Physically-based animation of deformable solids using Eulerian approaches in computer graphics

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The research goal of this project is the development of efficient and stable methods for the physically-based simulation of deformable solids in computer graphics applications. We investigate Eulerian simulation approaches that are based on a spatially fixed discretization. In the first phase of this project we successfully developed and published different methods in this research area. We were able to develop an efficient solution for the problem of volume conservation in Eulerian simulation methods. Moreover, a suitable implicit higher-order time integration scheme was identified that will be integrated in our simulator. At the same time we investigated hybrid simulation methods and approaches for the synthesis of details using machine learning. Here we leveraged the fact that the fixed grid structures in Eulerian approaches are very well suited for a combination with state-of-the-art learning algorithms. The first use of machine learning techniques within the scope of this project has successfully demonstrated their great potential. At the same time, these techniques are still poorly explored in the area of physically-based animation of deformable solids. In the next phase of this project, we want to address important unsolved problems in this relatively young research area and develop suitable solutions. The development of simulation methods with machine learning approaches is therefore a central topic of this research proposal.First, we plan to develop learning solutions for individual components of the simulator that was created in the first project phase. These components can then be tested and evaluated in the existing simulator. The plan is to develop new approaches for the computation of elastic forces and contact forces with friction, and a time integration method. After a successful test, the individual components should then be combined to form an overall system in which a strong coupling of the forces is particularly considered. In order to obtain a realistic material behavior in the simulation, we plan to reconstruct it from 3D scans using machine learning. In addition, a differentiable solver for deformable bodies is to be developed in this project. We then plan to use it to efficiently solve inverse problems in the area of art direction. The goal here is to give an artist flexible and intuitive control over the simulation.To summarize, in the second phase of our research project we plan to extend the simulation methods that were developed in the first phase with machine learning approaches. We believe that this research direction has a large potential for impact due to the significant advances in machine learning. In this context we can leverage our existing expertise with learning algorithms, and further establish the use of machine learning in the field of computer graphics.