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

本项目的研究目标是为计算机图形学应用中基于物理的可变形实体模拟开发高效而稳定的方法。我们研究了基于空间固定离散化的欧拉模拟方法。在这个项目的第一阶段，我们成功地开发并发表了这一研究领域的不同方法。我们能够为欧拉模拟方法中的体积守恒问题找到一种有效的解决方案。此外，还确定了一种合适的隐式高阶时间积分格式，该格式将被集成到我们的模拟器中。同时，我们还研究了基于机器学习的细节合成的混合模拟方法和途径。在这里，我们利用了欧拉方法中的固定网格结构非常适合与最先进的学习算法相结合的事实。在本项目范围内首次使用机器学习技术，成功地展示了它们的巨大潜力。与此同时，在基于物理的可变形固体动画领域，这些技术仍然没有得到很好的探索。在这个项目的下一阶段，我们希望解决这个相对年轻的研究领域中尚未解决的重要问题，并开发合适的解决方案。因此，开发具有机器学习方法的仿真方法是本研究计划的中心议题。首先，我们计划为第一个项目阶段创建的仿真器的单个组件开发学习解决方案。然后可以在现有的模拟器中对这些组件进行测试和评估。该计划将开发计算弹性力和有摩擦的接触力的新方法，以及一种时间积分方法。测试成功后，应将各个组件组合成一个整体系统，其中特别考虑了力的强耦合。为了在模拟中获得逼真的材质行为，我们计划使用机器学习从3D扫描中重建它。此外，本项目还将开发一种用于变形体的可微求解器。然后，我们计划使用它来有效地解决艺术方向领域的反问题。这里的目标是让艺术家对模拟进行灵活和直观的控制。综上所述，在我们的研究项目的第二阶段，我们计划使用机器学习方法来扩展第一阶段开发的模拟方法。我们认为，由于机器学习的重大进展，这一研究方向具有很大的影响潜力。在这种情况下，我们可以利用我们在学习算法方面的现有专业知识，进一步建立机器学习在计算机图形学领域的使用。

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.