CHS: Medium: Geometric Deep Learning for Accurate and Efficient Physics Simulation

从汽车和飞机设计到计算机图形学和动画，可变形物体的模拟是一项广泛应用的核心技术。模拟方法历来被分为两大类：要么被设计为精确但缓慢，要么被设计为以牺牲精度为代价进行实时操作。第一类通常基于材料和底层物理的高分辨率和复杂模型，这些模型使用密集的计算进行精确求解。而第二类则是在精度和速度之间进行权衡，以便使系统具有互动性。该项目将开发新的深度学习技术，通过在神经网络结构设计中利用物理先验，能够将准确性和效率结合起来。这样的先验可以用守恒定律(如能量或动量)来表示，或用预先指定的对称性(如系统对视点变化的不变性)来表示。如果成功，项目成果将把高精度科学计算、实时模拟和机器学习更紧密地结合在一起。这种重新定义的物理模拟的应用非常广泛，远远超出了本项目所涵盖的范围，影响了机械工程、材料设计和物理科学的广泛领域。该项目将促进工程学、机器学习和物理学不同领域的跨学科合作，并将通过创建整合上述学科的新课程和推广活动来支持教育和多样性。该项目的目标是开发一种新的物理模拟范例，其基础是对基本物理进行准确的数学建模，并建立提供适应和效率的数据驱动管道。为此，几何深度学习技术将通过基于物理的先验知识和一种新的自我监督训练范例来增强，从而可以明确地控制精度和计算效率之间的权衡。具体地说，在机器学习方面，将开发出在2D和3D网格上运行的神经网络，它包含了经典力学的归纳偏差，如刚性运动不变性和稳定性对局部变形的诱导偏差，并能够扩展到模拟应用中典型的数十万个自由度。在模拟方面，该项目将确定模拟管道的组件，这些组件可以通过神经网络有效地加速，同时保持对精度的完全控制。开发的技术将在两个具有代表性的应用中得到演示：超材料设计的模拟加速和飞机机翼的风险规避优化。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

The simulation of deformable objects is a widely used technology at the core of many disciplines, from automobile and aircraft design to computer graphics and animation. Simulation methods have been historically split into two broad categories: either they are designed to be accurate but slow, or they are designed to operate in real-time at the expense of accuracy. The first category is usually based on high-resolution and complex models for the materials and the underlying physics, which are accurately solved using intense computing. Whereas the second category trades-off such accuracy for speed, so that the systems can be made interactive. This project will develop novel deep learning techniques that are able to combine both accuracy and efficiency, by leveraging physical priors in the design of neural network architectures. Such priors may be expressed in terms of conservation laws (such as energy or momentum), or with prespecified symmetries (such as invariance of the system to viewpoint changes). If successful, project outcomes will bring closer together high-precision scientific computing, real-time simulation, and machine learning. The applications of such redefined physical simulation are vast and go far beyond those covered by the present project, impacting broad areas of mechanical engineering, material design, and physical sciences. The project will promote cross-disciplinary collaborations across different areas of engineering, machine learning and physics, and will support education and diversity by creating novel courses and outreach activities integrating the above disciplines.The goal of this project is to develop a novel paradigm for physical simulation, based on a tight integration between accurate mathematical modeling of the underlying physics and a data-driven pipeline that provides adaptation and efficiency. For this purpose, geometric deep learning techniques will be enhanced with physics-based priors and with a novel self-supervised training paradigm, whereby the tradeoff between accuracy and computational efficiency can be explicitly controlled. Specifically, on the machine learning side, neural networks that operate on 2D and 3D meshes will be developed that contain the inductive biases of classical mechanics such as rigid motion invariance and stability to local deformations, and are able to scale to the hundreds of thousands of degrees of freedom that are typical in simulation applications. On the simulation side, the project will determine the components of the simulation pipeline that can be effectively accelerated by neural networks while maintaining full control over accuracy. The developed techniques will be demonstrated on two representative applications: the acceleration of simulations for metamaterial design and the risk-averse optimization of aircraft wings.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.