CFC: Simulating Character-Fluid Coupling Using a Two-Level World Model

Our framework, CFC, generates physically plausible and diverse character-fluid interaction animations. The characters exhibit a wide range of skills, including (a) recovering from a fall in water, (b) maintaining balance during walking, (c) engaging in combat within high-viscosity mud, and (d) navigating through a pool and executing a strike task to hit a target.

An overview of the Character-Fluid Coupling World Model, a two-level framework. The Character World Model predicts the next character state (blue lines) based on the previous character states, external forces, and policy-driven actions. The Fluid World Model takes the states of both the fluid and the character to compute external forces on the character and predict the fluid's next state (orange lines). External forces serve as the interface connecting the two models (green lines). The dashed line represents state updates.

An overview of the proposed Lagrangian Fluid-inspired Network. We form a loss function based on the potential energy to optimize the policy using policy gradient by making use of its differentiable nature.

We visualize character animations in both dry (a) and water-filled environments (b–d) with varying viscosity coefficients. The visualization showcases the final rendered effects (top row), water particle flows alongside the character (middle row), and the character's motion details (bottom row). (b–d) illustrate different viscosity parameters of 0.01, 0.05, and 0.1, while maintaining consistent force scale factors.

Character performing a directional control task in a high-viscosity fluid environment. The character lifts its legs and walks forward under directional guidance. Our framework enables coordinated locomotion despite significant fluid resistance, demonstrating stability and control in viscous media.

Character executing a strike task in a low-viscosity fluid environment. The character navigates to a target location and uses a sword to strike the designated position. We visualize the motion both with and without water to highlight the influence of fluid dynamics on movement strategy and body coordination.

We demonstrate (a) how the character recovers to a standing posture after being knocked down by a powerful water flow and (b) how the character uses a shield and crouches to stabilize its center of gravity when resisting the water flow.

Distributions of knee and foot vertical heights (Z axis) under two conditions: without water (blue) and with water (orange). The presence of water results in higher mean and greater variability in foot and knee heights, demonstrating the emergence of adaptive foot-lifting strategies in response to fluid interactions.

Motion Diversity (APD). A higher APD value reflects greater diversity in the generated motions. Our method achieves higher motion diversity than the baseline ASE and AMP, benefiting from fluid-induced responsiveness.

Visualization of particle prediction errors between our PINN-based fluid model and SPH simulations under two viscosity levels ($\nu = 0.1$, top; $\nu = 0.01$, bottom) over time. Brighter colors indicate higher error. In this experiment, we report the RMSE error.

Qualitative comparison of character-fluid interactions between SPH simulations (GT) and our model's predictions under two viscosity settings ($0.1$ and $0.01$). Each row shows a temporal sequence of fluid and character states. Our model effectively captures fluid dynamics.

Character-fluid animations under varying fluid-simulation time-step sizes: (a) $4\times10^{-4}\mathrm{s}$, (b) $4\times10^{-3}\mathrm{s}$, (c) $4\times10^{-2}\mathrm{s}$, and (d) $8\times10^{-2}\mathrm{s}$.

Character animations with increasingly dense fluid discretizations. Our method produces stable and visually realistic results at high particle counts (up to $563,200$ particles) and gains a 15x speedup compared to the baseline SPH method.

Quantitative Evaluation of Water Model. Particle-wise RMSE and relative error for predicted positions (m) and velocities (m/s) compared to an SPH simulation under varying viscosity settings and time step sizes.

Runtime Performance. Comparison aligned to a macro-step of Δt=4×10^-2s. Our method runs roughly 15-30x faster than SPH.

Training time of the high-level policy for navigating the character in the task of directional control. Our proposed CFC method achieves a task return comparable to the traditional simulation-based approach (SPH) while significantly reducing the training time (approx 4.3 hours vs 34.5 hours).

User study results of fluid-character interactions. Most ratings were positive, with 88.1% ≥ 3 (Good + Very Good) and 57.1% rated as 4 (Very Good). The mean score was 3.53 (std: 0.76), indicating strong perceived realism.

Two-Player Animation Results. We present two players engaged in combat within a swamp environment, highlighting highly dynamic interactions between the entities and their surroundings.

Quadruped Animation. Visualization of quadruped-fluid interaction. The Ant agent moves through the fluid with stable gaits, generating smooth and coherent water disturbances over time.