Discrete Dynamical Systems with Memory: A New Tool for Modelling Complexity

这个项目将研究一种新的方法来模拟和模拟复杂的自然和人工系统。传统上，如果一个系统由大量更简单的元素组成，那么它就被称为复杂系统，而且通常情况下，除了计算机模拟之外，无法通过任何手段来预测系统的行为。这就是为什么计算模型在现代生物学、社会学、高等工程学、生态学、农业和城市研究中如此重要。已经提出了许多计算模型，用来研究和/或利用来自许多简单交互组件的聚集行为和自组织。通常，这项工作不包括组件级别的记忆，即先前的状态信息，但记忆是所有生命系统的基本特征，也是物理、化学和工程系统的重要组成部分。我们建议进行系统的研究，以增加离散动力系统组件中的记忆量和类型，目的是识别复杂系统的新的潜在原理，特别是使用随机布尔网络和元胞自动机，因为这类例子的基本形式已经得到了很好的研究。预计这类系统的动力学将更好地捕捉各种自然和人工现象的动力学。然而，即使对于无记忆离散动态系统，建模的逆问题，例如识别细胞自动机的更新规则，也是一个不平凡的任务。必须解决以下问题：给定一个高度非线性的系统，设计一个计算模型，该模型将重建系统行为的局部规则，然后模拟全局系统。在拟议的研究中，将通过以下方式实现这一点：开发一个基于有记忆的离散动力系统的通用模拟器框架，能够从给定系统的一系列全局描述/快照中识别局部事件，并行提取支配系统元素行为的局部规则，以及设计给定系统的最小完整模型(基本上是无监督的)。我们的方法是将问题作为一个数据挖掘任务来处理，并利用机器学习技术来执行识别，最近我们已经证明这对于传统的无记忆CA是有效的。

This project will investigate a novel approach to the simulation and modelling of complex natural and artificial systems. Conventionally, a system is called complex if it consists of a large number of simpler elements and, typically, the system's behaviour cannot be predicted by any means but computer simulation. This is why computational models are so important in modern biology, sociology, advanced engineering, ecology, agriculture and urban studies. A number of computational models have been presented with which to study and/or exploit aggregate behaviour and self-organisation from a number of simple interacting components. Typically, this work does not include memory, i.e., previous state information, at the component level but memory is an essential feature of all living systems and a significant part of physical, chemical, and engineering systems. We propose to undertake systematic studies in increasing both the amount and type of memory in the components of discrete dynamical systems with the aim of identifying new underlying principles of complex systems, using random Boolean networks and cellular automata in particular as such examples are well-studied in their basic forms.It is expected that the dynamics of such systems will better capture those of a wide variety of both natural and artificial phenomena. However the inverse problem for modelling even with memory-less discrete dynamical systems, such as the identification of the update rules for cellular automata, is a non-trivial task. The following problem must be tackled: given a highly non-linear system, design a computational model that will reconstruct the local rules of the system's behaviour and then simulate the global system. In the proposed research this will be achieved by developing a universal simulator framework based on discrete dynamical systems with memory, capable of recognizing local events from a series of global descriptions/snapshots of a given system, the parallel extraction of local rules, which govern the behaviour of the system's elements, and the, mostly unsupervised, design of a minimal complete model of the given system. Our approach to this is to cast the problem as a data mining task and to exploit machine learning techniques to perform the identification, which has recently been shown by us to be effective for traditional memory-less CAs.