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

TL;DR

This paper develops interpretable machine learning models to understand and predict neutrino energy spectra after fast flavor conversions in supernovae, balancing accuracy and simplicity to gain physical insights.

Contribution

It introduces two interpretable ML frameworks, KANs and SINDy, for modeling FFC outcomes, highlighting their trade-offs and physical interpretability.

Findings

KANs achieve up to 90% accuracy in spectral reconstruction

SINDy provides a compact, closed-form approximation

Initial heavy-lepton neutrino density critically influences FFCs

Abstract

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. Simulating fast flavor conversions under realistic astrophysical conditions requires substantial computational resources and poses significant analytical challenges. While machine learning methods such as 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 mitigate this limitation, we employ two distinct interpretable machine learning frameworks, Kolmogorov-Arnold Networks (KANs) and Sparse Identification of Nonlinear Dynamics (SINDy), to learn interpretable surrogates for the asymptotic input-output mapping from an FFC simulation dataset. Our analysis reveals a fundamental trade-off between predictive accuracy and model simplicity. KANs demonstrate high fidelity in reconstructing post-conversion neutrino energy spectra, achieving accuracies of up to 90%. In contrast, SINDy yields a low-rank, compact closed-form approximation of the input-output mapping, at the expense of some predictive accuracy. Critically, using these structured and sparse surrogates as diagnostic tools, we identify that the system's evolution is most sensitive to the initial number density of heavy-lepton neutrinos when FFCs are triggered, compared with other physical quantities. Ultimately, this work provides a methodological framework for interpretable machine learning that supports genuine data-driven scientific discovery in astronomy and astrophysics, going beyond prediction alone.