Table 3:

List of autoregressive dynamical models used for $\mathit{s}$-step ahead prediction of iEEG features in Eq. (2).

Model	Equation
Linear	${\hat{x}}_i[t+s]={\sum }_{n=0}^{l-1}{\alpha }_n{x}_i[t-n]$
Quadratic	${\hat{x}}_i[t+s]={\sum }_{m,n=0}^{l-1}{\beta }_{m,n}{x}_i[t-m]x_i[t-n]$
KNN	${\hat{x}}_i[t+s]=\frac{1}{K}{\sum }_{n=0}^{K-1}{x}_i^{\text{train}}\left[t_n+s\right]$ where $t_0,\dots ,t_{K-1}$ are time indices of the $K$-nearest neighbors among training data to $\left(x_i[t-l+1],\dots ,x_i\left[t\right]\right)$. We used $\text{K}=5$ for all patients.
MLP	${\hat{x}}_i[t+s]=\sigma \left({\mathbf{W}}_2\sigma \left({\mathbf{W}}_1{\mathbf{x}}_i^l\left[t\right]\right)\right)$ where $\sigma =\text{tanh}$ is the activation function, ${\mathbf{W}}_1\in {\mathbb{R}}^{H\times l},{\mathbf{W}}_2\in {\mathbb{R}}^{1\times H}$ are weight matrices, and ${\mathbf{x}}_i^l\left[t\right]=\left(x_i[t-l+1],\dots ,x_i\left[t\right]\right)$. We used $H=50$ for all patients.
Koopman autoencoder74	${\hat{x}}_i[t+s]=E{\left({\mathbf{x}}_i^l\left[t\right]\right)}^{\top }\theta +b$ and ${\mathbf{x}}_i^l[t+1]=D\left(KE\left({\mathbf{x}}_i^l\left[t\right]\right)\right)$, where the encoder is $E\left(\mathbf{x}\right)={\mathbf{W}}_e^2\sigma \left({\mathbf{W}}_e^1\mathbf{x}\right)$ with ${\mathbf{W}}_e^1\in {\mathbb{R}}^{p\times l},{\mathbf{W}}_e^2\in {\mathbb{R}}^{p\times p}$, and the decoder is $D\left(\mathbf{z}\right)={\mathbf{W}}_d^2\sigma \left({\mathbf{W}}_d^1\mathbf{z}\right)$ with ${\mathbf{W}}_d^1\in {\mathbb{R}}^{p\times p},{\mathbf{W}}_d^2\in {\mathbb{R}}^{l\times p}$. Here, $\sigma =\text{ReLU},p$ is the latent dimension (set to 64), and $K\in {\mathbb{R}}^{p\times p}$ is the learnable Koopman operator that evolves the latent state forward by one step. $\theta \in {\mathbb{R}}^{p\times 1}$ and $b\in \mathbb{R}$.

KNN: k-nearest neighbor; MLP: multi-layer perceptron.