OAC Core: Geometry-aware and Deep Learning-based Cyberinfrastructure for Scalable Modeling of Solids and Fluids

OAC 核心：基于几何感知和深度学习的网络基础设施，用于固体和流体的可扩展建模

• 批准号: 2211908
• 负责人: Ramin Bostanabad
• 金额: $ 60万
• 依托单位: University of California-Irvine
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2022
• 资助国家: 美国
• 起止时间: 2022-06-15 至 2025-05-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2211908&HistoricalAwards=false
• 关键词: OAC; Core; Geometry; aware; Deep

Many phenomena in solid and fluid mechanics are modeled via complex partial differential equations (PDEs). Since solving these PDEs via traditional numerical methods is prohibitively expensive, emulators such as deep neural networks (DNNs) are increasingly employed to approximate PDE solutions. While significant effort has been expended in this direction, existing technologies provide expensive solutions that are not transferable across different applications or scalable to complex PDEs. This project aims to address these limitations using a divide and conquer approach. In the framework that will be developed for the project, the project will first build a library of DNNs that solve single-physics PDE systems over small domains called genomes. Then, to solve multi-physics PDEs over large unseen domains, the project will develop an adaptive method that couples the DNNs and assembles their genome-wise predictions such that the governing equations are satisfied in the entire domain. The project expects that the pre-trained DNNs and coupling mechanism will greatly benefit scholars without access to the hardware or knowledge that are needed for scientific machine learning. The transferability of the framework has the potential to reduce the carbon footprint of the high computing costs that are associated with existing technologies that use DNNs to solve PDEs, providing great benefits to both scientific research and to society as a whole.The project will build LEarned Genomic Operators (LEGOs) that use Bayesian reinforcement learning (BRL) for generalization, i.e., for (1) emulating multi-physics systems, and/or (2) achieving spatiotemporal transferability and scalability. The contributions of this work are expected to enable on-the-fly approximation of the behavior of solids and fluids via pre-trained DNNs, thus eliminating long training times while increasing accuracy and scalability. The LEGO framework is hypothesis-driven and leverages the mathematics of domain decomposition methods that uniquely exploit parallel and heterogeneous machines. The framework solves a PDE system in a large domain with arbitrary initial and boundary conditions by first decomposing the domain into small subdomains called genomes. Then, the solution in each genome is approximated via pre-trained LEGOs such that the assembly of the genome-wise predictions approximates the solution in the large domain. In essence, the LEGOs model different physical phenomena (e.g., material deformation or fluid flow) in genomes while the BRL agent couples the LEGOs to model multi-physics phenomena and/or spatiotemporally extends the predictions of LEGOs while preserving solution consistency across the genomes. To achieve real-time and robust performance with high transferability and scalability, the framework (1) uses mixed-precision computing and hardware accelerators, (2) incorporates geometry-aware learning algorithms, and (3) mathematically estimates the propagated errors during solution assembly.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.

固体和流体力学中的许多现象都是通过复杂的偏微分方程 (PDE) 建模的。由于通过传统数值方法求解这些偏微分方程的成本极其昂贵，因此越来越多地采用深度神经网络 (DNN) 等模拟器来近似偏微分方程解。虽然在这个方向上付出了巨大的努力，但现有技术提供了昂贵的解决方案，这些解决方案无法跨不同的应用程序转移，也不能扩展到复杂的偏微分方程。该项目旨在使用分而治之的方法来解决这些限制。在为该项目开发的框架中，该项目将首先构建一个 DNN 库，用于解决称为基因组的小域上的单物理 PDE 系统。然后，为了解决大型未见域上的多物理偏微分方程，该项目将开发一种自适应方法，将 DNN 耦合并组装其基因组预测，以便在整个域中满足控制方程。该项目预计，预先训练的 DNN 和耦合机制将使那些无法获得科学机器学习所需的硬件或知识的学者受益匪浅。该框架的可转移性有可能减少与使用 DNN 解决偏微分方程的现有技术相关的高计算成本的碳足迹，为科学研究和整个社会带来巨大好处。该项目将构建学习基因组算子 (LEGO)，使用贝叶斯强化学习 (BRL) 进行泛化，即用于 (1) 模拟多物理系统，和/或 (2) 实现时空可转移性和可扩展性。这项工作的贡献预计将能够通过预先训练的 DNN 动态近似固体和流体的行为，从而消除较长的训练时间，同时提高准确性和可扩展性。乐高框架是假设驱动的，并利用领域分解方法的数学，独特地利用并行和异构机器。该框架首先将域分解为称为基因组的小子域，从而求解具有任意初始条件和边界条件的大域中的偏微分方程系统。然后，通过预先训练的乐高积木来近似每个基因组中的解决方案，以便基因组预测的组装近似于大域中的解决方案。本质上，乐高模型对基因组中的不同物理现象（例如材料变形或流体流动）进行建模，而 BRL 代理将乐高模型耦合起来以模拟多物理现象和/或时空扩展乐高模型的预测，同时保持整个基因组中解决方案的一致性。为了实现实时、稳健的性能以及高可转移性和可扩展性，该框架 (1) 使用混合精度计算和硬件加速器，(2) 结合了几何感知学习算法，(3) 在解决方案组装过程中以数学方式估计传播错误。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力价值和更广泛的影响审查进行评估，被认为值得支持 标准。

项目成果

Adaptive spatiotemporal dimension reduction in concurrent multiscale damage analysis

并发多尺度损伤分析中的自适应时空降维

• DOI: 10.1007/s00466-023-02299-7
• 发表时间: 2023
• 期刊: Computational Mechanics
• 影响因子: 4.1
• 作者: Deng, Shiguang;Apelian, Diran;Bostanabad, Ramin
• 通讯作者: Bostanabad, Ramin

Multi-fidelity cost-aware Bayesian optimization

• DOI: 10.1016/j.cma.2023.115937
• 发表时间: 2023-02-20
• 期刊: COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
• 影响因子: 7.2
• 作者: Foumani，Zahra Zanjani;Shishehbor，Mehdi;Bostanabad，Ramin
• 通讯作者: Bostanabad，Ramin