基于相图绘制的常微分方程主动符号发现
Active Symbolic Discovery of Ordinary Differential Equations via Phase Portrait Sketching
AI总结：
针对轨迹数据中常微分方程符号发现依赖固定数据集及蝴蝶效应导致的数据存储难题，提出APPS方法，通过在相空间识别信息区域并批量采样初始条件，显著降低了数据维护成本并提高了发现准确率。
摘要：
从轨迹数据中进行常微分方程（ODEs）的符号发现在AI驱动的科学发现中扮演着关键角色。现有的符号方法主要依赖于固定的、预先收集的训练数据集，这通常会导致次优的性能，如图1中的案例研究所示。受主动学习的启发，我们研究了查询信息性轨迹数据的策略，以增强对预测ODE的评估。然而，动力系统中的蝴蝶效应表明，初始条件的微小变化会导致截然不同的轨迹，因此使用传统的主动学习需要存储大量轨迹数据。为了解决这一问题，我们引入了基于相图绘制的常微分方程主动符号发现（APPS）。APPS不直接选择单个初始条件，而是首先在相空间中识别信息性区域，然后从该区域中采样一批初始条件。与传统主动学习方法相比，APPS缓解了维护大量数据的差距。大量实验表明，与使用被动收集数据集的基线方法相比，APPS能持续发现更准确的ODE表达式。
英文摘要：
The symbolic discovery of Ordinary Differential Equations (ODEs) from trajectory data plays a pivotal role in AI-driven scientific discovery. Existing symbolic methods predominantly rely on fixed, pre-collected training datasets, which often result in suboptimal performance, as demonstrated in our case study in Figure 1. Drawing inspiration from active learning, we investigate strategies to query informative trajectory data that can enhance the evaluation of predicted ODEs. However, the butterfly effect in dynamical systems reveals that small variations in initial conditions can lead to drastically different trajectories, necessitating the storage of vast quantities of trajectory data using conventional active learning. To address this, we introduce Active Symbolic Discovery of Ordinary Differential Equations via Phase Portrait Sketching (APPS). Instead of directly selecting individual initial conditions, our APPS first identifies an informative region within the phase space and then samples a batch of initial conditions from this region. Compared to traditional active learning methods, APPS mitigates the gap of maintaining a large amount of data. Extensive experiments demonstrate that APPS consistently discovers more accurate ODE expressions than baseline methods using passively collected datasets.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
