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部分微分方程（PDE）建模的。由于通过传统的数值方法求解这些PDE的昂贵，因此诸如深神经网络（DNN）等模拟器越来越多地用于近似PDE解决方案。尽管已经朝这个方向花费了大量努力，但现有技术提供了昂贵的解决方案，这些解决方案在不同的应用程序中无法传输或可扩展到复杂的PDE。该项目旨在使用鸿沟和征服方法来解决这些局限性。在将为该项目开发的框架中，该项目将首先建立一个DNN库，该库在称为基因组的小域上解决单物体PDE系统。然后，为了在大型看不见的域上求解多物理PDE，该项目将开发一种自适应方法，该方法将DNN耦合并组装其基因组的预测，以便在整个域中满足管理方程。该项目预计，预先培训的DNN和耦合机制将极大地使学者受益，而无需获得科学机器学习所需的硬件或知识。该框架的可转移性有可能减少与现有技术相关的高计算成本的碳足迹，这些技术使用DNN来解决PDE，为整个科学研究和整个社会提供了巨大的好处。实现时空可传递性和可扩展性。预计这项工作的贡献将通过预训练的DNN在固体和流体的行为上实现近似，从而消除了较长的训练时间，同时提高了准确性和可扩展性。乐高框架是由假设驱动的，并利用了唯一利用并行和异构机器的域分解方法的数学。该框架通过首先将域分解为称为基因组的小子域，在具有任意初始和边界条件的大域中解决了PDE系统。然后，通过预训练的乐高积木近似每个基因组中的溶液，以使基因组预测的组装近似于大域中的溶液。从本质上讲，乐高积木在基因组中模型不同的物理现象（例如，材料变形或流体流），而BRL药物将乐高积木与多物理现象建模和/或时空相结合，以扩展乐高积木的预测，而在基因组中保留溶液一致性。为了实现实时和稳健的性能，具有高的可传递性和可伸缩性，框架（1）使用混合精确计算和硬件加速器，（2）结合了几何学意识到的学习算法，（3）数学估算了解决方案组装过程中的依据。这些奖项通过评估NSF的依据，这表明了NSF的合法任务和依据，该奖项的范围是依据的，该奖项的范围是依据的，该奖项的依据是依据的依据。 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