Oscillatory activity is ubiquitous in natural and engineered network systems. The interaction scheme underlying interdependent oscillatory components governs the emergence of network-wide patterns of synchrony that regulate and enable complex functions. Yet, understanding, and ultimately harnessing, the structure-function relationship in oscillator networks remains an outstanding challenge of modern science. Here, we address this challenge by presenting a principled method to prescribe exact and robust functional configurations from local network interactions through optimal tuning of the oscillators’ parameters. To quantify the behavioral synchrony between coupled oscillators, we introduce the notion of functional pattern, which encodes the pairwise relationships between the oscillators’ phases. Our procedure is computationally efficient and provably correct, accounts for constrained interaction types, and allows to concurrently assign multiple desired functional patterns. Further, we derive algebraic and graph-theoretic conditions to guarantee the feasibility and stability of target functional patterns. These conditions provide an interpretable mapping between the structural constraints and their functional implications in oscillator networks. As a proof of concept, we apply the proposed method to replicate empirically recorded functional relationships from cortical oscillations in a human brain, and to redistribute the active power flow in different models of electrical grids.

振荡活动在自然和工程网络系统中无处不在。相互依赖的振荡组件背后的交互方案控制着调节和启用复杂功能的全网络同步模式的出现。然而，理解并最终利用振荡器网络中的结构-功能关系仍然是现代科学面临的一项突出挑战。在这里，我们通过提出一种原则性的方法来解决这一挑战，该方法通过优化振荡器参数的调整来从本地网络交互中规定精确和稳健的功能配置。为了量化耦合振荡器之间的行为同步，我们引入了功能模式的概念，它编码了振荡器相位之间的成对关系。我们的程序计算效率高且可证明是正确的，考虑了受约束的交互类型，并允许同时分配多个所需的功能模式。此外，我们推导出代数和图论条件，以保证目标功能模式的可行性和稳定性。这些条件提供了结构约束与其在振荡器网络中的功能含义之间的可解释映射。作为概念验证，我们应用所提出的方法从人脑中的皮层振荡复制经验记录的功能关系，并在不同的电网模型中重新分配有功功率流。