Discovering governing equations of complex network dynamics is a fundamental challenge in contemporary science with rich data, which can uncover the mysterious patterns and mechanisms of the formation and evolution of complex phenomena in various fields and assist in decision-making. In this work, we develop a universal computational tool that can automatically, efficiently, and accurately learn the symbolic changing patterns of complex system states by combining the excellent fitting ability from deep learning and the equation inference ability from pre-trained symbolic regression. We conduct intensive experimental verifications on more than ten representative scenarios from physics, biochemistry, ecology, epidemiology, etc. Results demonstrate the outstanding effectiveness and efficiency of our tool by comparing with the state-of-the-art symbolic regression techniques for network dynamics. The application to real-world systems including global epidemic transmission and pedestrian movements has verified its practical applicability. We believe that our tool can serve as a universal solution to dispel the fog of hidden mechanisms of changes in complex phenomena, advance toward interpretability, and inspire more scientific discoveries.

翻译：发现复杂网络动力学的控制方程是当代数据丰富科学中的一个根本性挑战，它能揭示各领域中复杂现象形成与演化的神秘模式和机制，并辅助决策。本研究开发了一种通用计算工具，通过结合深度学习的优异拟合能力与预训练符号回归的方程推断能力，能够自动、高效且准确地学习复杂系统状态的符号变化模式。我们在物理、生物化学、生态学、流行病学等领域的十余个代表性场景中进行了密集的实验验证。通过与网络动力学领域最先进的符号回归技术进行比较，结果证明了我们工具在有效性和效率方面的突出表现。该工具在全球疫情传播和行人运动等真实系统中的应用验证了其实用性。我们相信，该工具可作为通用解决方案，驱散复杂现象变化隐藏机制的迷雾，推进可解释性研究，并激发更多科学发现。