MadEvolve: Evolutionary Optimization of Cosmological Algorithms with Large Language Models

Abstract: We develop a general framework to discover scientific algorithms and apply it to three problems in computational cosmology. Our code, MadEvolve, is similar to Google's AlphaEvolve, but places a stronger emphasis on free parameters and their optimization. Our code starts with a baseline human algorithm implementation, and then optimizes its performance metrics by making iterative changes to its code. As a further convenient feature, MadEvolve automatically generates a report that compares the input algorithm with the evolved algorithm, describes the algorithmic innovations and lists the free parameters and their function. Our code supports both auto-differentiable, gradient-based parameter optimization and gradient-free optimization methods. We apply MadEvolve to the reconstruction of cosmological initial conditions, 21cm foreground contamination reconstruction and effective baryonic physics in N-body simulations. In all cases, we find substantial improvements over the base algorithm. We make MadEvolve and our three tasks publicly available at madevolve.org.