Learning an Effective Evolution Equation for Particle-Mesh Simulations Across Cosmologies

TL;DR

This paper introduces a data-driven approach to learn an effective evolution equation for particle-mesh simulations, improving accuracy and generalization across different cosmologies, and enabling unbiased cosmological parameter inference.

Contribution

It presents a novel neural network model trained in Fourier space to correct particle-mesh simulation errors, enhancing accuracy and applicability across unseen initial conditions.

Findings

The learned correction generalizes well to new initial conditions and cosmologies.

Corrected maps enable unbiased inference of cosmological parameters.

The Fourier space neural network effectively models small-scale corrections.

Abstract

Particle-mesh simulations trade small-scale accuracy for speed compared to traditional, computationally expensive N-body codes in cosmological simulations. In this work, we show how a data-driven model could be used to learn an effective evolution equation for the particles, by correcting the errors of the particle-mesh potential incurred on small scales during simulations. We find that our learnt correction yields evolution equations that generalize well to new, unseen initial conditions and cosmologies. We further demonstrate that the resulting corrected maps can be used in a simulation-based inference framework to yield an unbiased inference of cosmological parameters. The model, a network implemented in Fourier space, is exclusively trained on the particle positions and velocities.