The postmerger phase of binary neutron star (BNS) mergers encodes valuable information about the equation of state (EOS) of supranuclear matter. Extracting this information from the analysis of the postmerger waveforms remains challenging due to the high-frequency limitations of current detectors. Future third-generation observatories, such as the Einstein Telescope (ET) and NEMO, will have the sensitivity required to resolve post-merger signals with high fidelity. In this work, we apply clawdia, our recently developed sparse dictionary learning (SDL) framework, to classify different EOS models using the merger and postmerger gravitational-wave emission of simulated BNS mergers available in the core database. Our dataset comprises five EOS models representative of a broad range of neutron star properties. The SDL framework is optimized under realistic detection conditions by injecting signals into simulated noise matching the sensitivity curves of ET and NEMO. Our results show that classification is primarily driven by the dominant postmerger frequency, $f_2$, which encodes EOS-dependent information. At a modest signal-to-noise ratio of 5, our method achieves $F_1$ scores of 0.76 for ET and 0.70 for NEMO, with performance improving for higher signal-to-noise ratios. The reliability and generalization capabilities of the model are assessed with additional tests, including the classification of an EOS not included in the training dataset and the analysis of detector-specific biases.

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• Gravitational waves
• Nuclear matter in neutron stars
• Machine learning