Designing optimal perturbation inputs for system identification in neuroscience

AbstractInvestigating the dynamics of neural networks, which are governed by connectivity between neurons, is a fundamental challenge in neuroscience. Perturbation-based approaches allow the precise estimation of neural dynamic models and have been extensively applied in studies of brain functions and neural state transitions. However, the question of how optimal perturbations which most effectively identify dynamical models in neuroscience should be designed remains unclear. To address this, we propose a novel theoretical framework for estimating optimal perturbation inputs for system identification in linear time-invariant systems. The core theoretical insight underlying our approach is that perturbations reveal hidden dynamical modes that are otherwise obscured in the steady state, leading to improved accuracy in system identification. Guided by this insight, our framework derives an objective function to optimize perturbation inputs, which minimizes estimation errors in the model matrices. Building upon this, we further explore the relationship of this function with stimulation patterns commonly used in neuroscience, such as frequency, impulse, and step inputs. We then outline an iterative approach to perturbation input design. Our findings demonstrate that incorporating perturbation inputs significantly improves system identification accuracy as dictated by the objective function. Moreover, perturbation inputs tuned to a parameter related to the eigenvalues and a network structure of the intrinsic model enhance system identification. Through this iterative approach, the estimated model matrix gradually approaches the true matrix. As an application, we confirmed that the framework also contributes to the optimal control theory. This study highlights the potential of designing perturbation inputs to achieve the advanced identification of neural dynamics. By providing a framework for optimizing perturbations, our work facilitates deeper insights into brain functions and advances in the study of complex neural systems.