arXiv:2506.18522cs.LG2025-06KDD被引 1

用新方法提升动态系统建模精度,更稳更准。

DDOT: A Derivative-directed Dual-decoder Ordinary Differential Equation Transformer for Dynamic System Modeling

  • 基于双解码器和导数引导的Transformer模型,捕捉系统结构与动态。
  • 在ODEBench上重建与泛化性能分别提升4.58%和1.62%。
  • 适用于真实麻醉数据,适合做科学建模与复杂系统研究者使用。

揭示支配动态系统的隐含常微分方程(ODE)对理解复杂现象至关重要。传统符号回归方法难以捕捉时间动态与变量间相关性。当前先进方法ODEFormer虽在单轨迹推理上取得进展,但对初始点敏感,评估不全面。为此,我们提出发散差分度量(DIV-diff),通过目标区域网格点上的发散分析,实现对变量空间的全面稳定评估。同时引入DDOT(导数导向双解码器常微分方程Transformer),一种基于Transformer的模型,用于以符号形式重构多维ODE。通过引入预测ODE导数的辅助任务,有效捕获结构与动态行为。在ODEBench上的实验表明,DDOT在重建与泛化任务中分别实现$P(R^2 > 0.9)$绝对提升4.58%与1.62%,且DIV-diff降低3.55%。此外,在麻醉数据集上展示实际应用价值。

原文摘要 · Abstract (English)

Uncovering the underlying ordinary differential equations (ODEs) that govern dynamic systems is crucial for advancing our understanding of complex phenomena. Traditional symbolic regression methods often struggle to capture the temporal dynamics and intervariable correlations inherent in ODEs. ODEFormer, a state-of-the-art method for inferring multidimensional ODEs from single trajectories, has made notable progress. However, its focus on single-trajectory evaluation is highly sensitive to initial starting points, which may not fully reflect true performance. To address this, we propose the divergence difference metric (DIV-diff), which evaluates divergence over a grid of points within the target region, offering a comprehensive and stable analysis of the variable space. Alongside, we introduce DDOT (Derivative-Directed Dual-Decoder Ordinary Differential Equation Transformer), a transformer-based model designed to reconstruct multidimensional ODEs in symbolic form. By incorporating an auxiliary task predicting the ODE's derivative, DDOT effectively captures both structure and dynamic behavior. Experiments on ODEBench show DDOT outperforms existing symbolic regression methods, achieving an absolute improvement of 4.58% and 1.62% in $P(R^2 > 0.9)$ for reconstruction and generalization tasks, respectively, and an absolute reduction of 3.55% in DIV-diff. Furthermore, DDOT demonstrates real-world applicability on an anesthesia dataset, highlighting its practical impact.

动态系统符号回归TransformerODE建模

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