Fig. 5: Predicting dynamics from initial conditions using VAE embedding.
From: Autoencoder neural networks enable low dimensional structure analyses of microbial growth dynamics
a Two-step initial condition to trajectory mapping. We combined the pre-trained decoder component of the VAE with an MLP encoder. The MLP encoder maps initial conditions of growth dynamics to the VAE embedding. The VAE decoder then translates the latent embedding into phase space to generate a predicted trajectory. During training, the parameters of the MLP encoder are optimized to minimize the mean square error between predicted trajectory and a ground truth generated from ODE simulation starting from the initial condition. The parameters of the VAE decoder are fixed during MLP training. b Accuracy of predicted dynamics. We trained several predictive models using different sets of simulated growth curves, each corresponding to different sets of gLV parameters and/or community sizes. For two-member communities, we trained our predictive model, both VAE and MLP components, using 4800 training examples and then evaluated their performance on 1600 testing examples with an embedding dimension \(E=2.\) For the three-member and five-member communities, we used 3:1 train/test split for training and evaluation with \(E=3\) and \(E=5\) respectively (Methods). The top row shows a random subset of the simulated test set curves (in orange). The middle row shows the corresponding reconstructed curves (in blue). The bottom row shows a linear regression between predictions and the ground truth for all time points in all curves in the test set. Perfect alignment corresponds to the line y = x. The MLP-VAE models achieve high quality predictions (R2 \(\ge 0.99\)) for ecological dynamics with fixed point (columns 1,2, and 4), limit cycle (column 3), and chaotic attractors (column 5). c Sample predicted dynamics for two, three, and five member communities. Growth curves predictions (dashed blue) for two-member, three-member, and five-member communities and the corresponding ground truth curves (solid orange). For five-member communities simulated, the average R2 was 0.998.
