发表机构
Bundesanstalt für Materialforschung and -prüfung (BAM)（联邦材料研究与测试研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出基于扩散算子谱几何的投影方法，通过算子残差和有限宽度软投影选择与扩散流形一致的谱分量，实现噪声下的稳健恢复并保留主要热响应。
AI 中文摘要
扩散场遵循由算子强加的空间结构与时间衰减之间的关系，然而传统的谱滤波主要根据频率或波数大小来选择分量。在此，我们证明扩散算子在空间波数与模态衰减率的联合空间中定义了一种谱几何，其中物理上允许的模态位于流形 $\eta=\alpha|\mathbf{k}|^2$ 上。这种几何将谱尺度与物理一致性区分开来：高波数模态可以保持扩散一致性，而低波数模态可能违反控制动力学。我们利用这一区别，引入算子残差和有限宽度软投影，根据谱分量与扩散流形的距离而非其谱幅度来选择谱分量。数值研究证明了在噪声、扩散率失配和有限采集条件下的稳健恢复，并揭示了由流形宽度控制的一致性-保留权衡。光热实验进一步证实，该投影抑制了流形外谱内容，同时保留了主要热响应。这些结果确立了算子一致性作为扩散场的谱选择原则，并为耗散系统的物理信息处理提供了几何框架。
英文摘要
Diffusive fields obey operator-imposed relations between spatial structure and temporal decay, yet conventional spectral filtering selects components primarily according to frequency or wavenumber magnitude. Here we show that the diffusion operator defines a spectral geometry in the joint space of spatial wavenumber and modal decay rate, where physically admissible modes occupy the manifold $η=α|\mathbf{k}|^2$. This geometry separates spectral scale from physical consistency: high-wavenumber modes can remain diffusion-consistent, whereas lower-wavenumber modes can violate the governing dynamics. We exploit this distinction by introducing an operator residual and a finite-width soft projection that selects spectral components according to their distance from the diffusion manifold rather than their spectral magnitude. Numerical studies demonstrate robust recovery under noise, diffusivity mismatch, and finite acquisition, and reveal a consistency--retention tradeoff governed by the manifold width. Photothermal experiments further confirm that the projection suppresses off-manifold spectral content while retaining the dominant thermal response. These results establish operator consistency as a spectral-selection principle for diffusive fields and provide a geometric framework for physics-informed processing of dissipative systems.
