Interpretation of Computer Simulations and Experimental Data from Chaotic Processes

Sauer 9971798研究非线性动力系统的计算方面，重点是在科学和工程中具有多学科影响的问题。 第一个主要领域涉及到典型的非双曲混沌系统的长期计算机模拟的有效性。 问题是是否可以假设长的模拟轨迹近似匹配真实的系统行为。 这是一个影响深远的问题，涉及到数值计算的核心。 数值分析通常关注时间上局部的算法特性，但非线性系统中混沌轨迹的可能性使这种观点发生了显着变化。 该项目涉及为计算机模拟轨迹和计算机模型的正确轨迹之间的故障或不匹配之间的预期时间制定定量法律，并调查可能因不匹配而严重计算错误的统计量。 第二个主要领域是研究人员正在进行的关于解释产生非周期性数据流的实验室实验的工作。 利用由确定性物理过程产生的单变量或多变量时间序列或事件间时间间隔，可以忠实地重建过程的相空间，作为系统辨识、滤波、预测和控制等应用的基础。 这些应用的数学基础一直是研究人员和同事正在进行的研究的主题。 该项目试图扩大这些方法的有效性领域，并增加它们在复杂系统研究中的能力，特别是在存在观测噪声的情况下。计算机模拟是现代科学的重要组成部分。 随着在生物技术、合理药物设计、气象学、卫星轨道轨迹设计、风洞试验和神经生理学等领域建模取代实验和昂贵的传统设计方法，对非线性模型的长期计算机模拟的正确解释的重要性日益增加。 在这个项目中探索的问题是至关重要的非线性过程的复杂模拟的结果的基本理解。 这个项目的一个目标是在物理相关的模型中探索这些问题，特别是隔离和量化这些表示的局限性，特别是为了长期建模的目的。 这项研究的第二个重点是解释从实验室实验和自然中收集的混沌系统数据。 复杂的确定性时间序列正在探索作为物理，化学，工程和生物/医学环境中的关键信息。 作为一个例子，来自哺乳动物海马细胞和其他小神经系统的神经元放电数据由研究者与最近重新安置在乔治梅森大学的一组医学研究人员一起研究，目的是检测大脑中的确定性信息处理。 研究人员已经完成了扩展这些概念基础和开发相关计算实现的工作，并计划扩大其有效性领域，并增加其在自然，实验和工程相关背景下研究复杂系统的能力。 在这个项目中开发了这些应用的新技术，包括与现有信号处理方法结合使用的新计算技术。

Sauer9971798The investigator studies computational aspects of nonlinear dynamical systems, with emphasis on questions that have multidisciplinary implications in the sciences and engineering. The first main area involves the validity of long-term computer simulations of typical nonhyperbolic chaotic systems. The question is whether long simulation trajectories can be assumed to approximately match true system behavior. This is a far-reaching question that goes to the heart of numerical computation. Numerical analysis is typically concerned with algorithm properties that are local in time, but the possibility of chaotic trajectories in nonlinear systems is causing this view to shift markedly. The project involves the development of quantitative laws for the expected time between breakdowns, or mismatches, between computer simulation trajectories and the correct trajectories of computer models, and investigation of statistical quantities that may be severely miscalculated because of the mismatch. The second major area is ongoing work by the investigator on the interpretation of laboratory experiments that generate aperiodic data streams. Using univariate or multivariate time series or inter-event time intervals produced by a deterministic physical process, the phase space of the process can be faithfully reconstructed as the basis for applications such as system identification, filtering, prediction and control. The mathematical foundations of these applications has been the topic of ongoing research by the investigator and coworkers. The project attempts to widen the areas of validity of these methods, and increase their power for the study of complex systems, especially in the presence of observational noise.Computer simulations are an essential part of modern science. The importance of the correct interpretation of long-term computer simulations of nonlinear models is increasing as modeling replaces experiments and expensive traditional methods of design in areas as diverse as biotechnology, rational drug design, meteorology, satellite orbit trajectory design, wind tunnel testing, and neurophysiology. The questions explored in this project are critical to the fundamental understanding of the results of complex simulations of nonlinear processes. One goal of this project is to explore these questions in physically relevant models, and in particular to isolate and quantify the limitations of these representations, especially for the purpose of long-term modeling. The second focus of this research is the interpretation of data collected from chaotic systems in laboratory experiments and nature. Complex deterministic time series are being explored as key information in physical, chemical, engineering and biological/medical settings. As an example, neuron firing data from hippocampal cells of mammals and other small neural systems are studied by the investigator in conjunction with a group of medical researchers who have recently relocated at George Mason University, with the purpose of detecting deterministic information processing in the brain. The investigator has done previous work on expanding these conceptual foundations and developing related computational implementations, and plans to widen their areas of validity and increase their power for the study of complex systems in natural, experimental, and engineering-related contexts. New techniques for these applications are developed in this project, involving new computation techniques used in conjunction with existing signal processing methods.