多层热反射测量中快速不确定性传播的物理推导自然坐标
Physics-Derived Natural Coordinates for Fast Uncertainty Propagation in Multilayer Thermoreflectance
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中文总结 AI 辅助
针对多层热反射测量中非线性反演的不确定性量化难题，提出基于物理推导的自然坐标变换结合归一化MC基准，实现快速分析传播并保留非高斯不确定性，获得与MC匹配的不对称置信区间。
中文摘要 AI 辅助
多层结构热反射测量中的不确定性量化具有挑战性，因为热物理性质提取涉及具有强耦合参数的非线性反问题。基于协方差的分析传播方法效率高，但假设局部线性和近似高斯分布的拟合变量，而蒙特卡洛（MC）传播能够捕获非高斯行为，但计算成本高，并且在同时拟合跨越多个数量级的参数时可能不可靠。在此，我们通过将归一化MC采样（用于获得可靠的基准分布）与基于物理的变量变换相结合，用于分析不确定性传播，来解决这些问题。从多层热扩散方程中，我们识别出自然坐标：界面热阻1/G，基底组合sqrt(k_z k_r)和sqrt(k_z C)，以及薄膜组合k_r/C、hC和Ch^2/k_z。在多个代表性多层系统和热反射测量模式中，这些坐标近似服从高斯分布，即使原始物理参数是偏斜的。在变换空间中进行基于协方差的传播，并将结果映射回物理参数，可得到与归一化MC基准紧密匹配的不对称置信区间。该方法保留了恢复参数的非高斯不确定性结构，同时避免了重复的非线性拟合，为受扩散热传导控制的多层系统中的热反射测量不确定性量化提供了一种快速且具有物理可解释性的方法。
英文摘要
Uncertainty quantification in thermoreflectance measurements of multilayer structures is challenging because thermophysical-property extraction involves nonlinear inverse problems with strongly coupled parameters. Covariance-based analytical propagation is efficient but assumes local linearity and approximately Gaussian fitted variables, whereas Monte Carlo (MC) propagation captures non-Gaussian behavior but is computationally expensive and can be unreliable when simultaneously fitting parameters spanning very different orders of magnitude. Here, we address these issues by combining normalized MC sampling, used to obtain reliable benchmark distributions, with physics-based variable transformations for analytical uncertainty propagation. From the multilayer heat-diffusion equation, we identify natural coordinates: the interfacial thermal resistance 1/G, the substrate combinations sqrt(k_z k_r) and sqrt(k_z C), and the thin-film combinations k_r/C, hC, and Ch^2/k_z. Across several representative multilayer systems and thermoreflectance modalities, these coordinates are approximately Gaussian even when the original physical parameters are skewed. Performing covariance-based propagation in the transformed space and mapping the results back to physical parameters yields asymmetric confidence intervals that closely match normalized MC benchmarks. The approach preserves the non-Gaussian uncertainty structure of the recovered parameters while avoiding repeated nonlinear refitting, providing a fast and physically interpretable methodology for thermoreflectance uncertainty quantification in multilayer systems governed by diffusive heat conduction.
发表机构
- Huazhong University of Science and Technology（华中科技大学）
- University of Pittsburgh（匹兹堡大学）
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