Table 1.

Summary of key terminology and notations

Term	Symbol	Definition	Example
Input Dimension	$D$	The number of time points sampled in a bacterial growth curve used as input to an autoencoder, experimental or simulated.	For experimental growth curve in group 1, the number of features $D=98$ (Supplementary Table 1). For community simulations, $D$ ranges between $20$ and $40$.
Embedding Dimension	$E$	The dimension of the latent space to which individual population growth curves or a set of population growth curves corresponding to an entire communities’ dynamics are compressed in an autoencoder.	For Fig. 1a, $E=2$. For Fig. 2b, $E=30.$ For data in Figs. 3 and 5, $E$ is varied as a control parameter. For Fig. 3, $E$ varies between 2 and 30.
Community or Phase Space Dimension	$N$	The number of individual species in a microbial community. Since each species corresponds to an independent variable in the community growth dynamics ODE model, $N$ is also equal to the dimension of the ODE system phase space.	For Fig. 4, $N=2.$ For Fig. 6, $N$ varies between 3 and 6.
Parametric Space Dimension	$O\left(N^2\right)$	The number of parameters used to parameterize a growth dynamics ODE model. This varies between choice of underlying ODE model, but generally scales $O\left(N^2\right).$	For Fig. 6, the dimensionality of the parametric space is exactly $N^2+1$, with $N^2-N$ non-zero pairwise interaction terms ${\gamma }_{ij}$, $N$ growth rates ${\mu }_i$, and 1 fixed background stress term $\sigma$.