Emulating Wilson-Cowan neural mass dynamics with grey-box Neural ODEs: a progressive-complexity study of unmodelled behaviour

Neural mass modelling is a powerful tool in computational neuroscience. The Wilson-Cowan (WC) model is a well-established, low-dimensional description of population dynamics. Its simplicity, however, disregards subtler phenomena that may be present in the real plant. This work investigates a preliminary grey-box replication of neural mass dynamics using Neural ODEs. A WC-structured backbone is combined with a learnable NN correction for unmodelled behaviour. At this stage, data is generated by a WC simulator with refractoriness and optogenetic actuator dynamics. Fidelity is measured by rollout error on held-out stimuli. Each disturbance is isolated in a progressive-complexity protocol. The actuator lag adds a hidden state with its own memory, which no state-based correction can represent, while refractoriness, a pure function of the state, is capturable. Under refractoriness alone, a memoryless correction already reproduces the dynamics, and expanding the backbone with the physical form of the disturbance improves performance. . Under actuator dynamics alone, memoryless corrections fail. Only augmenting the model with a first-order filter of learnable time constant restores fidelity. The memory of the omitted physics, rather than its magnitude, determines whether accurate reproduction is achieved. This gives a criterion for when state augmentation is necessary. Future work will validate this on experimental recordings.