Modeling continuous-time dynamics constitutes a foundational challenge, and uncovering inter-component correlations within complex systems holds promise for enhancing the efficacy of dynamic modeling. The prevailing approach of integrating graph neural networks with ordinary differential equations has demonstrated promising performance. However, they disregard the crucial signed information intrinsic to graphs, impeding their capacity to accurately capture real-world phenomena and leading to subpar outcomes. In response, we introduce a novel approach: a signed graph neural ordinary differential equation, adeptly addressing the limitations of miscapturing signed information. Our proposed solution boasts both flexibility and efficiency. To substantiate its effectiveness, we seamlessly integrate our devised strategies into three preeminent graph-based dynamic modeling frameworks: graph neural ordinary differential equations, graph neural controlled differential equations, and graph recurrent neural networks. Rigorous assessments encompass three intricate dynamic scenarios from physics and biology, as well as scrutiny across four authentic real-world traffic datasets. Remarkably outperforming the trio of baselines, empirical results underscore the substantial performance enhancements facilitated by our proposed approach.Our code can be found at https://github.com/beautyonce/SGODE.

我们提出了一种新颖的方法：带有符号图神经常微分方程，巧妙地解决了误捕获符号信息的局限性。我们的方法在动态建模中显示出显著的性能提升，通过物理学、生物学领域的三个复杂动态场景以及四个真实世界交通数据集的验证结果，明显优于三种基准模型。

建模连续时间动态的带符号图神经常微分方程