Grey-Box Bayesian Optimization for ISAC in Fluid-Antenna Assisted Air-Ground Network

Fluid antenna systems (FAS) provide extra position agile spatial diversity for integrated sensing and communication (ISAC), by jointly optimizing the port selection and precoding. However, this optimization is challenging in air ground networks due to the intricate dual objective Pareto frontier, complex self-interference, and prohibitive channel state information overhead. To overcome these bottlenecks, this work proposes a novel grey box multi objective Bayesian optimization framework to address the joint design of discrete port selection and ISAC precoding. Unlike black box methods, this architecture explicitly leverages known physical system models to learn unknown channel constituents, dramatically reducing sample complexity. To navigate high dimensional combinatorial spaces, an adaptive trust region mechanism powered by expected hypervolume improvement (EHI) acquisition is implemented. Furthermore, the framework incorporates a spatio-temporal tracking strategy to handle the continuous mobility of users and targets, robustly capturing the drifting optimum in time varying environments. Simulations demonstrate that this framework achieves significantly faster convergence and discovers superior Pareto optimal configurations, validating its efficiency for dynamic real time FAS-ISAC deployments.