Data-driven modeling of interrelated dynamical systems

Non-linear dynamical systems describe numerous real-world phenomena, ranging from the weather, to financial markets and disease progression. Individual systems may share substantial common information, for example patients’ anatomy. Lately, deep-learning has emerged as a leading method for data-driven modeling of non-linear dynamical systems. Yet, despite recent breakthroughs, prior works largely ignored the existence of shared information between different systems. However, such cases are quite common, for example, in medicine: we may wish to have a patient-specific model for some disease, but the data collected from a single patient is usually too small to train a deep-learning model. Hence, we must properly utilize data gathered from other patients. Here, we explicitly consider such cases by jointly modeling multiple systems. We show that the current single-system models consistently fail when trying to learn simultaneously from multiple systems. We suggest a framework for jointly approximating the Koopman operators of multiple systems, while intrinsically exploiting common information. We demonstrate how we can adapt to a new system using order-of-magnitude less new data and show the superiority of our model over competing methods, in terms of both forecasting ability and statistical fidelity, across chaotic, cardiac, and climate systems.

Yonatan Elul, Eyal Rozenberg, Amit Boyarski, Yael Yaniv, Assaf Schuster, Alex M. Bronstein