用多个轨迹数据推断微分方程，提升模型泛化能力
Predicting symbolic ODEs from multiple trajectories
- 基于Transformer的符号回归，融合多实例学习
- 简单平均聚合策略显著提升推断性能
- 适用于多轨迹、含噪声的动力系统建模
我们提出MIO，一种基于Transformer的模型，用于从动力系统的多个观测轨迹中推断符号形式的常微分方程（ODE）。通过结合多实例学习与基于Transformer的符号回归，该模型有效利用同一系统的多次观测，学习更具泛化性的动态规律。我们研究了多种实例聚合策略，发现即使简单的均值聚合也能显著提升性能。MIO在1至4维系统及不同噪声水平下进行评估，始终优于现有基线方法。
原文摘要 · Abstract (English)
We introduce MIO, a transformer-based model for inferring symbolic ordinary differential equations (ODEs) from multiple observed trajectories of a dynamical system. By combining multiple instance learning with transformer-based symbolic regression, the model effectively leverages repeated observations of the same system to learn more generalizable representations of the underlying dynamics. We investigate different instance aggregation strategies and show that even simple mean aggregation can substantially boost performance. MIO is evaluated on systems ranging from one to four dimensions and under varying noise levels, consistently outperforming existing baselines.
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