RUI: Development of Fast Methods for Solving the Boltzmann Equation through Reduced Order Models, Machine Learning, and Optimal Transport
RUI:开发通过降阶模型、机器学习和最优传输求解玻尔兹曼方程的快速方法
基本信息
- 批准号:2111612
- 负责人:
- 金额:$ 15万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Standard Grant
- 财政年份:2021
- 资助国家:美国
- 起止时间:2021-09-01 至 2024-08-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
The Boltzmann equation arises in a wide range of applications from external aerodynamics and thruster plume flows to vacuum facilities and microscale devices. Emerging applications of the Boltzmann equation include self-organizing systems and flocking, as well as networks and bacterial dynamics. Continuing technological advances in these areas require improvement of algorithms and models to enable development of a “digital twin” for the problems at hand. While the Boltzmann equation provides the most accurate model for these systems, its use in multiple spatial dimensions remains limited due to its prohibitive computational costs. The goal of this project is to leverage data-driven reduced order models, machine learning, and optimal transport theory to make deterministic solution of the Boltzmann equation tractable so it can be applied to simulation of novel engineering applications. The project will support new courses and new training opportunities at California State University Northridge which is a minority serving institution.The key difficulties in solving the Boltzmann equation are its high dimensionality and the prohibitive costs of evaluating the five-fold collision integral. To address these, this project will focus on the development, implementation, and validation of data driven low dimensional discretizations of the Boltzmann equation. The project will develop methods to enforce long term stability of the reduced order models and to design stable macroscopic models that are based on solution data. Fast models for kinetic equations will be developed using deep residual neural networks and numerical gradient flow approaches. Additionally, efficient evaluation of convolution on octree meshes and optimal transport formulation of the Boltzmann equation will be studied. The solvers will be validated using available deterministic high order accurate solvers. The project will deliver algorithms for three-dimensional solutions of non-continuum flows, benchmark solutions as well as new approaches to develop and test approximate kinetic and macroscopic models of gas. The techniques will increase the range of applicability of non-continuum solvers and will include multiple physics into models that were previously prohibitively expensive. The new methods will apply to the simulations of atmospheric re-entry, hypersonic flows and also gas-driven lab-on-the-chip technologies, micropropulsion, and atomic force microscopy.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.
玻尔兹曼方程的应用范围很广,从外部空气动力学和推力器羽流到真空设备和微型设备。玻尔兹曼方程的新兴应用包括自组织系统和群集,以及网络和细菌动力学。这些领域的持续技术进步需要改进算法和模型,以便为手头的问题开发“数字孪生”。虽然玻尔兹曼方程为这些系统提供了最精确的模型,但由于其高昂的计算成本,其在多个空间维度中的使用仍然受到限制。该项目的目标是利用数据驱动的降阶模型,机器学习和最优传输理论,使玻尔兹曼方程的确定性解易于处理,因此它可以应用于新的工程应用的模拟。该项目将支持新的课程和新的培训机会,在加州州立大学北岭,这是一个少数民族服务机构。在解决玻尔兹曼方程的主要困难是它的高维性和昂贵的费用评估的五重碰撞积分。为了解决这些问题,该项目将重点关注数据驱动的波尔兹曼方程低维离散化的开发、实施和验证。该项目将开发方法,以加强长期稳定的降阶模型和设计稳定的宏观模型的基础上解决方案的数据。将使用深层残差神经网络和数值梯度流方法建立动力学方程的快速模型。此外,将研究八叉树网格上卷积的有效评估和玻尔兹曼方程的最佳传输公式。将使用可用的确定性高阶精确解算器对解算器进行验证。该项目将提供非连续流三维解决方案的算法,基准解决方案以及开发和测试气体近似动力学和宏观模型的新方法。这些技术将增加非连续解算器的适用范围,并将多个物理模型纳入以前昂贵的模型中。这些新方法将应用于大气层再入、高超音速流以及气体驱动芯片实验室技术、微推进和原子力显微镜的模拟。该奖项反映了NSF的法定使命,并通过使用基金会的知识价值和更广泛的影响审查标准进行评估,被认为值得支持。
项目成果
期刊论文数量(1)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Fast evaluation of the Boltzmann collision operator using data driven reduced order models
使用数据驱动的降阶模型快速评估玻尔兹曼碰撞算子
- DOI:10.1016/j.jcp.2022.111526
- 发表时间:2022
- 期刊:
- 影响因子:4.1
- 作者:Alekseenko, Alexander;Martin, Robert;Wood, Aihua
- 通讯作者:Wood, Aihua
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Alexander Alekseenko其他文献
Alexander Alekseenko的其他文献
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{{ truncateString('Alexander Alekseenko', 18)}}的其他基金
RUI: Development of Fast Scalable Adaptive High Order Methods for Solving the Boltzmann Equation
RUI:开发用于求解玻尔兹曼方程的快速可扩展自适应高阶方法
- 批准号:
1620497 - 财政年份:2016
- 资助金额:
$ 15万 - 项目类别:
Standard Grant
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