Industrial dynamical systems often exhibit multi-scale response due to material heterogeneities, operation conditions and complex environmental loadings. In such problems, it is the case that the smallest length-scale of the systems dynamics controls the numerical resolution required to effectively resolve the embedded physics. In practice however, high numerical resolutions is only required in a confined region of the system where fast dynamics or localized material variability are exhibited, whereas a coarser discretization can be sufficient in the rest majority of the system. To this end, a unified computational scheme with uniform spatio-temporal resolutions for uncertainty quantification can be very computationally demanding. Partitioning the complex dynamical system into smaller easier-to-solve problems based of the localized dynamics and material variability can reduce the overall computational cost. However, identifying the region of interest for high-resolution and intensive uncertainty quantification can be a problem dependent. The region of interest can be specified based on the localization features of the solution, user interest, and correlation length of the random material properties. For problems where a region of interest is not evident, Bayesian inference can provide a feasible solution. In this work, we employ a Bayesian framework to update our prior knowledge on the localized region of interest using measurements and system response. To address the computational cost of the Bayesian inference, we construct a Gaussian process surrogate for the forward model. Once, the localized region of interest is identified, we use polynomial chaos expansion to propagate the localization uncertainty. We demonstrate our framework through numerical experiments on a three-dimensional elastodynamic problem.
Improved Uncertainty Quantification in Physics-Informed Neural Networks Using Error Bounds and Solution Bundles
Departamento de Ciencia de la Computación, Pontificia Universidad Católica de Chile（计算机科学系，天主教智利大学）；Department of Computer Science, University of Tübingen（计算机科学系，图宾根大学）；John A. Paulson School of Engineering and Applied Sciences, Harvard University（工程与应用科学学院，哈佛大学）
Centre for Artificial Intelligence, University College London（人工智能研究中心，伦敦大学学院）；Heudiasyc Laboratory（Heudiasyc实验室）；Mila - Quebec AI Institute（魁北克人工智能研究所）
Physics-informed Bayesian Optimization for Quantitative High-Resolution Transmission Electron Microscopy
Institute of Materials Science, Technical University of Darmstadt（达姆施塔特工业大学材料科学研究所）；Ernst Ruska-Centre for Microscopy and Spectroscopy with Electrons, Forschungszentrum Jülich GmbH（于利希研究中心电子显微镜与光谱学恩斯特·鲁斯卡中心）；School of Microelectronics, Xi’an Jiaotong University（西安交通大学微电子学院）
Uncertainty quantification for noisy inputs-outputs in physics-informed neural networks and neural operators
Brown University（布朗大学）；Huazhong University of Science and Technology（华中科技大学）；Institute of Interdisciplinary Research for Mathematics and Applied Science, School of Mathematics and Statistics, Huazhong University of Science and Technology（华中科技大学数学与统计学院数学与应用科学交叉研究院）
A Primer on Variational Inference for Physics-Informed Deep Generative Modelling
University of Cambridge（剑桥大学）；Imperial College London（伦敦帝国理工学院）；London School of Economics and Political Science（伦敦政治经济学院）；The Alan Turing Institute（阿兰·图灵研究所）
Department of Mechanical Engineering, National University of Singapore（新加坡国立大学机械工程系）；Institute of High Performance Computing, Agency for Science Technology and Research（科技研究局高性能计算研究所）；Centre for Frontier AI Research, Agency for Science Technology and Research（科技研究局前沿人工智能研究中心）；College of Electronics and Information Engineering, Shenzhen University（深圳大学电子与信息工程学院）；Engineering Product Design Pillar, Singapore University of Technology and Design（新加坡科技设计大学工程产品设计支柱）；Technology Centre for Offshore and Marine, Singapore（新加坡海洋与近海技术中心）
Highly-scalable, physics-informed GANs for learning solutions of stochastic PDEs
Brown University（布朗大学）；NVIDIA（英伟达）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）；Julia Computing（朱莉娅计算公司）；Pacific Northwest National Lab（太平洋西北国家实验室）；Massachusetts Institute of Technology（麻省理工学院）
正问题和反问题的不确定性量化是物理学和生物医学学科的核心挑战。我们解决这一挑战的问题，模拟地下水流在汉福德网站的随机计算模型与观测数据相结合，使用物理信息的GAN模型。汉福德站点的地理范围、空间异质性和多个相关长度尺度要求训练计算密集型GAN模型到数千个维度。我们开发了一个层次化的计划，利用域并行，映射鉴别器和发电机到多个GPU，并采用有效的通信方案，以确保训练的稳定性和收敛性。我们开发了一个高度优化的方案，在Summit超级计算机上扩展到27，500个NVIDIA Volta GPU和4584个节点，扩展效率为93.1%，实现了1228 PF/s和1207 PF/s的峰值和持续半精度速率。
Uncertainty Quantification in PINNs for Turbulent Flows: Bayesian Inference and Repulsive Ensembles
Division of Applied Mathematics, Brown University（布朗大学应用数学系）；Department of Computing and Mathematical Sciences, California Institute of Technology（加州理工学院计算与数学科学系）；Department of Mechanical Engineering, Massachusetts Institute of Technology（麻省理工学院机械工程系）
本文提出了一种概率扩展的PINN框架，结合贝叶斯方法、麦克斯韦-玻尔兹曼抽样和斥力深度集合，以提高湍流建模中的不确定性校准，通过Van der Pol振荡器和圆柱绕流测试案例验证了其有效性。
Gryphon Center for Artificial Intelligence and Theoretical Sciences（格里芬人工智能与理论科学中心）；Georgia Institute of Technology（佐治亚理工学院）；University of Pennsylvania（宾夕法尼亚大学）
A differentiable PCA-GPR surrogate framework for full-transient Bayesian inverse uncertainty quantification of black-box nuclear thermal-hydraulic systems
