An Interpretable AI Framework to Disentangle Self-Interacting and Cold Dark Matter in Galaxy Clusters: The CKAN Approach

Convolutional neural networks have shown their ability to differentiate between self-interacting dark matter (SIDM) and cold dark matter (CDM) on galaxy cluster scales. However, their large parameter counts and ''black-box'' nature make it difficult to assess whether their decisions adhere to physical principles. To address this issue, we have built a Convolutional Kolmogorov-Arnold Network (CKAN) that reduces parameter count and enhances interpretability, and propose a novel analytical framework to understand the network's decision-making process. With this framework, we leverage our network to qualitatively assess the offset between the dark matter distribution center and the galaxy cluster center, as well as the size of heating regions in different models. These findings are consistent with current theoretical predictions and show the reliability and interpretability of our network. By combining network interpretability with unseen test results, we also estimate that for SIDM in galaxy clusters, the minimum cross-section $(\sigma/m)_{\mathrm{th}}$ required to reliably identify its collisional nature falls between $0.1\,\mathrm{cm}^2/\mathrm{g}$ and $0.3\,\mathrm{cm}^2/\mathrm{g}$. Moreover, CKAN maintains robust performance under simulated JWST and Euclid noise, highlighting its promise for application to forthcoming observational surveys.