Exact Interpolation under Noise: A Reproducible Comparison of Clough-Tocher and Multiquadric RBF Surfaces
This work provides a reproducible comparison for environmental engineers dealing with noisy thermodynamic process data, though it is incremental as it applies existing methods to a specific domain.
The paper compared cubic and radial basis function interpolants for multivariate surface analysis under noise-free and noisy regimes, finding that both achieved high accuracy without noise but exact interpolation degraded performance with noise, with the cubic interpolant being more stable in noisy conditions.
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.