System identification for complex dynamical systems: a survey

Abstract

System identification provides the data-to-model link for analysis, prediction, diagnosis, and control of dynamical systems. As engineering and scientific systems become increasingly nonlinear, high-dimensional, networked, time-varying, and partially observed, identification methods must handle noisy data, incomplete prior knowledge, safety constraints, and downstream control requirements. This review surveys system identification for complex dynamical systems through a unified framework that connects model structure, operating mode, estimation target, and computational setting. We first revisit single-system identification, including regularized regression, sparse Bayesian learning, Kalman-type filtering, and recent structured recursive methods such as auxiliary-model, multi-innovation, hierarchical, filtering-based, and coupled identification. We then review multi-system identification for families of interacting or related subsystems, covering deep neural architectures, sparse equation discovery for ordinary and partial differential equations, hybrid and topology-aware modeling, and meta-learning-based fast adaptation. Finally, we discuss large language model-assisted workflows for symbolic regression, equation discovery, feature generation, and scientific modeling. By comparing these methodological streams, this review highlights their strengths, limitations, and applicability to prediction, synchronization, diagnosis, and control. We identify key open challenges, including robust identification under biased or limited data, uncertainty-aware modeling, interpretable learning, reproducible benchmarking, and tighter integration between identification, experiment design, and control synthesis.