Validation and constrained optimization of a Gaussian process surrogate for arsenate removal by iron modified zeolite

Accurate interpolation of a small adsorption dataset does not establish reliable prediction at unrepresented operating conditions or safe treatment performance. This study developed and audited a surrogate-based decision framework for arsenate removal by iron-modified zeolite using 27 batch tests. Four inputs described initial arsenic concentration, adsorbent dose, pH and contact time. Six fixed model configurations were compared using leave-one-out cross-validation and ten repetitions of five-fold cross-validation, followed by leave-one-level-out stress tests for Gaussian process regression (GPR). GPR with an isotropic radial basis function kernel achieved a leave-one-out R² of 0.9943 and a root mean squared error (RMSE) of 0.887 percentage points. Its repeated five-fold RMSE increased to 1.510 ± 0.260 points, while withholding concentration or dose levels increased pooled RMSE to 4.176 and 4.282 points. Conditional intervals based on 1.96 model standard deviations covered only 19 of 27 held-out observations. Introducing a retrospective RMSE floor increased descriptive coverage to 25 of 27, without establishing future coverage. Optimization treated influent concentration as a disturbance and restricted operating combinations to the experimental convex hull. Retaining 95% of the reference conservative score allowed a predicted contact-time reduction from 180 to 132.1 min at 3 g/L, or a dose reduction to 2.740 g/L at 180 min. These are unconfirmed operating candidates. The framework identifies useful trade-offs while exposing dependence on validation design, geometric support and uncertainty assumptions; it does not convert predictive accuracy into evidence of drinking-water compliance.