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Neural ODEs on Biological Dynamics

Neural ODEs applied to the FitzHugh-Nagumo neuron model — phase-portrait recovery as a more honest diagnostic than trajectory MSE.

Part 1

FitzHugh-Nagumo & Why Continuity Matters

The FHN equations, autonomous vs non-autonomous dynamics, why continuous-time inductive biases match biological data.

Part 2

Implementation

Ground-truth FHN simulator, autonomous Neural ODE with RK4, discrete-RNN baseline.
View Code on GitHub

Part 3

Phase-Portrait Recovery

Both models fit trajectories to MSE 0.02; only the Neural ODE recovers the underlying flow field (cosine 0.94–0.96) — that's the difference between fitting data and learning the physics.