  Decision formation in perceptual decision-making involves sensory evidence
accumulation instantiated by the temporal integration of an internal decision
variable towards some decision criterion or threshold, as described by
sequential sampling theoretical models. The decision variable can be
represented in the form of experimentally observable neural activities. Hence,
elucidating the appropriate theoretical model becomes crucial to understanding
the mechanisms underlying perceptual decision formation. Existing computational
methods are limited to either fitting of choice behavioural data or linear
model estimation from neural activity data. In this work, we made use of sparse
identification of nonlinear dynamics (SINDy), a data-driven approach, to
elucidate the deterministic linear and nonlinear components of often-used
stochastic decision models within reaction time task paradigms. Based on the
simulated decision variable activities of the models, SINDy, enhanced with a
trial-averaging approach, could readily uncover the dynamical equations of the
models while predicting the models' choice accuracy and decision time across a
range of signal-to-noise ratio values. In particular, SINDy performed
relatively better for decision models which have an accelerating dynamical
component during decision formation, as expressed by a metastable linear
competing accumulator model and a nonlinear bistable model. Taken together, our
work suggests that SINDy can be a useful tool for uncovering the dynamics in
perceptual decision-making, and more generally, for first-passage time
problems.
