A data-driven approach to modeling brain activity using differential equations

TL;DR

This paper introduces a novel data-driven algorithm for deriving differential equations from incomplete electrophysiological data to model brain activity, leveraging prior knowledge and validated on synthetic and real datasets.

Contribution

It presents a new algorithm capable of extracting differential equations from incomplete data, advancing modeling of brain activity beyond traditional methods.

Findings

Successfully applied to synthetic data

Demonstrated effectiveness on real electrophysiological data

Outperforms existing approaches in handling incomplete data

Abstract

This research focuses on an innovative task of extracting equations from incomplete data, moving away from traditional methods used for complete solutions. The study addresses the challenge of extracting equations from data, particularly in the study of brain activity using electrophysiological data, which is often limited by insufficient information. The study provides a brief review of existing open-source equation derivation approaches in the context of modeling brain activity. The section below introduces a novel algorithm that employs incomplete data and prior domain knowledge to recover differential equations. The algorithm's practicality in real-world scenarios is demonstrated through its application on both synthetic and real datasets.