从多初始条件的网络动态数据中学习有效模型，提升噪声下的建模精度。
Learning effective models from network dynamics data with multiple initial conditions using weak form SINDy
- 基于弱形式SINDy方法，从多轨迹数据中发现系统演化方程
- 高噪声下增加轨迹数可显著提升模型准确率，少量额外轨迹即达主要收益
- 直接从随机过程数据推导连续常微分方程，优于传统均场近似
社会系统由个体间通过社交互动构成的网络组成。研究这些网络上的过程演化有助于理解社会行为模式。本文研究一个结合线上与线下社交活动的系统，利用弱形式稀疏非线性动力学识别（WSINDy）方法，从数据中直接学习支配方程。我们使用网络上随机交互过程的平均场近似模型生成数据，评估不同噪声水平下系统的恢复精度。结果表明，在噪声较高时，增加轨迹数量能提升准确性，但仅需少量额外轨迹即可获得大部分收益，后续改进趋于平缓。此外，我们还从网络随机数据的平均值中学习有效的常微分方程模型。当传统均场近似失效时，直接从随机过程识别出的连续常微分方程能更准确匹配数据，并揭示底层动态机制。
原文摘要 · Abstract (English)
Social systems consist of networks of individuals who influence one another through social interactions. Studying how processes evolve on these networks can help us better understand patterns of social behavior. We study a system that couples online and offline social activity and investigate how to learn effective models directly from data using Weak Form Sparse Identification of Nonlinear Dynamics (WSINDy), a method for discovering governing equations. We assess learning performance using data generated by a mean-field approximation model of a stochastic interaction process on networks and test how accurately the system can be recovered under different noise levels. Our results show that using more trajectories improves accuracy when noise is high, but only a small number of additional trajectories is needed to gain most of the benefit, with little improvement beyond that. We also learn effective ODE models from averaged stochastic data on networks. When traditional mean-field approximations fail, identifying continuum ODEs directly from stochastic processes yields efficient models that better match the data and provide deeper insight into the underlying dynamics.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。