CAREER: Next-generation Interactive Simulation

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Data-driven model reduction has enabled astonishing speedups in physical simulation. We can now experience interactive simulations of three-dimensional fluids and other complex phenomena that were impossible with traditional techniques. However, this approach's central limitation is inflexibility. Even small changes to the simulation domain require complete recomputation of the model. Moreover, the approach has been limited to a small class of dynamical systems. In this project, the PI seeks to radically generalize model reduction so that it is reconfigurable at runtime, handles a far greater range of phenomena, and supports heterogeneous coupling between reduced systems. The core goal of this research is to enable interactive simulations with the speed of model reduction, but without its inflexibility. The tension between these goals brings to light fundamental questions. What kinds of flexibility and runtime reconfigurability are possible? What kinds of reduced models maximize runtime flexibility? How can dynamical systems be projected onto these models? What is the broadest possible class of phenomena to which we can apply model reduction? How can we couple the model reduced dynamics across heterogeneous systems? The answers to questions such as these will provide a deeper understand of the conditions under which low-dimensional representations can successfully represent complex dynamical systems. The PI's approach will be to subdivide his research goals into three challenge areas: modular and deformable bases; particle systems and non-polynomial dynamics; and model coupling. Success within these areas will greatly increase the flexibility and extensibility of model reduction techniques, bringing us closer to interactive simulation of rich, heterogeneous virtual environments. The PI will also explore several advanced technologies enabled by these theoretical advances.Broader Impacts: Solving these challenges will be a transformative development directly applicable to a wide range of challenging fields including medical research, engineering, industrial design, architecture, training, and education. The interactive simulation of complex dynamics will allow people to rapidly explore physical design spaces, improve controllers for airplanes and other nonlinear systems, provide training for dangerous or remote environments, provide time-critical simulation for disaster scenarios, and will be a valuable tool for education. Interactive simulation will also allow students to play with remote phenomena, from wiggling proteins to curling smoke; interactively manipulating these structures will reveal concepts such as why a protein's helices are more rigid than its loops. Students could even modify the laws of physics; replace the famous force equals mass times acceleration with force equals mass times velocity and you find yourself in a strange molasses-like world where a rolling ball comes to rest as soon as it's no longer being pushed. In such impossible worlds, abstract equations suddenly resonate with truth.