Fluid control using the adjoint method

We describe a novel method for controlling physics-based fluid simulations through gradient-based nonlinear optimization. Using a technique known as the adjoint method, derivatives can be computed efficiently, even for large 3D simulations with millions of control parameters. In addition, we introduce the first method for the full control of free-surface liquids. We show how to compute adjoint derivatives through each step of the simulation, including the fast marching algorithm, and describe a new set of control parameters specifically designed for liquids.

[1]  J. Lions.  Optimal Control of Systems Governed by Partial Differential Equations , 1971 .

[2]  James T. Kajiya,et al.  Ray tracing volume densities , 1984, SIGGRAPH.

[3]  S. Osher,et al.  Algorithms Based on Hamilton-Jacobi Formulations , 1988 .

[4]  Gavin S. P. Miller,et al.  Rapid, stable fluid dynamics for computer graphics , 1990, SIGGRAPH.

[5]  John F. Hughes,et al.  Plausible motion simulation for computer graphics animation , 1996 .

[6]  Dimitris N. Metaxas,et al.  Realistic Animation of Liquids , 1996, Graphics Interface.

[7]  Dimitris N. Metaxas,et al.  Modeling the motion of a hot, turbulent gas , 1997, SIGGRAPH.

[8]  M. Ghil.  Data assimilation in meteorology and oceanography : theory and practice : a collection of papers presented at the WMO Second International Symposium on Assimilation of Observations in Meteorology and Oceanography, 13-17 March 1995, Tokyo, Japan , 1997 .

[9]  Dimitris N. Metaxas,et al.  Controlling fluid animation , 1997, Proceedings Computer Graphics International.

[10]  Jos Stam,et al.  Stable fluids , 1999, SIGGRAPH.

[11]  James A. Sethian,et al.  The Fast Construction of Extension Velocities in Level Set Methods , 1999 .

[12]  Steven M. Seitz,et al.  Interactive manipulation of rigid body simulations , 2000, SIGGRAPH.

[13]  David A. Forsyth,et al.  Sampling plausible solutions to multi-body constraint problems , 2000, SIGGRAPH.

[14]  Andreas Griewank,et al.  Evaluating derivatives - principles and techniques of algorithmic differentiation, Second Edition , 2000, Frontiers in applied mathematics.

[15]  Niles A. Pierce,et al.  An Introduction to the Adjoint Approach to Design , 2000 .

[16]  Ronald Fedkiw,et al.  Visual simulation of smoke , 2001, SIGGRAPH.

[17]  Roger Temam,et al.  DNS-based predictive control of turbulence: an optimal benchmark for feedback algorithms , 2001, Journal of Fluid Mechanics.

[18]  T. Saito,et al.  Fast simulation and rendering techniques for fluid objects , 2001, Comput. Graph. Forum.

[19]  Steven M. Seitz,et al.  Interactive design of rigid-body simulations for computer animation , 2001 .

[20]  Ronald Fedkiw,et al.  Practical animation of liquids , 2001, SIGGRAPH.

[21]  Ronald Fedkiw,et al.  Animation and rendering of complex water surfaces , 2002, ACM Trans. Graph..

[22]  Ross T. Whitaker,et al.  Particle‐Based Simulation of Fluids , 2003, Comput. Graph. Forum.

[23]  Adrien Treuille,et al.  Keyframe control of smoke simulations , 2003, ACM Trans. Graph..

[24]  Markus H. Gross,et al.  Particle-based fluid simulation for interactive applications , 2003, SCA '03.

[25]  Dani Lischinski,et al.  Target-driven smoke animation , 2004, SIGGRAPH 2004.