Probabilistic solvers enable a straight-forward exploration of numerical uncertainty in neuroscience models

Abstract

Understanding neural computation on the mechanistic level requires models of neurons and neuronal networks. To analyze such models one typically has to solve coupled ordinary differential equations (ODEs), which describe the dynamics of the underlying neural system. These ODEs are solved numerically with deterministic ODE solvers that yield single solutions with either no, or only a global scalar bound on precision. It can therefore be challenging to estimate the effect of numerical uncertainty on quantities of interest, such as spike-times and the number of spikes. To overcome this problem, we propose to use recently developed sampling-based probabilistic solvers, which are able to quantify such numerical uncertainties. They neither require detailed insights into the kinetics of the models, nor are they difficult to implement. We show that numerical uncertainty can affect the outcome of typical neuroscience simulations, e.g. jittering spikes by milliseconds or even adding or removing individual spikes from simulations altogether, and demonstrate that probabilistic solvers reveal these numerical uncertainties with only moderate computational overhead.