Autonomous learning of nonlocal stochastic neuron dynamics
This work provides improved methods for accurately modeling the stochastic dynamics of neurons, which is crucial for neuroscientists studying information processing in the brain, particularly when dealing with biologically realistic correlated noise sources.
This paper addresses the challenge of modeling neuronal dynamics driven by correlated noise, which typically requires closure approximations for probability density function (PDF) equations. The authors propose two closure methods: a modified nonlocal large-eddy-diffusivity closure and a data-driven sparse regression approach, testing them on non-spiking leaky integrate-and-fire and FitzHugh-Nagumo neurons.
Neuronal dynamics is driven by externally imposed or internally generated random excitations/noise, and is often described by systems of random or stochastic ordinary differential equations. Such systems admit a distribution of solutions, which is (partially) characterized by the single-time joint probability density function (PDF) of system states. It can be used to calculate such information-theoretic quantities as the mutual information between the stochastic stimulus and various internal states of the neuron (e.g., membrane potential), as well as various spiking statistics. When random excitations are modeled as Gaussian white noise, the joint PDF of neuron states satisfies exactly a Fokker-Planck equation. However, most biologically plausible noise sources are correlated (colored). In this case, the resulting PDF equations require a closure approximation. We propose two methods for closing such equations: a modified nonlocal large-eddy-diffusivity closure and a data-driven closure relying on sparse regression to learn relevant features. The closures are tested for the stochastic non-spiking leaky integrate-and-fire and FitzHugh-Nagumo (FHN) neurons driven by sine-Wiener noise. Mutual information and total correlation between the random stimulus and the internal states of the neuron are calculated for the FHN neuron.