Hybrid Neural-MPM for Accelerated and Controllable Fluid Simulations

We propose **Hybrid Neural-MPM**, a neural physics framework for accelerated, controllable fluid simulation. While traditional physics-based methods offer high accuracy, they are often computationally prohibitive and prone to latency. Recent machine-learning approaches have reduced these costs, yet most still struggle to support the demands of interactive applications. To bridge this gap, we introduce a novel hybrid method that integrates *numerical simulation, neural physics, and generative control.* Our neural physics model balances low-latency performance with physical fidelity by employing a fallback safeguard to classical numerical solvers. Furthermore, we design a diffusion-based controller, trained via a reverse modeling strategy, to generate external dynamic force fields for intuitive fluid manipulation. Our system demonstrates improved performance across diverse 2D/3D scenarios, material types, and obstacle interactions, achieving accelerated simulations ($11\sim 29$\% latency reduced) while enabling fluid control guided by user-friendly freehand sketches. We include video results in the supplement, and commit to releasing models and data upon acceptance.