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.

可变形对象的模拟是许多学科核心的广泛使用的技术，从汽车和飞机设计到计算机图形和动画。历史上，仿真方法已被分为两个广泛的类别：它们的设计为准确但缓慢，或者它们被设计为实时操作，而以牺牲准确性为代价。第一类通常基于用于材料和基础物理的高分辨率和复杂模型，这些模型是使用强烈的计算来准确解决的。而第二类交易的速度准确性，以便使系统可以交互。该项目将开发新颖的深度学习技术，通过利用身体先验的神经网络体系结构设计，能够结合精度和效率。这样的先验可以用保护法（例如能量或动量）或预先指定的对称性（例如系统对观点变化的不变性）来表达。如果成功，项目成果将使高精度科学计算，实时模拟和机器学习更加紧密。此类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物理模拟，影响了机械工程，材料设计和物理科学的广泛领域。该项目将促进跨工程，机器学习和物理学领域的跨学科合作，并通过创建新颖的课程和外观活动来支持教育和多样性，以整合上述学科。该项目的目的是基于对基础物理和有量化的物理学的准确数学建模的紧密整合，以制定新颖的物理模拟范式，以提供适用于数据的量化和量化的量。为此，基于物理学的先验以及一种新颖的自学训练范式将增强几何深度学习技术，从而可以明确控制准确性和计算效率之间的权衡。具体而言，在机器学习方面，将开发在2D和3D网格上运行的神经网络，其中包含经典力学的电感性偏见，例如刚性运动不变性和对局部变形的稳定性，并且能够扩展到数十万个自由度，这些自由度在模拟应用中是典型的。在模拟侧，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，同时保持对准确性的完全控制。已开发的技术将在两个代表性应用上进行证明：超材料设计的模拟加速和飞机机翼的风险避免风险优化。该奖项反映了NSF的法定任务，并被认为是通过基金会的知识分子优点和更广泛影响的审查标准通过评估来获得支持的。