Multi-task learning of complex networks via nonlinear ordinary differential equations
Ang Dong, Changjian Fa, Zhifan Li, Shing–Tung Yau, Rongling Wu · Communications Physics · 2026
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. Traditional network models struggle to untangle the complex, nonlinear dynamics of interacting biological components. By integrating differential equations with multi‑task learning, the authors reconstruct regulatory networks that reveal previously unknown, biologically plausible patterns of gene regulation mediating malaria infection.