Structural identifiability in fractional-order networks

Abstract

Identifying parameters of fractional-order discrete-time dynamical networks from input–output data is crucial for modeling complex systems in neuroscience and biology. Despite existing methods, fundamental conditions ensuring structural identifiability based solely on network structure remain unexplored. This paper establishes identifiability theory for fractional-order networks by proving that a network is structurally identifiable if and only if all its subsystems are identifiable. We introduce a graph-theoretical hierarchical algorithm that systematically partitions networks into identifiable subsystems via input–output reachability, enabling decomposition-based parameter learning with provable guarantees. Extensive simulation experiments validate that this approach preserves identifiability while achieving significant computational speedup, demonstrating scalability for large-scale systems.