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.

辐射传递方程在许多重要的应用中都产生，例如医学成像，天体物理学，天气和气候。例如，它描述了太阳在大气中传播并被云吸收或散布时的行为。在这些应用中，计算机模拟通常用于获取辐射传输方程的解决方案。但是，由于描述每个空间位置的辐射强度以及在每个可能的传播方向（东西方，向北，向北，向下）所需的辐射强度所需的大量尺寸，因此在这些模拟中产生了重大挑战。大量维度需要大量的计算机内存和计算时间。由于这笔较高的计算费用，通常使用简化（例如一维（1D）近似值或在天气和气候应用中近似近似值）。该项目旨在克服这一1D障碍并解决完整的辐射传输方程，并通过快速，低内存的计算机模拟进行操作。计算方法，对这些方法的理论理解以及软件工具的开发将改善对气候，天气和医学成像的理解，从而影响社会中个人的福祉。博士后研究人员和数学和大气科学的学生的跨学科培训也是该项目的重要组成部分。从代表性不足的群体中的学生参与并扩大了对本地K-12学校的宣传活动也将成为该项目的一部分。本项目旨在开发快速，低内存的数值方法，以克服一维屏障并求解完整的辐射传递方程，并将其用于较低连接的元素属性的方法包括在内，并包括其低音元素的属性 - （HP-AMR）处理医学成像或大气中云中产生的陡峭梯度。除了解决给定大气状态的辐射传递方程（即解决向前问题）外，还将解决反问题，其中使用辐射的测量来推断大气状态。逆问题在医学成像，遥感和数据同化的天气预测中具有重要的应用。面向目标的HP适应性将用于克服对反问题产生的一些独特挑战。最后，将使用上述方法实现的合成数据对基于机器的模拟器进行培训。为了更好地理解大气科学中的3D辐射效应，将从观测和/或大型涡流模拟的云场景中分析数据。该奖项反映了NSF的法定任务，并被认为是通过基金会的智力优点和更广泛影响的审查标准通过评估来通过评估来获得支持的。