Fluid Control with Localized Spacetime Windows

We present a physics-based fluid control method utilizing localized spacetime windows, extending force-based spacetime control to simulation scales that were previously intractable. Building on the observation that optimal control force distributions are often localized, we show that operating only in a localized spacetime window around the edit of interest can improve performance. To determine the optimal spacetime window size, we employ the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) method to search for the optimal temporal window size within a user-defined spatial region. Instead of using a Lagrangian representation, we optimize and apply control forces on a "floating" background grid, decoupling the control dimensionality from the simulation and enabling seamless integration with particle-based methods. Moreover, since the boundary conditions of the localized areas are encoded in the objective function, no extra effort is required to ensure consistency between the local control region and the global simulation domain. We demonstrate the effectiveness and efficiency of our method with various 2D and 3D particle-based free-surface simulation examples.