We consider the problem of optimizing initial conditions and timing in dynamical systems governed by unknown ordinary differential equations (ODEs), where evaluating different initial conditions is costly and there are constraints on observation times. To identify the optimal conditions within several trials, we introduce a few-shot Bayesian Optimization (BO) framework based on the system's prior information. At the core of our approach is the System-Aware Neural ODE Processes (SANODEP), an extension of Neural ODE Processes (NODEP) designed to meta-learn ODE systems from multiple trajectories using a novel context embedding block. Additionally, we propose a multi-scenario loss function specifically for optimization purposes. Our two-stage BO framework effectively incorporates search space constraints, enabling efficient optimization of both initial conditions and observation timings. We conduct extensive experiments showcasing SANODEP's potential for few-shot BO. We also explore SANODEP's adaptability to varying levels of prior information, highlighting the trade-off between prior flexibility and model fitting accuracy.

翻译：本文研究在由未知常微分方程（ODE）支配的动力系统中优化初始条件与观测时机的课题，其中评估不同初始条件的代价高昂，且观测时间存在约束。为在有限次试验内确定最优条件，我们提出一种基于系统先验信息的少样本贝叶斯优化（BO）框架。该方法的核心是系统感知神经ODE过程（SANODEP）——这是神经ODE过程（NODEP）的扩展，通过新型上下文嵌入模块从多轨迹数据中元学习ODE系统。此外，我们专门针对优化目标提出了一种多场景损失函数。我们的两阶段BO框架有效整合了搜索空间约束，实现了对初始条件与观测时序的高效协同优化。通过大量实验，我们展示了SANODEP在少样本BO任务中的潜力，并探究了其对不同先验信息水平的适应能力，揭示了先验灵活性与模型拟合精度之间的权衡关系。