Dynamic Tikhonov State Forecasting Based on Large-Scale Deep Neural Network Constraints

Abstract

This work presents dynamic Tikhonov state forecasting based on large-scale deep neural network constraint for the solution to a dynamic inverse problem of electroencephalographic brain mapping. The dynamic constraint is obtained by using a large-scale deep neural network to approximate the dynamics of the state evolution in a discrete large-scale state-space model. An evaluation by using neural networks with several hidden layer configurations is performed to obtain the adequate structure for large-scale system dynamic tracking. The proposed approach is evaluated over two models of 2004 and 10,016 states in discrete time. The models are related to an electroencephalographic problem for EEG generation. A comparison analysis is performed by using static and dynamic Tikhonov approaches with simplified dynamic constraints. By considering the obtained results it can be concluded that the deep neural networks adequately approximate large-scale state dynamics by improving the dynamic inverse problem solutions.

Keywords

• dynamic state forecasting
• deep neural network
• large scale