Attention-Enhanced CNN Surrogate for Inverse Parameter Estimation in Cellular Automata

Abstract

Cellular automata (CA) are powerful discrete models for complex spatiotemporal systems, yet estimating hidden parameters governing their dynamics remains challenging. We propose an attention-enhanced convolutional neural network (Attention-CNN) as a surrogate optimizer for identifying the jump parameter () in a two-phase CA model. The jump parameter regulates neighborhood radius and cell mobility, shaping emergent spatial structures. The architecture combines convolutional layers for local feature extraction with a spatial-attention module that captures global dependencies, enabling adaptive focus on informative regions of the domain. Training data were generated across varying domain sizes (–) and CA iterations (0, 5, 25, and 50), yielding 80,000 labeled samples. The model achieved 90.53% top-1 accuracy and a 50 faster inference than AlexNet, demonstrating robustness and efficiency across resolutions. Attention heatmaps further reveal interpretable focus patterns aligned with CA dynamics. This framework provides a fast, data-driven surrogate for inverse parameter estimation in CA-based models.