DerivKit is a Python package for derivative-based statistical inference. It implements stable numerical differentiation and derivative assembly utilities for Fisher-matrix forecasting and higher-order likelihood approximations in scientific applications, supporting scalar- and vector-valued models including black-box or tabulated functions where automatic differentiation is impractical or unavailable. These derivatives are used to construct Fisher forecasts, Fisher bias estimates, and non-Gaussian likelihood expansions based on the Derivative Approximation for Likelihoods (DALI). By extending derivative-based inference beyond the Gaussian approximation, DerivKit forms a practical bridge between fast Fisher forecasts and more computationally intensive sampling-based methods such as Markov chain Monte Carlo (MCMC).
Estimating redshift is a central task in astrophysics, but its measurement is costly and time-consuming. In addition, current image-based methods are often validated on homogeneous datasets. The development and comparison of networks able generalize across different morphologies, ranging from galaxies to gravitationally-lensed transients, and observational conditions, remain an open challenge. This work proposes DeepRed, a deep learning pipeline that demonstrates how modern computer vision architectures, including ResNet, EfficientNet, Swin Transformer, and MLP-Mixer, can estimate redshifts from images of galaxies, gravitational lenses, and gravitationally-lensed supernovae. We compare these architectures and their ensemble to both neural networks (A1, A3, NetZ, and PhotoZ) and a feature-based method (HOG+SVR) on simulated (DeepGraviLens) and real (KiDS, SDSS) datasets. Our approach achieves state-of-the-art results on all datasets. On DeepGraviLens, DeepRed achieves a significant improvement in the Normalized Mean Absolute Deviation compared to the best baseline (PhotoZ): 55% on DES-deep (using EfficientNet), 51% on DES-wide (Ensemble), 52% on DESI-DOT (Ensemble), and 46% on LSST-wide (Ensemble). On real observations from the KiDS survey, the pipeline outperforms the best baseline (NetZ), improving NMAD by 16% on a general test set without high-probability lenses (Ensemble) and 27% on high-probability lenses (Ensemble). For non-lensed galaxies in the SDSS dataset, the MLP-Mixer architecture achieves a 5% improvement over the best baselines (A3 and NetZ). SHAP shows that the models correctly focus on the objects of interest with over 95% localization accuracy on high-quality images, validating the reliability of the predictions. These findings suggest that deep learning is a scalable, robust, and interpretable solution for redshift estimation in large-scale surveys.
Reconstructing the early Universe from the evolved present-day Universe is a challenging and computationally demanding problem in modern astrophysics. We devise a novel generative framework, Cosmo3DFlow, designed to address dimensionality and sparsity, the critical bottlenecks inherent in current state-of-the-art methods for cosmological inference. By integrating 3D Discrete Wavelet Transform (DWT) with flow matching, we effectively represent high-dimensional cosmological structures. The Wavelet Transform addresses the ``void problem'' by translating spatial emptiness into spectral sparsity. It decouples high-frequency details from low-frequency structures through spatial compression, and wavelet-space velocity fields facilitate stable ordinary differential equation (ODE) solvers with large step sizes. Using large-scale cosmological $N$-body simulations, at $128^3$ resolution, we achieve up to $50\times$ faster sampling than diffusion models, combining a $10\times$ reduction in integration steps with lower per-step computational cost from wavelet compression. Our results enable initial conditions to be sampled in seconds, compared to minutes for previous methods.