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<p>Complex systems are characterized by many underlying entities and their intricate interactions. We contextualize ecological niche theory and evolutionary game theory through a system of nonlinear mixed ordinary differential equations (nMODEs) to reconstruct informative, dynamic, omnidirectional, and personalized networks (idopNetworks) for complex systems at any dimension. We implement a multi-task learning (MTL) algorithm into the matrix form of linearized nMODEs to execute two coupled tasks for group-level and elementwise sparsity on nonlinear feature representations. Beyond existing networking practice, MTL-based idopNetworks can capture all-around interacting links, nonlinearities, and emergent properties of a complex system, which, to a larger extent, approximate the complexity of complex systems. We apply our model to learn gene regulatory idopNetworks from transcriptional data for parasite <i>Plasmodium falciparum</i>, identifying previously-unknown regulatory roles of several genes in mediating malaria infection. Our model provides insight of machine learning to analyze, model, and interpret complex data in a non-Euclidean space.</p><p></p>

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Multi-task learning of complex networks via nonlinear ordinary differential equations

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年5月19日

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  • Ang Dong,
  • Changjian Fa,
  • Zhifan Li,
  • Shing-Tung Yau,
  • Rongling Wu

摘要

Complex systems are characterized by many underlying entities and their intricate interactions. We contextualize ecological niche theory and evolutionary game theory through a system of nonlinear mixed ordinary differential equations (nMODEs) to reconstruct informative, dynamic, omnidirectional, and personalized networks (idopNetworks) for complex systems at any dimension. We implement a multi-task learning (MTL) algorithm into the matrix form of linearized nMODEs to execute two coupled tasks for group-level and elementwise sparsity on nonlinear feature representations. Beyond existing networking practice, MTL-based idopNetworks can capture all-around interacting links, nonlinearities, and emergent properties of a complex system, which, to a larger extent, approximate the complexity of complex systems. We apply our model to learn gene regulatory idopNetworks from transcriptional data for parasite Plasmodium falciparum, identifying previously-unknown regulatory roles of several genes in mediating malaria infection. Our model provides insight of machine learning to analyze, model, and interpret complex data in a non-Euclidean space.