Modeling human intuitions about liquid flow with particle-based simulation

Abstract

Humans can easily describe, imagine, and, crucially, predict a wide variety of behaviors of liquids-splashing, squirting, gushing, sloshing, soaking, dripping, draining, trickling, pooling, and pouring-despite tremendous variability in their material and dynamical properties. Here we propose and test a computational model of how people perceive and predict these liquid dynamics, based on coarse approximate simulations of fluids as collections of interacting particles. Our model is analogous to a "game engine in the head", drawing on techniques for interactive simulations (as in video games) that optimize for efficiency and natural appearance rather than physical accuracy. In two behavioral experiments, we found that the model accurately captured people's predictions about how liquids flow among complex solid obstacles, and was significantly better than several alternatives based on simple heuristics and deep neural networks. Our model was also able to explain how people's predictions varied as a function of the liquids' properties (e.g., viscosity and stickiness). Together, the model and empirical results extend the recent proposal that human physical scene understanding for the dynamics of rigid, solid objects can be supported by approximate probabilistic simulation, to the more complex and unexplored domain of fluid dynamics.

Fig 1. Humans are adept at reasoning about liquids.

(A) Dynamic fluids are very complex, yet ubiquitous in everyday scenes. (B) Humans–even young children–can reason about and interact with liquids effectively.

Fig 2. Experimental stimuli.

(A) Examples of water and honey stimuli from Experiment 1 after gravity was applied. (B) Examples of water and honey stimuli from Experiment 2. (Subjects only saw liquid in motion as part of the practice phase, and otherwise only saw a static image of the liquid in its starting position).

Fig 3. SPH overview.

(A) How SPH approximates a fluid. For any location in the fluid, marked “X” on the diagram, particles in the local neighborhood are used to approximate the fluid’s, density, pressure, and dynamics at that point. The bell-shaped envelope depicts the strength of each neighbor’s influence on the approximation, which falls off with distance. (B) SPH simulations can be allocated more resources to achieve more precise approximations. In the second and third panels, more particles are allocated than in the first, which will result in more accurate and stable simulated fluid dynamics. (C) The rules by which particles interact can be varied to produce different qualitative fluids and materials. The first three panels show differences in splashing behavior as a function of viscosity. The fourth panel shows a non-Newtonian fluid that sticks to rigid surfaces (like honey).

Fig 4. Gravity heuristic.

(A) Each panel depicts the path of a different particle. (B) Depiction of ‘momentum’ (left) for m = 0.1, and ‘global noise’ with g ≠ 0 (right), for a single particle that has chosen the “wrong” direction (going against gravity). See text for details. (C) Visualization of model from Gardin and Meltzer (1989). The simulated fluid (blue cubes) travels straight down under gravity, which is analogous to A.

Fig 5. Example scenes from Experiment 2 for which water and honey trials had very different outcomes.

(A) A scene in which much more honey flowed into the cup than water. (B) A scene in which much more water flowed into the cup than honey.

Fig 6. Distribution of individual participant correlations with ground truth (dark colors) versus the null hypothesis (light colors).

Fig 7. Correlations between mean participant data and all models that make different predictions for water versus honey trials (in both experiments).

A and B show the IFE models and ground truth, while C and D show the alternative models (ConvNet, MarbleSim, and SimpleSim). The alternative models exclude the gravity heuristic, as it makes the same predictions for both water and honey. In Experiment 2, the bars with small or negative values (in B) establish that participants’ responses are sensitive to the stickiness and viscosity of a liquid. Model 1 and Model 2 refer to the two different versions of IFE honey. Model 1 simulates honey as a fluid with high particle friction and stickiness, while Model 2 simulates honey as water with high damping. Summary of parameters for all models are found in Table 1.

Fig 8. Uncertain IFE performance across a range of α and damping values at 50 particles.

Results are qualitatively similar to the deterministic IFE, but with higher correlations.

Fig 9. Comparison of the best-fitting versions of the IFE model and alternative models.

All bars for the IFE, MarbleSim, SimpleSim, and ConvNet are identical to their corresponding bars in Fig 7, and their values are given in Table 1.