Dynamical Systems Approach to Computer Simulation Accuracy and Data Analysis

绍尔0208092 研究人员研究非线性动力系统的计算方面，强调混沌动力学在解释长期模拟结果和复杂动力过程数据中的作用。 模拟的工作是一项正在进行的研究，研究在确定性建模中发生的对结果有宏观影响的微妙偏差。 对于典型的非双曲型混沌系统的长期计算机模拟是否能够在原理上近似地匹配真实的系统行为，这是一个悬而未决的问题。 第二个主要领域是对产生非周期性数据的物理和生物实验的解释。 将随机建模应用于从实验室和自然过程中收集的时间序列和尖峰时间有很长的历史。 研究者研究了使用动力系统技术的方法，包括嵌入理论和尖峰序列重建，以扩展实验数据的确定性建模的能力。 计算机模拟是现代科学的重要组成部分。 重要的是要知道，用于模拟的数学模型的解决方案是否可以预期是准确的定性和定量表示的自然现象被建模，在面对小modelingerrors，以及是否计算机解决方案的模型可以representations的模型，在面对小floating pointerrors。 该研究为回答物理相关模型的这类问题奠定了基础。 特别是调查员参与隔离和量化的确定性表示的限制，特别是为了长期建模的目的。 该项目的第二个主要重点是当没有第一原理数学或计算机模型可用时，对从实验系统和自然中收集的数据进行解释。 如果可以从过程中测量物理相关量的时间轨迹，则存在尝试重建过程的动力学行为的技术，具有预测或控制过程的潜力。复杂的确定性时间序列正在物理，化学，工程和生物/医学环境中被识别。研究人员已经在扩展这些概念基础和开发相关的计算实现方面取得了先前的进展，并致力于提高他们在科学和工程相关背景下研究复杂系统的能力。

Sauer0208092 The investigator studies computational aspects of nonlineardynamical systems, emphasizing the role of chaotic dynamics inthe interpretation of long-time simulation outcomes and data fromcomplicated dynamical processes. The work on simulation is anongoing study of subtle biases occurring in deterministicmodeling that have macroscopic effects on outcomes. It is anopen question whether it is possible in principle for long-termcomputer simulations of typical nonhyperbolic chaotic systems toapproximately match true system behavior. The second major areais ongoing work on the interpretation of physical and biologicalexperiments that generate aperiodic data. There is a long historyof applying random modeling to time series and spike timing datacollected from laaboratory and natural processes. Theinvestigator syudies ways to use dynamical systems techniques,including embedding theory and spike train reconstruction, toextend the power of deterministic modeling for experimental data. Computer simulation is a critical ingredient of modernscience. It is important to know whether solutions of amathematical model used for simulation can be expected to beaccurate qualitative and quantitative representations of thenatural phenomena being modeled, in the face of small modelingerrors, and whether computer solution of the model can representsolutions of the model, in the face of small floating pointerrors. This reseach builds a foundation for answering questionslike this for physically relevant models. In particular theinvestigator is involved in isolating and quantifying thelimitations of deterministic representations, especially for thepurpose of long-term modeling. The second major focus of theproject is the interpretation of data collected from experimentalsystems and nature when no first-principles mathematical orcomputer model is available. If time traces of physicallyrelevant quantities can be measured from the process, techniquesexist to attempt to reconstruct the dynamical behavior of theprocess, with potential to predict or control the process.Complex deterministic time series are being identified inphysical, chemical, engineering and biological/medical settings.The investigator has made previous progress on expanding theseconceptual foundations and developing related computationalimplementations, and is working to increase their power for thestudy of complex systems in scientific and engineering-relatedcontexts.