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

arXiv: https://arxiv.org/abs/2407.00824 · HTML: https://mlsanity.com/paper/2407.00824/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 22 references that are in the map.
- First posted on arXiv 14 Apr 2024.

## Builds on (most cited first, 9 of 9)

- [DeepXDE: A deep learning library for solving differential equations](https://mlsanity.com/paper/1907.04502/) (2019)
- [PDE-Net: Learning PDEs from Data](https://mlsanity.com/paper/1710.09668/) (2017)
- [PDE-Net 2.0: Learning PDEs from Data with A Numeric-Symbolic Hybrid Deep Network](https://mlsanity.com/paper/1812.04426/) (2018)
- [Hidden Physics Models: Machine Learning of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1708.00588/) (2017)
- [Physics Informed Deep Learning (Part II): Data-driven Discovery of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1711.10566/) (2017)
- [PySINDy: A comprehensive Python package for robust sparse system identification](https://mlsanity.com/paper/2111.08481/) (2021)
- [Data-driven discovery of Green's functions with human-understandable deep learning](https://mlsanity.com/paper/2105.00266/) (2021)
- [Data-driven discovery of free-form governing differential equations](https://mlsanity.com/paper/1910.05117/) (2019)
- [Data-driven Identification of 2D Partial Differential Equations using extracted physical features](https://mlsanity.com/paper/2010.10626/) (2020)

## Abstract (arXiv)

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.