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Scientific Machine Learning of Chaotic Systems Discovers Governing Equations for Neural Populations
Arxiv
|July 17, 2025
Summary
The new Prediction-Error Method with Universal Differential Equations (PEM-UDE) successfully extracts governing equations from chaotic systems, even with noisy data. This method outperforms traditional techniques in physics and neuroscience applications.
Area of Science:
- Complex Systems Dynamics
- Computational Physics
- Computational Neuroscience
Background:
- Extracting governing equations from chaotic systems is a significant challenge in physics and neuroscience.
- Traditional methods often fail with limited or noisy observational data.
Purpose of the Study:
- To introduce a novel method, PEM-UDE, for discovering interpretable mathematical expressions from chaotic dynamical systems.
- To demonstrate the method's efficacy in handling noisy and limited data where other techniques falter.
Main Methods:
- Combined the Prediction-Error Method (PEM) with Universal Differential Equations (UDEs).
- Smoothed optimization landscapes and removed chaotic properties during fitting without parameter distortion.
- Applied to chaotic systems like the Rossler system and noise-corrupted electrical circuit data.
Main Results:
- Successfully recovered hidden states and reconstructed dynamics from significantly noise-corrupted data.
- PEM-UDE outperformed symbolic regression methods like SINDy in recovering correct dynamics.
- Derived biologically constrained governing equations for neural populations, respecting network sparsity.
Conclusions:
- PEM-UDE offers a robust approach for equation discovery in chaotic systems, excelling with imperfect data.
- The derived neural population equations reveal emergent relationships between connection density, oscillation frequency, and synchrony.
- This work facilitates the development of mechanistic, multi-scale brain models bridging neuronal and macroscale activity.
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