Identification and Control for Pattern Steering in Dynamical Networks

这个项目的目标是开发一个用于识别和控制网络和时空系统中复杂动态模式的基础设施，用于模式控制目标的工具包括复杂吸引子重建、状态识别和适当的控制协议。将研究将复杂动态网络的活动从一种状态改变到另一种状态的计算方法。复杂的非线性网络似乎是多稳态和多节奏的，是混沌和周期稳定吸引子的混合，以及在工程应用的时间间隔内可能有效稳定的其他亚稳态暂态。将开发计算方法，以便能够在这些吸引子或动态模式之间进行转向，并快速和自动地执行这种切换。该项目包括理论、计算和实验部分。特别是，将在以前的探索性工作的推动下，开展关于自适应卡尔曼滤波的基础工作。具有多个吸引子的尖峰网络将进行理论研究，并通过仿真验证假设，以此来验证转向技术的概念。更大的网络将被设计为通向实验的桥梁。一种新的数据驱动的计算方法称为扩散映射延迟坐标，这是先前探索性研究的结果，将用于在吸引子盆地之间导航。开发的方法将在两个不同的实验平台上进行测试，神经细胞培养和向列相液晶中的对流辊。这项工作为动态和尖峰生物、生物启发和更一般的工程网络的分析和有效控制提供了潜在的开创性贡献。更好地理解这一测试案例可能是朝着优化能源转移和生产的新方法迈出的第一步。这些实验例子都缺乏已知的运动方程，这严重限制了经典控制理论的使用，并推动了我们新技术的发展。在整个研究过程中，重点将放在开发可广泛推广到其他多稳态动态网络的方法上。该项目将为研究生和博士后提供具体的跨学科培训，他们将从三个不同的背景领域进行选择，物理、数学和工程。

The objective of this project is to develop an infrastructure for the identification and steering of complex dynamical patterns in networks and spatiotemporal systems, tools for the goal of pattern steering include complex attractor reconstruction, state identification, and appropriate control protocols. Computational methods for changing the activity of a complex dynamical network from one state to another will be investigated. Complicated nonlinear networks appear to be multi-stable and multi-rhythmic, a mix of chaotic and periodic stable attractors, together with other metastable transients that may be effectively stable for the time interval of an engineering application. Computational methods will be developed to enable steering between these attractors, or dynamical patterns, and to perform this switching quickly and automatically. The project includes theoretical, computational, and experimental components. In particular, foundational work on adaptive Kalman filtering will be carried out that was motivated by previous exploratory work. Spiking networks with multiple attractors will be studied theoretically and hypotheses tested by simulation, as a proof of concept of steering techniques. Larger networks will be designed as a bridge to experiments. A new data-driven computational method called Diffusion-Mapped Delay Coordinates, a result of previous exploratory study, will be used for steering between basins of attractors. The developed methodologies will be tested in two different experimental platforms, neuronal cell cultures, and convection rolls in nematic liquid crystals. This work provides potentially pathbreaking contributions to the analysis and effective control of dynamical and spiking biological, bio-inspired, and more general engineering networks. Better understanding of this test case could be a first step to new approaches to optimization of energy transfer and production. The experimental examples have in common a lack of known equations of motion, which severely limits the use of classical control theory and motivates development of our new techniques. Throughout this study, emphasis will be placed on development of methodologies that generalize widely to other multistable dynamical networks. The project will provide concrete interdisciplinary training for graduate and postdoctoral students, who will be chosen from three different background areas, physics, mathematics, and engineering.