Physics-Informed Machine Learning Improves Weak Lensing Shear Estimation

The study introduces a novel approach to weak gravitational lensing shear estimation, combining a D4-equivariant deep neural network (D4CNN) with the Analytical Calibration framework (AnaCal). Traditional weak lensing shear estimators often struggle with realistic galaxy morphologies, point-spread-function (PSF) effects, blending, and noise in deep surveys. Blindly trained machine learning (ML) models can introduce calibration biases. The D4CNN architecture enforces symmetry under 90-degree rotations and mirror transformations, while AnaCal calibrates the model using its backpropagated gradients. Results from LSST-like single-band simulations demonstrate a ~10% reduction in shape noise compared to the moment-based Fourier Power Function Shapelets estimator in high-noise conditions, equivalent to a ~20% gain in effective galaxy number density. Multiplicative biases remain consistent with zero across various noise levels, PSF sizes and ellipticities, and magnitude selection cuts, satisfying the stringent requirements of the LSST survey. The framework establishes a physics-informed foundation for future extensions of ML-based shear estimation to blended sources and multi-band observations in Stage-IV surveys. The public availability of codes and data products will facilitate further research and development in this area.

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