Reconstructing the Type Ia Supernova Absolute Magnitude with Two-Probe Physics-Informed Neural Networks

TL;DR

This study employs physics-informed neural networks to reconstruct the absolute magnitude of Type Ia supernovae from cosmological data, revealing systematic residuals and model-independent tensions that merit further exploration.

Contribution

It introduces two variants of PINNs for supernova magnitude reconstruction, demonstrating the importance of the Etherington relation and separating probe data for detailed analysis.

Findings

Models recover M_B ≈ -19.3 mag with biases below 0.05 mag.

No significant M_B evolution detected in z ∈ [0.3, 1.5].

Persistent residual at z ~ 0.4–0.5 suggests underlying tension.

Abstract

We apply two variants of Physics-Informed Neural Networks (PINNs) to reconstruct the Type~Ia supernova absolute magnitude $M_B(z)$ from joint BAO and supernova data under four cosmological models ($\Lambda$CDM, CPL, GEDE, $\Lambda_s$CDM) and two DESI~DR2 fiducial sets. A heteroscedastic single-network method tested across four constraint configurations establishes that the Etherington distance duality relation is a more fundamental constraint than cosmological model priors, reducing internal inconsistencies by up to an order of magnitude. Under full constraints all models recover $M_B \approx -19.3$~mag with biases below 0.05~mag. A Fisher information-weighted two-network variant trains independent networks on BAO and SN data, providing clean probe separation; it finds no significant pointwise $M_B$ evolution in $z \in [0.3, 1.5]$, but reveals a systematic separation of redshift-binned $M_B$ distributions. The heteroscedastic method identifies a persistent $2$--$3\sigma$ residual at $z \sim 0.4$--$0.5$ that is consistent across all four models and both fiducials, implying the same underlying tension. While the origin of this feature remains ambiguous, its model-independence and cross-method consistency warrant further investigation with forthcoming data.