A Robust Gaussian Process Paradigm for Predictive Modeling on Small Data sets in Environmental Science: A Case Study in Ballasted Flocculation

Environmental
processes including ballasted flocculation
(BF) present
significant optimization challenges due to complex multicomponent
interactions and small, heterogeneous experimental data sets that
frequently lead to overfitted machine learning (ML) models with poor
real-world performance. To address this, we developed GP-BT, a Gaussian
Process Bayesian Tuning framework that systematically optimizes kernel
selection and hyperparameters by directly minimizing cross-validation
loss, explicitly prioritizing generalization over training set fitting.
Comprehensive evaluation across three environmental data sets demonstrated
GP-BT’s superior robustness compared to conventional algorithms
(Random Forest, XGBoost, CatBoost) and standard GP models. The GP-BT’s
practical value was confirmed through 52 independent laboratory experiments,
achieving lower prediction errors on unseen conditions. The method’s
conservative learning strategyavoiding aggressive fitting
of sparse, noisy data pointsproved crucial for reliable real-world
performance. Applied to combined sewer overflows treatment optimization,
GP-BT uncovered experimental conditions achieving 98% removal efficiency,
compared to 89% predicted by the overfitted Random Forest model. Experimental
validation confirmed these predictions, revealing substantial process
potential masked by traditional modeling approaches. SHapley Additive
exPlanations (SHAP) analysis showed that GP-BT’s interpretations
better aligned with established physicochemical mechanisms, properly
emphasizing reagent importance over less controllable factors. Beyond
specific applications, this work provides environmental researchers
with a ready-to-use, rigorously validated framework for extracting
reliable insights from costly, small-scale experimental data sets.
To maximize impact, we provide an open-source Python package (pip
install bayesian-gp-cvloss) and interactive web platform (www.ai4env.world), enabling widespread
adoption of robust ML practices that can accelerate discovery of hidden
performance potential in environmental technologies.