Learning network topology from partial observations in nonlinear dynamical systems

Inferring the underlying topology of complex dynamical networks is a fundamental problem in network science and system identification. In practical applications, topology inference is challenging due to unknown system dynamics, measurement noise, and partial state observability. To address these challenges, we propose a data-driven topology identification framework based on Koopman operator theory, delay embedding, and neural-network-based nonlinear representation learning. The Koopman dictionary functions are learned adaptively using neural networks, enabling flexible lifted representations directly from observed data. The proposed approach supports topology inference under partial state observability and demonstrates robust performance in the presence of measurement noise. Experimental results on both synthetic and realistic benchmark datasets show that the proposed approach can effectively recover network interaction structures while simultaneously learning a structured lifted dynamical representation of the underlying system.