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| Format: | Preprint |
| Published: |
2026
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| Online Access: | https://arxiv.org/abs/2603.10590 |
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| _version_ | 1866917332867088384 |
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| author | Sancak, Mirkan Emir |
| author_facet | Sancak, Mirkan Emir |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_10590 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Exact Interpolation under Noise: A Reproducible Comparison of Clough-Tocher and Multiquadric RBF Surfaces Sancak, Mirkan Emir Graphics 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. |
| title | Exact Interpolation under Noise: A Reproducible Comparison of Clough-Tocher and Multiquadric RBF Surfaces |
| topic | Graphics |
| url | https://arxiv.org/abs/2603.10590 |