趋化性中的尺度衔接：游动-翻滚核估计的尺度一致前向稳定性
Bridging Scales in Chemotaxis: Scale-Uniform Forward Stability for Run-and-Tumble Kernel Estimation
AI总结：
该研究针对趋化性微观与宏观尺度模型的衔接问题，开发变分损失泛函估计游动-翻滚转向核，建立尺度一致前向稳定性估计，结合稀疏反演可鲁棒恢复各类异质性转向核。
AI中文摘要：
趋化运动在微观尺度由游动-翻滚动力学模型描述，在宏观尺度由Keller--Segel方程描述。我们开发变分损失泛函以估计转向核$T_\epsilon=T_0+\epsilon T_1$的两个分量$T_0(x)$和$T_1(x)$，其中$T_0$决定主导阶转向速率与扩散，$T_1$控制宏观趋化漂移。在合适的正则性与数据信息性假设下，我们建立了条件尺度一致前向稳定性估计，表明小损失会导致真实核与估计核在动力学和扩散 regime 下产生的前向解之间的差异很小。结合稀疏反演，该方法可准确恢复光滑、非光滑及强异质性核，且在测量噪声下保持鲁棒性。
英文摘要：
Chemotactic motion is described by run-and-tumble kinetic models at microscopic scales and by Keller--Segel equations at macroscopic scales. We develop variational loss functionals for estimating the two components $T_0(x)$ and $T_1(x)$ of a turning kernel $T_ε=T_0+εT_1$, where $T_0$ determines the leading-order turning rate and diffusion, while $T_1$ governs the macroscopic chemotactic drift. Under suitable regularity and data-informativeness assumptions, we establish conditional scale-uniform forward-stability estimates showing that a small loss leads to a small discrepancy between the forward solutions generated by the true and estimated kernels across the kinetic and diffusive regimes. Combined with sparse inversion, the method accurately recovers smooth, nonsmooth, and strongly heterogeneous kernels and remains robust under measurement noise.
