Euler-Maruyama-Based Data-Driven State Restoration and Parameter Adaptation in Stochastic Neural Fields With Finite Signal Transmission Rate

In this paper, we propose a data-driven parameters’ adaptation technique for Stochastic Dynamic Neural Field (SDNF) models with finite signal transmission rate modeled by a distance-dependent delay. Our approach integrates nonlinear Bayesian filtering methods into mathematical neuroscience by establishing the state-space representation for the SDNF models with the delays. This allows to formulate the filtering problem in order to reconstruct the average membrane potential from incomplete data available from measurement devices. Additionally, when the state-space model is set up, the unknown system parameters can be estimated in a systematic way, for example, by using the method of maximum likelihood. In this paper, we derive for the first time the SDNF-oriented adaptive Extended Kalman filter (EKF) with the space-dependent delays in order to calibrate the SDNF models and to reconstruct the average membrane potential from incomplete data collected. The main benefit of the novel methodology is that both problems–the state and parameter estimation–are solved in parallel. The numerical experiments are provided to illustrate a performance of the novel methodology.