Cluster-Based Latent Control of Unsteady Fluid Flows

We present a data-driven framework for controlling unsteady fluid flows by steering the system from arbitrary initial conditions to prescribed high-dimensional target states. The core idea is to discover a low-dimensional, interpretable representation of the flow dynamics using a variational autoencoder. In this latent space, we perform unsupervised clustering to identify anchor states and associate discrete control actions with each of them. A Bayesian optimization strategy is then employed to determine control sequences that drive the system toward the target state while minimizing actuation energy. Demonstrations on the 1D Burgers equation and flow past a cylinder show that our approach not only accurately reaches the desired flow configuration but also uncovers energetically efficient control paths. This work lays the foundation for scalable, interpretable control of complex fluid systems.