Paper
Exact Interpolation under Noise: A Reproducible Comparison of Clough-Tocher and Multiquadric RBF Surfaces
Authors
Mirkan Emir Sancak
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.
Metadata
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Raw Data (Debug)
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"raw_xml": "<entry>\n <id>http://arxiv.org/abs/2603.10590v1</id>\n <title>Exact Interpolation under Noise: A Reproducible Comparison of Clough-Tocher and Multiquadric RBF Surfaces</title>\n <updated>2026-03-11T09:46:30Z</updated>\n <link href='https://arxiv.org/abs/2603.10590v1' rel='alternate' type='text/html'/>\n <link href='https://arxiv.org/pdf/2603.10590v1' rel='related' title='pdf' type='application/pdf'/>\n <summary>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.</summary>\n <category scheme='http://arxiv.org/schemas/atom' term='cs.GR'/>\n <published>2026-03-11T09:46:30Z</published>\n <arxiv:primary_category term='cs.GR'/>\n <author>\n <name>Mirkan Emir Sancak</name>\n </author>\n </entry>"
}