluate, at least across the five-parameter envelope sampled here.