  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.
