Data-Driven Pattern Formation in Oscillator Networks Using Partial Observations

Effective control of oscillator networks is a fundamental challenge with applications across neuroscience, circadian biology, and engineering. The absence of accurate dynamical models has driven a shift toward data-driven control approaches. However, these methods often rely on measuring individual network elements and can only achieve simple binary patterns, such as synchronization and desynchronization, limiting their practical applicability. In this paper, we overcome these limitations and propose a data-driven control framework that can attain arbitrary synchronization patterns in oscillator populations without requiring measurements from all network elements. Our principal idea is to characterize a network synchronization pattern as a sequence of order parameters and formulate the control task as a stochastic optimization problem, which is solved using stochastic gradient descent. Through a range of numerical simulations, we demonstrate the effectiveness of our approach in forming diverse synchronization patterns in both simplified phase models and biophysical neuron models.