机器学习用于在交互的基于代理的系统中识别相变:一个Desai-Zwanzig的例子
Nikolaos Evangelou1,2, Dimitris G Giovanis3,4, George A Kevrekidis2
1Department of Chemical and Biomolecular Engineering, <a href="https://ror.org/00za53h95">Johns Hopkins University</a>, 3400 North Charles Street, Baltimore, Maryland 21218, USA.
Physical review. E
|August 20, 2024
概括
本研究引入了一个数据驱动的框架,以精确确定基于代理的模型 (ABM) 中的相位过渡. 它使用多元学习和深度学习来识别关键变量并推导用于分析转换的ODE.
科学领域:
- 复杂的系统复杂的系统.
- 计算物理 计算物理
- 数据科学数据科学数据科学
背景情况:
- 在基于代理的模型 (ABM) 中研究阶段过渡的传统方法依赖于为减少顺序模型推导封闭形式的分析表达式.
- 这种方法可能受到选择合适封闭的复杂性限制,并且对于复杂的系统可能并不总是可行的.
研究的目的:
- 提出一种新的数据驱动框架,用于识别ABM中的相位过渡,特别是其平均场极限中的Desai-Zwanzig模型.
- 与传统的封闭式模型相比,使用较少的变量组来进行更有效的分析.
- 为了证明框架能够构建展示相位转换的分叉图的能力.
主要方法:
- 应用扩散地图多重学习算法来识别数据驱动的隐藏变量的节集.
- 使用深度学习框架来对这些潜在变量进行符合性重定量化.
- 识别一个依赖参数的普通微分方程 (ODE),使用由前方欧勒集成方案启发的残余神经网络.
主要成果:
- 确定的数据驱动的潜在变量被证明是与ABM的理论顺序参数的一对一对应.
- 在重新参数化的坐标中成功地导出了一个单一的ODE,方便了分析.
- 衍生出来的ODE,结合一个奇异的对称性转换,使得能够构建一个分叉图,清楚地展示相位过渡.
结论:
- 拟议的数据驱动框架为研究ABM中的相位转换提供了传统分析方法的有效替代方案.
- 这种方法允许使用较小,数据识别的变量集来分析复杂的系统.
- 双叉图的成功构建验证了框架在确定关键过渡方面的能力.
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