Cellular Automaton With CNN

2025-03-04

AI Summary

This work addresses the challenge of identifying implicit jump parameters—governing neighborhood size and cell transition rules—in two-dimensional cellular automata (CA). We propose an end-to-end classification framework based on a custom lightweight convolutional neural network (CNN). By constructing a spatiotemporal evolution image dataset from CA simulations, we discover that discriminative parameter information resides only in specific spatiotemporal segments, revealing a novel interpretable modeling principle for CA. Our method achieves 89.31% parameter identification accuracy on 150×150 grids, substantially outperforming LeNet-5 and AlexNet baselines, while maintaining high inference efficiency suitable for real-time parameter inversion. To our knowledge, this is the first systematic application of domain-specific CNNs to jump parameter recognition in CA. The approach establishes a new paradigm for uncovering latent mechanisms in complex dynamical systems through data-driven, interpretable deep learning.

Technology Category

• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Machine Learning: Causal Learning
• Knowledge Representation and Reasoning: Action, Change, and Causality

Application Category

• Web Mining and Content Analysis: Models for Web evolution
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

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.

Problem

• Identify hidden parameters in cellular automata models.
• Use CNN to classify jump parameters in 2D CA.
• Improve accuracy and speed for real-time CA applications.

Innovation

• CNN identifies jump parameters in CA models
• Custom CNN architecture for CA-generated data classification
• Real-time application with fast inference times