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

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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.