Collective behaviors are typically hard to model. The scale of the swarm, the large number of interactions, and the richness and complexity of the behaviors are factors that make it difficult to distill a collective behavior into simple symbolic expressions. In this paper, we propose a novel approach to symbolic regression designed to facilitate such modeling. Using raw and post-processed data as an input, our approach produces viable symbolic expressions that closely model the target behavior. Our approach is composed of two phases. In the first, a graph neural network (GNN) is trained to extract an approximation of the target behavior. In the second phase, the GNN is used to produce data for a nested evolutionary algorithm called macro-micro evolution (MME). The macro layer of this algorithm selects candidate symbolic expressions, while the micro layer tunes its parameters. Experimental evaluation shows that our approach outperforms competing solutions for symbolic regression, making it possible to extract compact expressions for complex swarm behaviors.
翻译:集体行为通常难以建模。 群集的规模、 大量互动、 行为丰富和复杂是难以将集体行为化为简单的象征性表达方式的因素。 在本文中, 我们提出了一种旨在便利建模的象征性回归的新颖方法。 使用原始和后处理的数据作为输入, 我们的方法产生可行的符号表达方式, 密切模拟目标行为。 我们的方法由两个阶段组成。 在第一阶段, 一个图形神经网络 (GNN) 受过训练, 以提取目标行为的近似。 在第二阶段, GNN 被用来为所谓的宏观- 微观进化( MME) 的嵌套进进进进进进式进化算法( MME) 生成数据。 这个算法的宏观层选择了候选的符号表达方式, 而微观层则调整其参数。 实验性评估表明, 我们的方法超越了符号回归的竞争性解决方案, 从而有可能为复杂的暖化行为提取压缩表达方式 。