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

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 (ΛCDM, CPL, GEDE, Λ 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 ≈ − 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 ∈ 0.3, 1.5, but reveals a systematic separation of redshift-binned M B distributions. The heteroscedastic method identifies a persistent 2–3 σ residual at z ∼ 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.