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

CHS：中：几何深度学习用于准确高效的物理模拟

基本信息

批准号：
1901091
负责人：
Joan Bruna Estrach
金额：
$ 118.08万
依托单位：
New York University
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2019
资助国家：
美国
起止时间：
2019-09-01 至 2024-08-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1901091&HistoricalAwards=false
关键词：
CHS Medium Geometric Deep Learning

项目摘要

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.

可变形物体的模拟是一项广泛应用的技术，从汽车和飞机设计到计算机图形学和动画，它是许多学科的核心。模拟方法历来分为两大类：要么它们被设计为准确但缓慢，要么它们被设计为以牺牲准确性为代价实时操作。第一类通常基于材料和底层物理的高分辨率和复杂模型，这些模型可以通过密集的计算精确求解。而第二类则在速度上权衡了这种准确性，因此系统可以进行交互。该项目将开发新型深度学习技术，通过利用神经网络架构设计中的物理先验，能够将准确性和效率联合收割机结合起来。这种先验可以用守恒定律（如能量或动量）或预先指定的对称性（如系统对视点变化的不变性）来表示。如果成功，项目成果将使高精度科学计算、实时仿真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是巨大的，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、机器学习和物理学等不同领域的跨学科合作，并将通过创建整合上述学科的新颖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，基于底层物理的精确数学建模和提供适应性和效率的数据驱动管道之间的紧密集成。为此，几何深度学习技术将通过基于物理的先验知识和新的自我监督训练范式来增强，从而可以显式控制准确性和计算效率之间的权衡。具体来说，在机器学习方面，将开发在2D和3D网格上运行的神经网络，这些网络包含经典力学的归纳偏差，例如刚性运动不变性和局部变形的稳定性，并且能够扩展到模拟应用中典型的数十万个自由度。在仿真方面，该项目将确定仿真管道的组件，这些组件可以通过神经网络有效加速，同时保持对准确性的完全控制。开发的技术将在两个有代表性的应用中得到展示：超材料设计的加速模拟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知识价值和更广泛的影响审查标准进行评估，被认为值得支持。