Applications of machine learning to detecting fast neutrino flavor instabilities in core-collapse supernova and neutron star merger models

Neutrinos propagating in a dense neutrino gas, such as those expected in core-collapse supernovae (CCSNe) and neutron star mergers (NSMs), can experience fast flavor conversions on relatively short scales. This can happen if the neutrino electron lepton number ($\nu \mathrm{ELN}$) angular distribution crosses zero in a certain direction. Despite this, most of the state-of-the-art CCSN and NSM simulations do not provide such detailed angular information and instead, supply only a few moments of the neutrino angular distributions. In this study we employ, for the first time, a machine learning (ML) approach to this problem and show that it can be extremely successful in detecting $\nu \mathrm{ELN}$ crossings on the basis of its zeroth and first moments. We observe that an accuracy of $\sim 95\%$ can be achieved by the ML algorithms, which almost corresponds to the Bayes error rate of our problem. Considering its remarkable efficiency and agility, the ML approach provides one with an unprecedented opportunity to evaluate the occurrence of fast flavor conversions in CCSN and NSM simulations on the fly. We also provide our ML methodologies on GitHub.

Figure 1

The points/crosses show the $F_{{\nu }_e}-F_{{\overline{\nu }}_e}$’s for which there is a crossing in the $\nu \mathrm{ELN}$ angular distribution for the maximum entropy and Gaussian distributions, for some values of $\alpha$. Note that the crossing (no-crossing) region patterns are very similar for the two angular distributions. The classifications can be different only at some narrow zones at the boundary of the crossing/no-crossing regions, where the labels get noisy meaning that there are different labels at the same point.

Figure 2

The accuracy and precision of the LR algorithm for the training and development datasets as a function of the polynomial degree of the nonlinear transformations. The scores reach their maximum at $n\simeq 9$, though they are more or less acceptable for $n\gtrsim 3$.

Figure 3

The accuracy of the LR algorithm for the training and development sets. Note that the overfitting disappears once at least a few thousand points are considered to train the LR algorithm.

Figure 4

The accuracy of the SVM algorithm on the training and development sets, as a function of the $\gamma$ parameter defined in Eq. (10). The best performance of the SVM algorithm on the development set is reached at $\gamma \simeq 100$.

Figure 5

$\nu \mathrm{ELN}$ crossings (white crosses) in the polar plane of the axisymmetric simulation (model M3A8m3a5 from Ref. [63]) at $t=50\mathrm{ms}$. The z axis is the symmetry axis and x is the cylindrical radius, the color map shows the ${\nu }_e-{\overline{\nu }}_e$ asymmetry parameter, $\alpha =n_{{\overline{\nu }}_e}/n_{{\nu }_e}$, and the solid (dashed) lines indicate the locations of the ${\nu }_e$ (${\overline{\nu }}_e$) neutrinospheres. While the upper left panel shows the crossings captured by the polynomial method, the rest of the panels indicate the $\nu \mathrm{ELN}$ crossings captured by the LR algorithm with different threshold densities, $p_c$, and polynomial degrees ($n=9$ for the upper right and lower left panels and $n=3$ for the lower middle and right panels).