Guiding simulations of highly dynamic phenomena

Abstract

Highly dynamic phenomena, such as fluid flow or the motion of a crowd, are hard topredict and control since their behavior varies dramatically with a small perturbation in their initial or environmental conditions. Computer simulations let us recreate these dynamic systems and design techniques to control their behavior based on our desired goal. In my work, I have developed techniques that efficiently modify the dynamics of a complex system to achieve the desired motion. This can be achieved by changing the local or global dynamics of the system to control its small- or large-scale behaviors, respectively. Part of my work focuses on utilizing a statistical-mechanical model governing pedestrian motion for multi-agent navigation. I developed two specific models that account for uncertainty in the future trajectories of interacting agents: an isotropic model which conservatively considers all possible errors and an anisotropic model that assumes the error is only in a direction toward a head-on collision. I compare the two models experimentally via a number of simulation scenarios, and also provide theoretical guarantees about the collision avoidance behavior of the agents considering the uncertainties in the sensing data each agent receives. In my more recent work, I propose a simple and efficient method for guiding an Eulerian smoke simulation to match the behavior of a specified velocity field, such as a low-resolution animation of the same scene, while preserving the rich, turbulent details arising in the simulated fluid. The method works by simply combining the high-frequency component of the simulated fluid velocity with the low-frequency component of the input guiding field. I provide a frequency-domain analysis that motivates the use of ideal low-pass and high-pass filters to prevent the artificial dissipation of small-scale details. I demonstrate this method in many scenes including those with static and moving obstacles and show that it produces high-quality results with very little computational overhead. Following my last guiding technique for smoke simulation, in my last project, I proposed a machine learning model for the same problem that learns the desired behavior of the smoke from low-resolution simulated data and generates the high-resolution smoke. I utilized a generative adversarial network with the recurrency of frames in the network. The trained model is capable of maintaining the spatial and temporal consistency of simulation. Compare to the physics-based guiding model, the machine-learning model can generate guided smoke interactively. Although, it can not still beat the quality that the frequency-domain guiding model can produce.