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

TL;DR

Fast flavor conversions (FFCs) in dense neutrino gases pose a significant computational challenge due to multi-scale dynamics. The authors develop two interpretable data-driven surrogates—Kolmogorov-Arnold Networks (KANs) and Sparse Identification of Nonlinear Dynamics (SINDy/SINDy-SA)—to map from two radial moments to post-FFC neutrino energy spectra, enabling both accurate reconstruction and physical insight. Parametric KAN achieves up to about 90% average accuracy across species, while SINDy offers concise, interpretable governing equations at somewhat lower accuracy; both methods consistently identify the initial heavy-lepton neutrino density as the dominant driver of FFC evolution. This work provides a practical framework for embedding FFC physics into large-scale CCSN/NSM simulations and illustrates how interpretable ML can guide data-driven discovery in astrophysics, with potential extensions to richer neutrino gases and many-body effects.

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. 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.

Figures (6)

• Figure 1: The evolution of key metrics during the training process. The plot displays the training loss, validation loss, and two physics-informed error terms as a function of the training epoch. The logarithmic scale on the y-axis highlights the convergence behavior of the network.
• Figure 2: Visualization of the trained KAN architecture used to model the fast flavor conversion process. The eleven input neurons at the bottom correspond, from left to right, to the physical features of the pre-conversion neutrino gas as detailed in \ref{['input']}. The eight output neurons at the top yield the predicted post-conversion radial moments for all relevant flavors ($I_{0}^{\nu_e}, I_{1}^{\nu_e}, I_{0}^{\bar{\nu}_e}, I_{1}^{\bar{\nu}_e}, I_{0}^{\nu_x}, I_{1}^{\nu_x}, I_{0}^{\bar{\nu}_x}, I_{1}^{\bar{\nu}_x}$, from left to right). The curves on the edges represent the learned one-dimensional activation functions, which are parameterized by B-splines. The activation shapes shown are taken from a representative training run, illustrating the complex functional relationships captured by the model. Edge darkness denotes the contribution of the connected input (darker means higher contribution); nearly invisible edges indicate negligible contribution.
• Figure 3: The plot illustrates the energy distributions of three types of neutrinos: electron-type neutrinos ($\nu_e$), anti-electron neutrinos ($\bar{\nu}_e$), and heavy-lepton flavor neutrinos ($\nu_x$). The theoretical distributions for these neutrinos are shown by the blue, orange, and green curves, respectively. Sampled data points are represented by blue circles for $\nu_e$, orange squares for $\bar{\nu}_e$, and green triangles for $\nu_x$.
• Figure 4: This figure compares the reconstructed post-FFC energy spectra from our models with exact calculations. The exact calculations are performed using the benchmark setup described in PhysRevD.109.083019. The panels show results for $\nu_e$ (top-left), $\bar{\nu}_e$ (top-right), $\nu_x$ (bottom-left), and $\bar{\nu}_x$ (bottom-right). The legend indicates results from Exact (blue squares), Param. KAN (red circles), Symbolic KAN (orange circles), and SINDy (green circles).
• Figure 5: Heatmap of normalized absolute partial derivatives for the SINDy-SA. Each entry reports the sample mean of $|\partial y_j / \partial x_i|$ evaluated at the original data points Warmer colors indicate stronger influence of input variable $x_i$ on output $y_j$, cooler colors indicate weaker influence. Here, we set all values less than $10^{-3}$ to zero.