Abstract: A central problem in science concerns forecasting sudden changes in complex systems, which are difficult to anticipate and disrupt the system’s functioning. Predicting these switching dynamics, particularly in brain systems, is vital for personal lives. Even though we collect data of complex systems at rapidly increasing rates, data availability does not lead to a better understanding of a system if the dynamics and interactions governing the system’s behavior remain unknown. Without insight into these rules, our predictive power remains limited. We addressed this question by introducing a unified reconstruction scheme by blending dynamical systems theory and statistical learning techniques. Although our approach works perfectly under given assumptions, the model reconstruction scheme can also surprisingly lead to recovering emergent hypernetworks with triplet and higher interactions among oscillators. This appears paradoxical at first glance because, initially, such models are defined as oscillator networks with pairwise interactions. In this work, we uncover a general mechanism for emerging hypernetworks when recovering models of nonlinearly coupled oscillators from data. We present a full description of such emergent hypernetworks using normal form theory and the local tree structure of the original network. Our findings shed light on the apparent abundance of hypernetworks and provide a constructive way to predict their emergence. Using the approach, we can create a proxy of a complex system and thereby make predictions about the critical transitions in the system.

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