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.

翻译：本文提出了一种基于物理的流体控制方法，利用局部时空窗口将基于力的时空控制扩展到以往难以处理的仿真尺度。基于最优控制力分布通常具有局部性的观察，我们证明仅在感兴趣编辑区域周围的局部时空窗口内操作可提升性能。为确定最优时空窗口尺寸，我们采用协方差矩阵自适应进化策略（CMA-ES）方法，在用户定义的空间区域内搜索最优时间窗口尺寸。区别于拉格朗日表示法，我们在“浮动”背景网格上优化并施加控制力，将控制维度与仿真解耦，从而实现与粒子方法的无缝集成。此外，由于局部区域的边界条件已编码在目标函数中，无需额外处理即可保证局部控制区域与全局仿真域的一致性。我们通过多种二维与三维基于粒子的自由表面仿真算例，验证了本方法的有效性与高效性。