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

Abstract

Understanding neural computation on the mechanistic level requires biophysically realistic neuron models. To analyze such models one typically has to solve systems of 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 aglobal scalar bound on precision. To overcome this problem, we propose to use recently developed probabilistic solvers instead, which are able to reveal and quantify numerical uncertainties, for example as posterior sample paths. Importantly, these solvers neither require detailed insights into the kinetics of themodels nor are they difficult to implement. Using these probabilistic solvers, we show that numerical uncertainty strongly affects the outcome of typical neuroscience simulations, in particular due to the non-linearity associated with the generation of action potentials. We quantify this uncertainty in individual single Izhikevich neurons with different dynamics, a large population of coupled Izhikevich neurons, single Hodgkin-Huxley neuron and a small network of Hodgkin-Huxley-like neurons. For commonly used ODE solvers, we find that the numerical uncertainty in these models can be substantial, possibly jittering spikes by milliseconds or even adding or removing individual spikes from the simulation altogether.