DOUBLE PROJECTION FOR RECONSTRUCTING DYNAMICAL SYSTEMS: BETWEEN STOCHASTIC AND DETERMINISTIC REGIMES

Understanding how to train dynamical models from neural data is central to interpreting the computations neural populations perform. Yet, despite many methods for system identification in neuroscience, the conditions under which stochastic versus deterministic modeling is preferable are insufficiently explored. We propose a novel method from the dynamical variational autoencoder family: DPDSR (Double Projection Dynamical System Reconstruction). Our proposed method uses two projections: one mapping observed data into latent system states, and the other mapping into an underlying noise time series. This decomposition allows the model to reconstruct both state trajectories and driving noise, enabling more expressive stochastic models.
Importantly, DPDSR admits a deterministic special case, which gives us a fair comparison between the deterministic and stochastic formulations under the same architectural backbone. We benchmark DPDSR across six test problems, which include both synthetically generated systems and real data, and compare it against state-of-the-art methods. Our results show that DPDSR delivers robust performance across all problems, outperforming or matching existing approaches in reconstructing latent dynamics.
Furthermore, we examine how the teacher forcing interval shapes the nature of the trained dynamics. We uncover two distinct regimes: (i) for short forcing intervals, the model learns a chaotic deterministic regime, and (ii) for longer forcing intervals, it defaults to a stochastic noise-driven regime.
Overall, DPDSR provides a new method for learning dynamical models from neural data and contributes to a better conceptual understanding of emergence of dynamical regimes in the trained models.