Evaluating Physically Motivated Loss Functions for Photometric Redshift Estimation

TL;DR

This study evaluates the impact of adding soft physical constraints to neural networks for photometric redshift estimation, finding no significant regularization benefit over data augmentation.

Contribution

It introduces physically motivated soft constraint terms for neural networks estimating galaxy redshifts and compares their effects to unconstrained models.

Findings

No evidence that soft physical constraints outperform augmentation as regularizers.

Physical constraints did not improve the fidelity of the conditional density estimates.

The work is an ablation study on the effect of physical constraints in this context.

Abstract

Physical constraints have been suggested to make neural network models more generalizable, act scientifically plausible, and be more data-efficient over unconstrained baselines. In this report, we present preliminary work on evaluating the effects of adding soft physical constraints to computer vision neural networks trained to estimate the conditional density of redshift on input galaxy images for the Sloan Digital Sky Survey. We introduce physically motivated soft constraint terms that are not implemented with differential or integral operators. We frame this work as a simple ablation study where the effect of including soft physical constraints is compared to an unconstrained baseline. We compare networks using standard point estimate metrics for photometric redshift estimation, as well as metrics to evaluate how faithful our conditional density estimate represents the probability over the ensemble of our test dataset. We find no evidence that the implemented soft physical constraints are more effective regularizers than augmentation.