Goal: given the current state of a contact network — who is infected and who is connected to whom — predict the network's state at a future time, including both updated infection labels and rewired edges, without simulating every microscopic event. This is an equation-free approach: rather than writing down a closed-form ODE for the macroscopic dynamics, we learn an effective evolution in a low-dimensional latent space directly from simulation data.
In the standard SIS model, each node is either susceptible (S) or infected (I). Infected nodes transmit the disease to susceptible neighbors at rate β and recover back to susceptible at rate γ.
On a graph, the topology matters. We extend the model with adaptive rewiring: susceptible nodes can sever edges to infected neighbors and form new connections elsewhere—analogous to how people avoid contact with the sick.
This co-evolution of disease state and network structure makes the system high-dimensional and difficult to simulate. Our approach compresses the full graph into a latent space, learns the dynamics there, and projects back.
The encoder $f_\theta$ maps the full graph state $G(t)$ into a low-dimensional latent vector $z$. A learned velocity $\vec{v}$ advances the latent state forward by $\Delta t$. The decoder $g$ lifts the updated latent representation back to a predicted graph state $\hat{G}(t + \Delta t)$.
SIS simulation on a stochastic contact network. Infection spreads along edges and nodes recover stochastically, producing the training data our autoencoder learns to compress and forecast.