等响应探测与重复校准识别复杂系统噪声观测中的标度关系
Equal-response probing with replicate calibration identifies scaling relations from noisy observations of complex systems
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中文总结 AI 辅助
本文提出带重复校准的等响应探测方法，从噪声观测中识别复杂系统的标度结构，区分真实响应与噪声，并在八个基准场景中验证其有效性。
中文摘要 AI 辅助
复杂物理系统的无量纲描述有时可进一步简化，当多个输入组组合成单一复合标度坐标时。从噪声响应评估中识别此类结构具有挑战性，因为表观偏差可能反映真实的响应结构或评估噪声。本文发展了带重复校准的等响应探测方法，以评估两个无量纲输入在规定的方向和坍缩容差下是否支持单组表示。等响应几何提供了无需直接数值微分的候选坐标，而第二阶段评估所得一维坍缩的准确性。重复评估估计两个阶段的噪声贡献，从而得出可约化、不可约和不确定三种结果。我们在八个基于模型的基准场景中评估该框架，涵盖粗糙管流、细胞单层伤口闭合、微流控液滴生成和柱屈曲。六个场景满足两个标准，两个场景均不满足，而在精确约化基准中恢复了已知的约化坐标。受控合成测试评估了误报行为、对结构偏差的敏感性以及噪声校准。这些结果表明，重复校准的等响应探测如何区分特定场景的标度结构与可归因于评估噪声的变化，同时在评估噪声妨碍在规定容差下做出明确判定时保留不确定结果。
英文摘要
Dimensionless descriptions of complex physical systems can sometimes be reduced further when multiple input groups combine into a single composite scaling coordinate. Identifying such structure from noisy response evaluations is difficult because apparent departures may reflect either genuine response structure or evaluation noise. Here we develop equal-response probing with replicate calibration to assess whether two dimensionless inputs support a one-group representation under prescribed directional and collapse tolerances. Equal-response geometry provides a candidate coordinate without direct numerical differentiation, while a second stage evaluates the accuracy of the resulting one-dimensional collapse. Replicate evaluations estimate the noise contribution to both stages, enabling reducible, not-red and unresolved outcomes. We evaluate the framework across eight model-based benchmark regimes spanning rough-pipe flow, cell-monolayer wound closure, microfluidic droplet generation and column buckling. Six regimes satisfy both criteria and two fail both, while known reduced coordinates are recovered in exact-reduction benchmarks. Controlled synthetic tests assess false-alarm behaviour, sensitivity to structural departures and noise calibration. These results show how replicate-calibrated equal-response probing distinguishes regime-specific scaling structure from variation attributable to evaluation noise while retaining an unresolved outcome when evaluation noise precludes a definitive verdict at the prescribed tolerances.
发表机构
- Chalmers University of Technology（查尔姆斯理工大学）
- Wageningen University（瓦赫宁根大学）
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