Efficient state and parameter estimation for high-dimensional nonlinear system identification with application to MEG brain network modeling

TL;DR

This paper introduces a scalable, efficient dual-estimation method combining pseudo-optimal state estimation with a differentiable parameter optimization, demonstrated on high-dimensional brain network models from MEG data.

Contribution

It presents a novel, computationally efficient approach for large dual-estimation problems by integrating the Extended Kalman Filter into a differentiable optimization framework.

Findings

Achieves comparable accuracy to joint Kalman Filters with lower complexity.

Successfully applied to individualized brain models from MEG data.

Demonstrates scalability to high-dimensional systems.

Abstract

System identification poses a significant bottleneck to characterizing and controlling complex systems. This challenge is greatest when both the system states and parameters are not directly accessible leading to a dual-estimation problem. Current approaches to such problems are limited in their ability to scale with many-parameter systems as often occurs in networks. In the current work, we present a new, computationally efficient approach to treat large dual-estimation problems. Our approach consists of directly integrating pseudo-optimal state estimation (the Extended Kalman Filter) into a dual-optimization objective, leaving a differentiable cost/error function of only in terms of the unknown system parameters which we solve using numerical gradient/Hessian methods. Intuitively, our approach consists of solving for the parameters that generate the most accurate state estimator (Extended Kalman Filter). We demonstrate that our approach is at least as accurate in state and parameter estimation as joint Kalman Filters (Extended/Unscented), despite lower complexity. We demonstrate the utility of our approach by inverting anatomically-detailed individualized brain models from human magnetoencephalography (MEG) data.