KDI: Structure Preserving Algorithms and Model Reduction in the Natural Sciences

KDI：自然科学中的结构保持算法和模型简化

• 批准号: 9873133
• 负责人: Jerrold Marsden
• 金额: $ 162.9万
• 依托单位: California Institute of Technology
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1998
• 资助国家: 美国
• 起止时间: 1998-10-01 至 2002-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9873133&HistoricalAwards=false
• 关键词: KDI; Structure; Preserving; Algorithms; Model

Structure Preserving Algorithms and Model Reduction in the Natural SciencesProject SummaryNew theoretical and computational techniques will be developed that combine research in mathematics, computer science, and the geophysical sciences. Understanding and controlling modern physical systems typically requires numerical simulations of multiscale dynamics that occur over a wide range of time and space scales. It is generally prohibitively expensive (e.g., a great deal of computational time) to simulate all of the scales involved in many naturally occurring phenomena. Scales outside the computable range must be described by a reduced model that conscientiously represent the effects of the unresolved degrees of freedom on the resolved scales. These models may also have constraints that provide reduced descriptions of the interactions with other systems. The goal of this study will be to develop both the model reduction techniques and new algorithms to address these problems.

自然科学中的结构保持算法和模型简化项目摘要将开发结合数学、计算机科学和地球物理科学研究的新理论和计算技术。 理解和控制现代物理系统通常需要对发生在广泛的时间和空间尺度上的多尺度动力学进行数值模拟。 模拟许多自然发生的现象所涉及的所有尺度通常非常昂贵（例如，大量的计算时间）。 可计算范围之外的尺度必须通过简化模型来描述，该模型认真地表示未解析的自由度对解析尺度的影响。 这些模型还可能具有提供与其他系统交互的简化描述的约束。 本研究的目标是开发模型简化技术和新算法来解决这些问题。