D$_4$CNN$\times$AnaCal: Physics-Informed Machine Learning for Accurate and Precise Weak Lensing Shear Estimation

TL;DR

This paper introduces a physics-informed, D4-equivariant neural network for weak lensing shear estimation that outperforms traditional methods in accuracy and noise reduction, with zero bias across various conditions.

Contribution

The paper develops a novel D4-equivariant neural network combined with Analytical Calibration for improved shear measurement accuracy in weak lensing surveys.

Findings

Achieves ~10% lower shape noise than traditional estimators.

Maintains multiplicative biases within LSST requirements.

Demonstrates robustness across noise levels, PSF sizes, and galaxy properties.

Abstract

Traditional weak gravitational lensing shear estimators are carefully calibrated but struggle to fully capture realistic galaxy morphologies, point-spread-function (PSF) effects, blending, and noise in deep surveys, while blindly trained machine learning (ML) models can introduce significant calibration biases. Here we construct a fully D$_4$-equivariant deep neural network for galaxy shape measurement whose architecture enforces symmetry under 90$^{\circ}$ rotations and mirror transformations, and adopt the Analytical Calibration framework (AnaCal) to calibrate the model using its backpropagated gradients. For isolated galaxies in LSST-like single-band simulations, we demonstrate that our approach achieves $\sim$10% lower shape noise than the traditional moment-based Fourier Power Function Shapelets estimator in the high-noise regime, equivalent to a $\sim$20% gain in effective galaxy number density, while simultaneously achieving multiplicative biases consistent with zero across a wide range of noise levels, PSF sizes and ellipticities, and magnitude selection cuts, with all measurements satisfying $|m| {<} 10^{-3}$ (i.e., within the 0.2% LSST requirement) and most at the ${\sim}10^{-4}$ level. We demonstrate this framework on isolated single-band galaxy images with Gaussian noise and known PSF, establishing a rigorous, physics-informed foundation for future extensions of ML-based shear estimation to blended sources and multi-band observations in Stage-IV surveys. All codes and data products will be made publicly available upon acceptance.