Machine learning to discover the governing dynamical mathematical equations underlying perceptual decision-making

Most computational modelling studies on perceptual decision-making identify computational model parameters based on fitting choice behavioural data, and to a lesser extent, fitting neural dynamics. However, no study has made use of data-driven approaches to elucidate the underlying dynamical mathematical equations generating the observed neural dynamics, which can be nonlinear in nature. In this work, we make use of a data-driven algorithm called sparse identification of nonlinear dynamics (SINDy), originally developed to discover governing physical equations from measurement data, to discover the dynamical equations of various stochastic two-choice decision-making models based on simulated data. In particular, we collated simulated data from the standard drift-diffusion model (DDM), the linear leaky competing accumulator (LCA) model and its DDM-approximated version, and a nonlinear dynamical model endowed with working memory.
Model parameters were estimated by applying the SINDy algorithm to the neural dynamics. To reduce noise effects, we proposed an averaging method in which model parameters were estimated across trials. After model parameters were estimated, neural dynamics and choice behaviour (accuracy and decision time) of the deduced model were simulated and compared with that of the original model.
We found that SINDy could readily identify the linear LCA model parameters for across-trial and single-trial conditions, especially for higher signal-to-noise ratio. This was expected as SINDy was originally developed for deterministic dynamical systems. In contrast, for the rest of the models, as signal-to-noise ratio increased, the SINDy-derived models’ behaviour became more dissimilar to that of the original respective models. To understand this, we determined the root-mean-square error for these models’ parameters and found strong positive correlation with the model’s choice behaviour discrepancy for the DDM and nonlinear model. However, this was not the case for the DDM-approximated LCA model; as signal-to-noise ratio increased within the reaction time task (a first-passage time framework), the dynamics generated by the original models ramp up too fast towards decision thresholds, thus revealing less data and SINDy becoming less accurate in elucidating the underlying governing dynamics.
Taken together, we showed for the first time, the potential and limitation of SINDy applied to stochastic first-passage time problem for decision-making. Further investigations include applying to fuller neural dynamics with different decision task paradigm and exploring other averaging approaches.