Time Sery Is All You Need

[Physics-Lee]

Hey, I am going to tell you a funny thing: Time Sery Is All You Need (to reconstruct the topology)

Remember in HH model, we do some simulations, using 4 non-linear ODEs to get 4 time series $V(t), n(t), m(t), h(t)$?

Now, follow my instructions:

• First, only pick $V(t)$, drop all other time series.
• Second, choose 2 super-parameters $\tau$ and $n$
• Third, save $V(t), V(t-\tau), V(t-2\tau) ... V(t-n\tau)$.

Then, we will get an amazing result: when you plot $V(t), V(t-\tau), V(t-2\tau) ... V(t-n\tau)$ in $n+1$ dimension and then use dimension-reduction technique like PCA to 4D, you can get the same topology as the original ODEs!

For example, below figure is for the case of Lorenz ODES.

[Physics-Lee]

My own simulation!

Just use GPT~

[Pripribiologist]

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