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NeuralUQ: A Comprehensive Library for Uncertainty Quantification in Neural Differential Equations and Operators
SIAM Review ( IF 10.2 ) Pub Date : 2024-02-08 , DOI: 10.1137/22m1518189 Zongren Zou , Xuhui Meng , Apostolos F. Psaros , George E. Karniadakis
SIAM Review ( IF 10.2 ) Pub Date : 2024-02-08 , DOI: 10.1137/22m1518189 Zongren Zou , Xuhui Meng , Apostolos F. Psaros , George E. Karniadakis
SIAM Review, Volume 66, Issue 1, Page 161-190, February 2024.
Uncertainty quantification (UQ) in machine learning is currently drawing increasing research interest, driven by the rapid deployment of deep neural networks across different fields, such as computer vision and natural language processing, and by the need for reliable tools in risk-sensitive applications. Recently, various machine learning models have also been developed to tackle problems in the field of scientific computing with applications to computational science and engineering (CSE). Physics-informed neural networks and deep operator networks are two such models for solving partial differential equations (PDEs) and learning operator mappings, respectively. In this regard, a comprehensive study of UQ methods tailored specifically for scientific machine learning (SciML) models has been provided in [A. F. Psaros et al., J. Comput. Phys., 477 (2023), art. 111902]. Nevertheless, and despite their theoretical merit, implementations of these methods are not straightforward, especially in large-scale CSE applications, hindering their broad adoption in both research and industry settings. In this paper, we present an open-source Python library (ŭlhttps://github.com/Crunch-UQ4MI), termed NeuralUQ and accompanied by an educational tutorial, for employing UQ methods for SciML in a convenient and structured manner. The library, designed for both educational and research purposes, supports multiple modern UQ methods and SciML models. It is based on a succinct workflow and facilitates flexible employment and easy extensions by the users. We first present a tutorial of NeuralUQ and subsequently demonstrate its applicability and efficiency in four diverse examples, involving dynamical systems and high-dimensional parametric and time-dependent PDEs.
中文翻译：
NeuralUQ：神经微分方程和运算符不确定性量化的综合库
SIAM Review，第 66 卷，第 1 期，第 161-190 页，2024 年 2 月。
机器学习中的不确定性量化 (UQ) 目前引起了越来越多的研究兴趣，这得益于深度神经网络在不同领域的快速部署，例如计算机视觉和自然语言处理，以及风险敏感应用程序中对可靠工具的需求。最近，还开发了各种机器学习模型来解决科学计算领域的问题，并应用于计算科学与工程（CSE）。物理信息神经网络和深度算子网络是分别用于求解偏微分方程（PDE）和学习算子映射的两种模型。在这方面，[AF Psaros et al., J. Comput.] 中提供了专门为科学机器学习 (SciML) 模型定制的 UQ 方法的全面研究。物理学，477 (2023)，艺术。 111902]。然而，尽管这些方法具有理论上的优点，但其实施并不简单，尤其是在大规模 CSE 应用中，这阻碍了它们在研究和行业环境中的广泛采用。在本文中，我们提出了一个名为 NeuralUQ 的开源 Python 库 (ŭlhttps://github.com/Crunch-UQ4MI)，并附有教育教程，用于以方便且结构化的方式将 UQ 方法用于 SciML。该库专为教育和研究目的而设计，支持多种现代昆士兰大学方法和 SciML 模型。它基于简洁的工作流程，方便用户灵活使用和轻松扩展。我们首先介绍 NeuralUQ 的教程，然后在四个不同的示例中展示其适用性和效率，涉及动力系统以及高维参数和时间相关的偏微分方程。
更新日期：2024-02-08
Uncertainty quantification (UQ) in machine learning is currently drawing increasing research interest, driven by the rapid deployment of deep neural networks across different fields, such as computer vision and natural language processing, and by the need for reliable tools in risk-sensitive applications. Recently, various machine learning models have also been developed to tackle problems in the field of scientific computing with applications to computational science and engineering (CSE). Physics-informed neural networks and deep operator networks are two such models for solving partial differential equations (PDEs) and learning operator mappings, respectively. In this regard, a comprehensive study of UQ methods tailored specifically for scientific machine learning (SciML) models has been provided in [A. F. Psaros et al., J. Comput. Phys., 477 (2023), art. 111902]. Nevertheless, and despite their theoretical merit, implementations of these methods are not straightforward, especially in large-scale CSE applications, hindering their broad adoption in both research and industry settings. In this paper, we present an open-source Python library (ŭlhttps://github.com/Crunch-UQ4MI), termed NeuralUQ and accompanied by an educational tutorial, for employing UQ methods for SciML in a convenient and structured manner. The library, designed for both educational and research purposes, supports multiple modern UQ methods and SciML models. It is based on a succinct workflow and facilitates flexible employment and easy extensions by the users. We first present a tutorial of NeuralUQ and subsequently demonstrate its applicability and efficiency in four diverse examples, involving dynamical systems and high-dimensional parametric and time-dependent PDEs.
中文翻译：
NeuralUQ：神经微分方程和运算符不确定性量化的综合库
SIAM Review，第 66 卷，第 1 期，第 161-190 页，2024 年 2 月。
机器学习中的不确定性量化 (UQ) 目前引起了越来越多的研究兴趣，这得益于深度神经网络在不同领域的快速部署，例如计算机视觉和自然语言处理，以及风险敏感应用程序中对可靠工具的需求。最近，还开发了各种机器学习模型来解决科学计算领域的问题，并应用于计算科学与工程（CSE）。物理信息神经网络和深度算子网络是分别用于求解偏微分方程（PDE）和学习算子映射的两种模型。在这方面，[AF Psaros et al., J. Comput.] 中提供了专门为科学机器学习 (SciML) 模型定制的 UQ 方法的全面研究。物理学，477 (2023)，艺术。 111902]。然而，尽管这些方法具有理论上的优点，但其实施并不简单，尤其是在大规模 CSE 应用中，这阻碍了它们在研究和行业环境中的广泛采用。在本文中，我们提出了一个名为 NeuralUQ 的开源 Python 库 (ŭlhttps://github.com/Crunch-UQ4MI)，并附有教育教程，用于以方便且结构化的方式将 UQ 方法用于 SciML。该库专为教育和研究目的而设计，支持多种现代昆士兰大学方法和 SciML 模型。它基于简洁的工作流程，方便用户灵活使用和轻松扩展。我们首先介绍 NeuralUQ 的教程，然后在四个不同的示例中展示其适用性和效率，涉及动力系统以及高维参数和时间相关的偏微分方程。
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