Collaborative Research: Breaking the 1D barrier in radiative transfer: Fast, low-memory numerical methods for enabling inverse problems and machine learning emulators

合作研究：打破辐射传输中的一维障碍：用于实现逆问题和机器学习模拟器的快速、低内存数值方法

• 批准号: 2324369
• 负责人: Robert Pincus
• 金额: $ 14.88万
• 依托单位: Columbia University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2023
• 资助国家: 美国
• 起止时间: 2023-09-01 至 2026-08-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2324369&HistoricalAwards=false
• 关键词: Collaborative; Research; Breaking; 1D; barrier

The radiative transfer equation arises in many important applications, such as medical imaging, astrophysics, weather and climate. It describes, for example, the behavior of the sun's rays as they propagate through the atmosphere and are absorbed or scattered by clouds. In these applications, computer simulations are often used to obtain solutions to the radiative transfer equation. However, a substantial challenge arises in these simulations due to the large number of dimensions needed to describe the radiant intensity at each spatial location, and in each possible direction of propagation (east-west, north-south, up-down). The large number of dimensions requires a large amount of computer memory and computing time. Due to this high computational expense, it is common to use simplifications, such as a one-dimensional (1D) approximation or two-stream approximation in weather and climate applications. This project aims to overcome this 1D barrier and solve the full radiative transfer equation, and do so with fast, low-memory computer simulations. The computational methods, the theoretical understanding of these methods, and the development of software tools will improve understanding of climate, weather, and medical imaging, and thus influence the well-being of individuals in society. The interdisciplinary training of a postdoctoral researcher and students in mathematics and atmospheric science is also an important component of the project. Mentoring and broadening the participation of students from underrepresented groups, with outreach activities to local K-12 schools will also be part of the project.This project aims to develop fast, low-memory numerical methods that overcome the 1D barrier and solve the full radiative transfer equation, The methods include discontinuous Galerkin spectral element methods used for their low-memory properties, and hp-adaptive mesh refinement (hp-AMR) to handle steep gradients that arise in medical imaging or from clouds in the atmosphere. In addition to solving the radiative transfer equation for a given atmospheric state (i.e., solving the forward problem), the inverse problem will also be solved, where measurements of the radiation are used to infer the state of the atmosphere. The inverse problem has important applications in medical imaging, remote sensing and data assimilation for weather forecasting. A goal-oriented version of hp-adaptivity will be used to overcome some of the unique challenges that arise for the inverse problem. Finally, machine-learning-based emulators will be trained using synthetic data that is made possible by the methods above. To better understand 3D radiative effects in atmospheric science, data will be analyzed from cloud scenes from observations and/or large eddy simulations.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.

辐射传递方程在医学成像、天体物理、气象和气候等领域有着重要的应用。例如，它描述了太阳光线在大气中传播并被云吸收或散射时的行为。在这些应用中，经常使用计算机模拟来获得辐射传递方程的解。然而，由于描述每个空间位置和每个可能的传播方向(东-西、北-南、上-下)的辐射强度所需的大量维度，在这些模拟中出现了实质性的挑战。大量的维度需要大量的计算机内存和计算时间。由于这种高的计算成本，在天气和气候应用中通常使用简化，例如一维(1D)近似或两流近似。该项目旨在克服这一一维障碍，求解完整的辐射传输方程，并通过快速、低内存的计算机模拟来做到这一点。计算方法、对这些方法的理论理解以及软件工具的开发将提高对气候、天气和医学成像的理解，从而影响社会中个人的福祉。数学和大气科学方面的博士后研究人员和学生的跨学科培训也是该项目的重要组成部分。通过与当地K-12学校的外联活动，指导和扩大来自代表不足群体的学生的参与也将是该项目的一部分。该项目旨在开发快速、低内存的数值方法，以克服一维障碍并求解完整的辐射传递方程，这些方法包括利用其低记忆性而使用的不连续Galerkin谱元素方法，以及处理医学成像中或大气中云产生的陡峭梯度的hp自适应网格细化(hp-AMR)。除了求解给定大气状态的辐射传输方程(即解决正问题)外，还将求解逆问题，其中使用对辐射的测量来推断大气状态。逆问题在医学成像、遥感和天气预报数据同化等领域有着重要的应用。面向目标的HP适应性版本将被用来克服逆问题中出现的一些独特的挑战。最后，将使用通过上述方法实现的合成数据来训练基于机器学习的仿真器。为了更好地了解大气科学中的3D辐射效应，将从观测和/或大涡模拟的云场景中分析数据。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。