Computing Nonlinear Power Spectra Across Dynamical Dark Energy Model Space with Neural ODEs

I show how to compute the nonlinear power spectrum across the entire \(w(z)\) dynamical dark energy model space. Using synthetic ΛCDM data, I train a neural ordinary differential equation (ODE) to infer the evolution of the nonlinear matter power spectrum as a function of the background expansion and mean matter density across ∼9 Gyr of cosmic evolution. After training, the model generalises to any dynamical dark energy model parameterised by \(w(z)\). With little optimisation, the neural ODE is accurate to within 4% up to \(k = 5\, h\, {\mathrm Mpc}^{−1}\). Unlike simulation rescaling methods, neural ODEs naturally extend to summary statistics beyond the power spectrum that are sensitive to the growth history.