斯蒂尔杰斯时间反应扩散模型中陷阱定时与放置的精确离散伴随优化：加利西亚案例研究
Exact discrete-adjoint optimization of trap timing and placement in a Stieltjes-time reaction-diffusion model: A Galicia case study
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中文总结 AI 辅助
研究针对斯蒂尔杰斯时间反应扩散模型的陷阱定时与放置控制问题，通过推导精确离散伴随等方法，经基准测试和实际案例验证，实现机器精度一致性及伴随加速，联合控制优于其他控制，降低诊断目标，框架可重现。
中文摘要 AI 辅助
季节性种群模型需结合扩散、非活动期和突然的生物转移，同时对于局部干预保持可微性。我们为斯蒂尔杰斯时间反应扩散模型制定了一个有限维定时与放置控制问题，并推导了完全离散残差的精确伴随。连续有限元及隐式斯蒂尔杰斯 - 欧拉格式表示传播、隔室替换、重置和历史阶段平均值。对于所得的盒约束惩罚问题，我们证明了离散控制到状态映射的适定性和可微性、极小值的存在性、一阶平稳性以及直接灵敏度和伴随梯度之间的等价性。基准测试表明，随着陷阱数量从1增加到4，机器精度一致性（低于\(3\times10^{-15}\)）以及伴随加速从约7.5提高到30.9。该方法应用于加利西亚实际网格上的黄蜂陷阱活动。平滑激活窗口、域归一化移动核和完整伴随得到独立验证。最终的双簇控制仍然是可接受的，在每月120个时间细分时，缩放梯度无穷范数为\(2.97\times10^{-5}\)。在60、120和240细分下的固定控制评估产生的细化增量比为0.4984。在最精细级别，联合控制优于仅时间控制和参考控制，将诊断目标降低了0.49209%。这种降低取决于未校准的陷阱到死亡率强度，不应解释为现场捕获效率。该框架完全可重现，不声称全局最优或校准的现场管理处方。
英文摘要
Seasonal population models must combine diffusion, inactive periods and abrupt biological transfers while remaining differentiable with respect to localized interventions. We formulate a finite-dimensional timing-and-placement control problem for a Stieltjes-time reaction--diffusion model and derive the exact adjoint of the fully discrete residual. Continuous finite elements and an implicit Stieltjes--Euler scheme represent propagation, compartment replacement, resets and historical phase averages. For the resulting box-constrained penalized problem, we prove well-posedness and differentiability of the discrete control-to-state map, existence of a minimizer, first-order stationarity, and equivalence between direct-sensitivity and adjoint gradients. Benchmark tests show machine-precision agreement (below $3\times10^{-15}$) and adjoint speed-ups from about $7.5$ to $30.9$ as the number of traps increases from one to four. The method is applied to \textit{Vespa velutina} trap campaigns on a realistic Galicia mesh. Smoothed activation windows, domain-normalized moving kernels and the complete adjoint are independently verified. The final two-cluster control remains admissible and has a scaled gradient infinity norm of $2.97\times10^{-5}$ with 120 temporal subdivisions per month. Fixed-control evaluations at 60, 120 and 240 subdivisions yield a refinement-increment ratio of $0.4984$. At the finest level, the joint control outperforms time-only and reference controls, reducing the diagnostic objective by $0.49209%$. This reduction depends on uncalibrated trap-to-mortality intensities and should not be interpreted as field capture efficacy. The framework is fully reproducible, without claiming global optimality or a calibrated field-management prescription.
