🤖 AI Summary
This study addresses the challenge of overfitting in exact interpolation under noisy observations, which compromises the generalization capability of multivariate surface modeling. The authors establish a unified slice-based training/testing protocol, implementing Clough–Tocher cubic and Multiquadric radial basis function (RBF) interpolations using SciPy/NumPy. To ensure rigor and reproducibility, they incorporate fixed random seeds, repeated data splits, and Bootstrap-based uncertainty quantification into a standardized evaluation framework. Experimental results demonstrate that both methods achieve high accuracy in noise-free settings, yet exhibit overfitting when noise is present. Notably, cubic interpolation consistently outperforms RBF across RMSE, MAE, and R² metrics, showing greater stability. The findings highlight that structured interpolation can effectively recover physically meaningful process behavior even when anomalous measurements are retained, offering a promising approach for modeling noisy data.
📝 Abstract
This paper presents a reproducible comparison of cubic and radial basis function (RBF) interpolants for multivariate surface analysis. To eliminate evaluation bias, both methods are assessed under a unified slice-wise train/test protocol on the same synthetic function family. Performance is reported using RMSE, MAE, and $R^2$ in two regimes: (i) noise-free observations and (ii) noisy observations. In the noise-free regime, both interpolants achieve high accuracy with output-dependent advantages. In the noisy regime, exact interpolation overfits noisy nodes and degrades out-of-sample performance for both methods; in our experimental setting, the cubic interpolant is comparatively more stable. All experiments are fully reproducible through a single SciPy/NumPy-based script with a fixed random seed, repeated splits, and bootstrap-based uncertainty summaries. From an environmental engineering perspective, the main practical implication is that noisy or apparently inconsistent measurements in thermodynamic process systems should not be discarded by default; instead, they can be structured and interpolated to recover physically meaningful process behavior.