Interactive 4D Volumetric Liquid Forecasting under Moving-Solid Interaction

Jongwon Ryu, Sunjae Yoon, Junyeong Kim

We propose the task of Interactive 4D Volumetric Liquid Forecasting: predicting the spatiotemporal evolution of a future dense 3D liquid velocity field conditioned on how a solid object moves through it. This task provides an upstream physical forecasting primitive for systems that need to reason about motion-conditioned liquid response, including robotic liquid manipulation, digital twins, and rigid-fluid video generation. Existing works have made efforts in predicting flow around static or prescribed solid geometries and synthesizing visually plausible fluid motion. Yet these approaches provide limited coverage for interactive liquid dynamics, as they are not capable of forecasting how a moving solid induces a future full-domain liquid response. In this forecasting scenario, the hydrodynamic effect is condensed near an evolving liquid-solid interface, but the prediction target is a global spatiotemporal rollout. To address this challenge, we propose a two-level recurrent forecasting framework, TIDE/TIDES: TIDE isolates localized interface-driven forecasting, while TIDES adds transport-aware coupling and explicit stabilization to reduce accumulated rollout error. Across adapted…