Cellular automata (CA) models are widely used to simulate complex systems with emergent behaviors, but identifying hidden parameters that govern their dynamics remains a significant challenge. This study explores the use of Convolutional Neural Networks (CNN) to identify jump parameters in a two-dimensional CA model. We propose a custom CNN architecture trained on CA-generated data to classify jump parameters, which dictates the neighborhood size and movement rules of cells within the CA. Experiments were conducted across varying domain sizes (25 x 25 to 150 x 150) and CA iterations (0 to 50), demonstrating that the accuracy improves with larger domain sizes, as they provide more spatial information for parameter estimation. Interestingly, while initial CA iterations enhance the performance, increasing the number of iterations beyond a certain threshold does not significantly improve accuracy, suggesting that only specific temporal information is relevant for parameter identification. The proposed CNN achieves competitive accuracy (89.31) compared to established architectures like LeNet-5 and AlexNet, while offering significantly faster inference times, making it suitable for real-time applications. This study highlights the potential of CNNs as a powerful tool for fast and accurate parameter estimation in CA models, paving the way for their use in more complex systems and higher-dimensional domains. Future work will explore the identification of multiple hidden parameters and extend the approach to three-dimensional CA models.

翻译：元胞自动机（CA）模型被广泛用于模拟具有涌现行为的复杂系统，但识别控制其动态特性的隐藏参数仍是一个重大挑战。本研究探索了使用卷积神经网络（CNN）识别二维CA模型中跳跃参数的方法。我们提出了一种定制化的CNN架构，该架构在CA生成的数据上进行训练，用于对跳跃参数进行分类，这些参数决定了CA中细胞的邻域大小和运动规则。实验在不同域尺寸（25×25至150×150）和CA迭代次数（0至50）下进行，结果表明，随着域尺寸增大，分类准确率得到提升，因为更大的域尺寸为参数估计提供了更丰富的空间信息。有趣的是，虽然初始的CA迭代次数能提升性能，但超过一定阈值后，继续增加迭代次数并不能显著提高准确率，这表明只有特定的时间信息与参数识别相关。与LeNet-5和AlexNet等成熟架构相比，所提出的CNN实现了具有竞争力的准确率（89.31%），同时推理速度显著更快，使其适用于实时应用。本研究凸显了CNN作为CA模型中快速准确参数估计的强大工具的潜力，为其在更复杂系统和更高维域中的应用铺平了道路。未来的工作将探索对多个隐藏参数的识别，并将该方法扩展到三维CA模型。