D4CNN×AnaCal: Physics-informed Machine Learning for Accurate and Precise Weak-lensing Shear Estimation
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 D4-equivariant deep neural network for galaxy shape measurement whose architecture enforces symmetry under 90° rotations and mirror transformations, and adopt the Analytical Calibration framework to calibrate the model using its backpropagated gradients. For isolated galaxies in LSST-like single-band simulations, we demonstrate that our approach achieves ∼10% lower shape noise than the traditional moment-based Fourier Power Function Shapelets estimator in the high-noise regime, equivalent to a 23% 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 ∼10−4 level. We demonstrate this framework on isolated single-band galaxy images with Gaussian noise and known PSFs, establishing a rigorous, physics-informed foundation for future extensions of ML-based shear estimation to blended sources and multiband observations in Stage-IV surveys. All codes and data products will be made publicly available upon acceptance.