Learning to Decouple Complex Systems
This addresses the challenge of handling irregularly sampled and cluttered sequential data in real-world complex systems, which is an incremental improvement in a less considered setting.
The paper tackles the problem of decoupling complex systems with cluttered observations into simpler subsystems and a meta-system for interactions, using a sequential learning approach with projected differential equations, and shows advantages over state-of-the-art methods on synthetic and real-world datasets.
A complex system with cluttered observations may be a coupled mixture of multiple simple sub-systems corresponding to latent entities. Such sub-systems may hold distinct dynamics in the continuous-time domain; therein, complicated interactions between sub-systems also evolve over time. This setting is fairly common in the real world but has been less considered. In this paper, we propose a sequential learning approach under this setting by decoupling a complex system for handling irregularly sampled and cluttered sequential observations. Such decoupling brings about not only subsystems describing the dynamics of each latent entity but also a meta-system capturing the interaction between entities over time. Specifically, we argue that the meta-system evolving within a simplex is governed by projected differential equations (ProjDEs). We further analyze and provide neural-friendly projection operators in the context of Bregman divergence. Experimental results on synthetic and real-world datasets show the advantages of our approach when facing complex and cluttered sequential data compared to the state-of-the-art.