BECS: Understanding Complex Systems: Large-Scale Data Driven Modeling

该提案的目的是发现复杂系统的一般特性，以便这些原则可以应用于操纵现有的复杂系统和设计工程复杂系统，以供未来应用。作为一个模型复杂的系统，该提案解决了金融市场和金融时间序列的建模和分析。在金融系统的各个尺度上，都有许多非平凡的波动模式。这些系统由许多主体组成，微观尺度上的相互作用和策略逐渐扩展到宏观尺度，并反映在经济中单一和多种资产的价格中。大尺度动力学和结构往往与微观相互作用的具体细节无关。这种“普适性”使得设计最方便的“最小模型”变得有意义。金融市场和金融时间序列显然就是这样的现象。利用基于统计物理的模型，少数博弈，自适应系统和非线性系统理论的思想，我们提出开发多智能体简洁模型，可以捕获高度可观察系统的各种特征。该项目将导致对导致全球系统出现的微观规则类型及其相互作用的基本理解，以及对引起波动，长期相关性和记忆等复杂行为的理解，以及从此类系统的重大崩溃中成功恢复的理解。在大型复杂系统中成功研究的社会影响范围从全球信息经济，到共享基础设施，到全球生态和人类健康。科学影响扩展到统计力学，非线性动力学和系统以及许多其他领域。与此同时，我们的项目将大大有助于培训、教育和外联。例如，研究生和博士后研究人员将通过与数学家和工程学院共同工作来扩大他们的曝光度，我们将使用一个经过验证的模型，通过纯粹与应用数学研究所（IPAM at UCLA）让本科生参与我们的研究。我们将开办一个暑期学校，培训更多的年轻科学家掌握相关技术。

The objective of the proposal is to discover the general properties of complex systems so that these principles can be applied to both manipulate existing complex systems and to design engineered complex systems for future applications. As a model complex system, this proposal addresses modeling and analysis of the financial markets and the financial time series. There are numerous non-trivial fluctuation patterns in financial systems at every scale. These systems are composed of many agents, and the interactions and strategies on the microscopic scale build up to the macroscopic scale, which get reflected in the prices of single and multiple assets in the economy. The large scale dynamics and structure are often independent of the particular details of the microscopic interaction. This "universality" makes it meaningful to design the most convenient "minimal model". The financial markets and the financial time series are clearly such phenomena. Using ideas from statistical physics based models, minority games, adaptive systems, and non-linear systems theory, we propose to develop multi-agent succinct models that can capture various features of the highly-observable systems. The project will lead to a fundamental understanding of the types of microscopic rules and their interactions that lead to the emergence of global systems and an understanding of what gives rise to complex behavior such as fluctuations, long-term correlations and memory, and successful recovery from a major collapses in such systems.The societal impact of successful research in large complex systems ranges from theglobal information economy, to shared infrastructure, to global ecology and human health. The scientific impact extends to statistical mechanics, nonlinear dynamics and systems and numerous other areas. At the same time, our project will contribute significantly to training, education and outreach. For example, graduate students and postdoctoral researchers will broaden their exposure by working jointly with both a mathematician and an engineering faculty, and we will use a proven model for engaging undergraduates in our research through the Institute for Pure and Applied Mathematics (IPAM at UCLA). We will offer a summer school to train many more young scientists in the relevant techniques.