Predicting Future State of Nonlinear Dynamical Systems with Multi-View Embedding

Future state prediction of nonlinear dynamical systems has significant applications in diverse fields, ranging from Earth science to social science and neuroscience. Yet, we still lack systematic methods to achieve accurate and synchronous prediction of nonlinear dynamical systems without knowing the underlying dynamical systems. Here we overcome this challenge by developing a data-driven framework based on multi-view embedding with a spatiotemporal information transformation (MVIT). Our approach efficiently converts spatial information of the system into temporal information by reconstructing multiple delayed attractors matched with optimal non-delayed attractor manifolds. By integrating with parallel reservoir computing, MVIT clearly outperforms other existing predictive methods in synchronous dynamic predictions for various paradigmatic models as well as real-world systems from medicine and infrastructure. Notably, our approach also demonstrates robustness against noise and exhibits scalable long-term prediction capabilities. Our approach offers an avenue to discover hidden mechanisms of complex systems and has potential to be applied to more real-world systems from diverse fields.