Accelerating Eulerian Fluid Simulation With Convolutional Networks

Efficient simulation of the Navier-Stokes equations for fluid flow is a long standing problem in applied mathematics, for which state-of-the-art methods require large compute resources. In this work, we propose a data-driven approach that leverages the approximation power of deep-learning with the precision of standard solvers to obtain fast and highly realistic simulations. Our method solves the incompressible Euler equations using the standard operator splitting method, in which a large sparse linear system with many free parameters must be solved. We use a Convolutional Network with a highly tailored architecture, trained using a novel unsupervised learning framework to solve the linear system. We present real-time 2D and 3D simulations that outperform recently proposed data-driven methods; the obtained results are realistic and show good generalization properties.Comment: Significant revisio

Position-Based Multi-Agent Dynamics for Real-Time Crowd Simulation (MiG paper)

Exploiting the efficiency and stability of Position-Based Dynamics (PBD), we introduce a novel crowd simulation method that runs at interactive rates for hundreds of thousands of agents. Our method enables the detailed modeling of per-agent behavior in a Lagrangian formulation. We model short-range and long-range collision avoidance to simulate both sparse and dense crowds. On the particles representing agents, we formulate a set of positional constraints that can be readily integrated into a standard PBD solver. We augment the tentative particle motions with planning velocities to determine the preferred velocities of agents, and project the positions onto the constraint manifold to eliminate colliding configurations. The local short-range interaction is represented with collision and frictional contact between agents, as in the discrete simulation of granular materials. We incorporate a cohesion model for modeling collective behaviors and propose a new constraint for dealing with potential future collisions. Our new method is suitable for use in interactive games.Comment: 9 page

Consensus State Gram Matrix Estimation for Stochastic Switching Networks from Spectral Distribution Moments

Reaching distributed average consensus quickly and accurately over a network through iterative dynamics represents an important task in numerous distributed applications. Suitably designed filters applied to the state values can significantly improve the convergence rate. For constant networks, these filters can be viewed in terms of graph signal processing as polynomials in a single matrix, the consensus iteration matrix, with filter response evaluated at its eigenvalues. For random, time-varying networks, filter design becomes more complicated, involving eigendecompositions of sums and products of random, time-varying iteration matrices. This paper focuses on deriving an estimate for the Gram matrix of error in the state vectors over a filtering window for large-scale, stationary, switching random networks. The result depends on the moments of the empirical spectral distribution, which can be estimated through Monte-Carlo simulation. This work then defines a quadratic objective function to minimize the expected consensus estimate error norm. Simulation results provide support for the approximation.Comment: 52nd Asilomar Conference on Signals, Systems, and Computers (Asilomar 2017