From nonlinear dynamics to proof of conceptfor Heteroclinic Computing

从非线性动力学到异宿计算的概念证明

• 批准号: 419424741
• 负责人: Professor Dr. Marc Timme, Ph.D.
• 金额: --
• 依托单位: Institut für Theoretische Physik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2019
• 资助国家: 德国
• 起止时间: 2018-12-31 至 2022-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/419424741?language=en
• 关键词: nonlinear; dynamics; proof; conceptfor; Heteroclinic

Heteroclinic dynamics naturally emerges in coupled nonlinear dynamical systems, in particular in networks of phase-coupled and pulse-coupled oscillators. As a dynamical phenomenon it is reasonably well understood mathematically. Heteroclinic networks, a collection of saddle states linked via heteroclinic connections, form the skeleton determining much of the collective dynamics in a range of systems. Dynamics near heteroclinic networks has been proposed to provide computing mechanisms in biological and bio-inspired systems and to offer highly effective, universal computational features. Heteroclinic networks also enable a new computing framework that is independent of specific implementations, such as networks of phase-coupled or pulse-coupled oscillators or competitive Lotka-Volterra-like systems. The core computational principles of encoding are reasonably understood. In particular, the direction of the driving signal vector acting on a state near a saddle determines the direction a trajectory leaves that saddle and thus the next saddle approached by the trajectory. On longer time scales, the driving signal thereby determines the sequence of saddles and reversely, the sequence of saddles reveals information about specific properties of the driving signal, i.e. a computation has been performed on that input signal. Here, signals with components in the same partial rank order are associated with each other and yield the same computational result, i.e. the computation is robust in this sense. Recent works also demonstrated how noise affects reliable switching in both phase-coupled and pulse-coupled oscillator systems, thereby offering hints into computational reliability and providing first insights about how heteroclinic computing systems may actually behave under noisy, real world conditions. Heteroclinic computing, however, has so far not been demonstrated in any real device and it remains an open question how exactly to realize it.In the proposed project, we plan to address three remaining key questions. One about efficient decoding and its interplay with encoding, one about how to realize intrinsic, self-organized memory in suitable coupled oscillator systems, and one about identifying potential substrates, architectures and implementation techniques to provide a proof of concept for heteroclinic computers in hardware. We will combine known properties about coupled oscillator networks, especially the theory of pulse-coupled oscillators and generally the theory of coupled dynamical systems, with ideas from neural network theory to address these questions. A successful study would not only yield new insights into theoretical aspects of the nonlinear dynamics of the heteroclinic computing paradigm but also provide crucial steps towards a new form of robust analogue computers, creating a bridge from the mathematical level of nonlinear dynamics and the conceptual level of the computing idea towards options for the technological level.

异宿动力学自然出现在耦合非线性动力系统中，特别是在相位耦合和脉冲耦合振荡器网络中。作为一种动力学现象，它在数学上得到了合理的理解。异宿网络是通过异宿连接连接的鞍态的集合，形成了一系列系统中决定大部分集体动力学的骨架。近异宿网络动力学已经被提出来在生物和生物启发系统中提供计算机制，并提供高效、通用的计算特征。异宿网络还实现了独立于特定实现的新计算框架，例如相位耦合或脉冲耦合振荡器或竞争性Lotka-Volterra类系统的网络。编码的核心计算原理得到了合理的理解。特别地，作用于鞍附近的状态的驱动信号矢量的方向确定轨迹离开该鞍的方向，并且因此确定轨迹接近的下一个鞍的方向。在较长的时间尺度上，驱动信号由此确定鞍和鞍的序列，鞍的序列揭示了关于驱动信号的特定属性的信息，即，已经对该输入信号执行了计算。这里，具有相同部分秩序中的分量的信号彼此相关联并且产生相同的计算结果，即，在这个意义上，计算是鲁棒的。最近的工作还表明，噪声如何影响相位耦合和脉冲耦合振荡器系统的可靠切换，从而提供线索到计算的可靠性，并提供第一次洞察异宿计算系统如何实际上可能会表现在嘈杂的，真实的世界条件下。然而，异宿计算到目前为止还没有在任何真实的设备中得到证明，如何确切地实现它仍然是一个悬而未决的问题。在拟议的项目中，我们计划解决三个剩余的关键问题。一个是关于有效的解码及其与编码的相互作用，一个是关于如何在合适的耦合振荡器系统中实现固有的自组织存储器，一个是关于识别潜在的基板，架构和实现技术，以提供硬件中的异宿计算机的概念证明。我们将结合联合收割机已知的耦合振荡器网络，特别是脉冲耦合振荡器的理论和一般的耦合动力系统的理论，从神经网络理论的想法来解决这些问题。一个成功的研究不仅会产生新的见解异宿计算范式的非线性动力学的理论方面，但也提供了一个新的形式的强大的模拟计算机的关键步骤，创建一个桥梁，从数学水平的非线性动力学和概念水平的计算思想的选择，技术水平。