AI 中文总结
研究可压缩空气动力学中信息传输与可观测性，用可微激波捕捉浸入边界求解器，通过传播梯度引入可观测性度量，发现信息传输不均，可观测性与可学习性相关但不同，流动状态和翼型几何影响其分布与逆学习收敛，建立定量框架。
AI 中文摘要
压力测量为可压缩空气动力学流动提供了稀疏但直接的观测结果，然而关于隐藏空气动力学参数的信息如何在流动中传输并编码在这些观测中仍知之甚少。本文利用可微激波捕捉浸入边界求解器研究可压缩空气动力学中的信息传输和可观测性。通过在完整的非定常流动解中传播梯度，引入了基于自动微分的可观测性度量，以量化稀疏压力测量对未知空气动力学参数的敏感性，并确定用于逆学习的信息传感位置。结果表明，空气动力学信息在流场中不均匀传输，产生高可观测性的局部区域。逆学习实验进一步表明，可观测性和可学习性是相关但不同的概念：虽然高可观测性探头通常有助于准确的参数恢复，但最高可观测性探头并不总是对参数推断最有效。此外，流动状态和翼型几何形状都对可观测性分布和逆学习的收敛行为有很大影响。这些发现建立了一个定量框架，用于理解空气动力学信息如何在稀疏测量中编码，并证明了自动微分在可观测性分析、信息传感器选择和空气动力学逆分析中的潜力。
英文摘要
Pressure measurements provide sparse but direct observations of compressible aerodynamic flows, yet how information about hidden aerodynamic parameters is transported through the flow and encoded in these observations remains poorly understood. Here, we investigate information transport and observability in compressible aerodynamics using a differentiable shock-capturing immersed-boundary solver. By propagating gradients through the full unsteady flow solution, an automatic-differentiation-based observability metric is introduced to quantify the sensitivity of sparse pressure measurements to unknown aerodynamic parameters and identify informative sensing locations for inverse learning. The results reveal that aerodynamic information is transported non-uniformly through the flow field, producing localized regions of high observability. Inverse-learning experiments further demonstrate that observability and learnability are related but distinct concepts: although highly observable probes generally facilitate accurate parameter recovery, the highest-observability probe is not consistently the most effective for parameter inference. Furthermore, both the flow regime and the airfoil geometry substantially influence the distribution of observability and the convergence behavior of inverse learning. These findings establish a quantitative framework for understanding how aerodynamic information is encoded in sparse measurements and demonstrate the potential of automatic differentiation for observability analysis, informative sensor selection, and aerodynamic inverse analysis.
