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.

翻译：本文对多元曲面分析中的三次插值与径向基函数（RBF）插值方法进行了可复现的比较。为消除评估偏差，两种方法均在统一的切片式训练/测试协议下，对同一合成函数族进行评估。性能报告采用均方根误差（RMSE）、平均绝对误差（MAE）和决定系数（$R^2$）两个指标，分别在以下两种情况下进行：（i）无噪声观测；（ii）含噪声观测。在无噪声情况下，两种插值方法均能达到高精度，并各自展现出与输出相关的优势。在含噪声情况下，对噪声节点的精确插值会导致两种方法的样本外性能下降，出现过拟合现象；在我们的实验设置中，三次插值方法相对更为稳定。所有实验均通过一个基于SciPy/NumPy的单一脚本实现完全可复现，该脚本采用固定随机种子、重复分割以及基于自助法的不确定性汇总。从环境工程的角度来看，主要实践意义在于：热力学过程系统中存在噪声或表面不一致的测量数据不应被默认舍弃；相反，可以通过结构化处理和插值来恢复具有物理意义的过程行为。