Application of interpretable data-driven methods for the reconstruction of supernova neutrino energy spectra following fast neutrino flavor conversions

Neutrinos can experience fast flavor conversions (FFCs) in highly dense astrophysical environments, such as core-collapse supernovae and neutron star mergers, potentially affecting energy transport and other processes. The simulation of fast flavor conversions under realistic astrophysical conditions requires substantial computational resources and involves significant analytical challenges. While machine learning methods like Multilayer Perceptrons have been used to accurately predict the asymptotic outcomes of FFCs, their 'black-box' nature limits the extraction of direct physical insight. To address this limitation, we employ two distinct interpretable machine learning frameworks-Kolmogorov-Arnold Networks (KANs) and Sparse Identification of Nonlinear Dynamics (SINDy)-to derive physically insightful models from a FFC simulation dataset. Our analysis reveals a fundamental trade-off between predictive accuracy and model simplicity. The KANs demonstrates high fidelity in reconstructing post-conversion neutrino energy spectra, achieving accuracies of up to $90%$. In contrast, SINDy uncovers a remarkably concise, low-rank set of governing equations, offering maximum interpretability but with lower predictive accuracy. Critically, by analyzing the interpretable model, we identify the number density of heavy-lepton neutrinos as the most dominant factor in the system's evolution. Ultimately, this work provides a methodological framework for interpretable machine learning that supports genuine data-driven physical discovery in astronomy and astrophysics, going beyond prediction alone.