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

自然科学中的结构保持算法和模型简化项目摘要将开发新的理论和计算技术，结合数学，计算机科学和地球物理科学的联合收割机研究。 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。 它通常昂贵得令人望而却步（例如，大量的计算时间）来模拟许多自然发生的现象中涉及的所有尺度。 在可计算范围之外的尺度必须用简化模型来描述，该简化模型认真地表示未解析的自由度对解析尺度的影响。 这些模型也可能有约束条件，提供减少与其他系统的相互作用的描述。 本研究的目标将是开发模型简化技术和新的算法来解决这些问题。

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.