COSMONET: fast cosmological parameter estimation in non-flat models using neural networks

We present a further development of a method for accelerating the calculation of cosmic microwave background (CMB) power spectra, matter power spectra and likelihood functions for use in cosmological Bayesian inference. The algorithm, called COSMONET, is based on training a multilayer perceptron neural network. We demonstrate the capabilities of COSMONET by computing CMB power spectra (up to l = 2000) and matter transfer functions over a hypercube in parameter space encompassing the 4 sigma confidence region of a selection of CMB [Wilkinson Microwave Anisotropy Probe (WMAP) + high-resolution experiments] and large-scale structure surveys [2dF and Sloan Digital Sky Survey (SDSS)]. We work in the framework of a generic seven parameter non-flat cosmology. Additionally, we use COSMONET to compute the WMAP 3 yr, 2dF and SDSS likelihoods over the same region. We find that the average error in the power spectra is typically well below cosmic variance for spectra, and experimental likelihoods calculated to within a fraction of a log unit. We demonstrate that marginalized posteriors generated with COSMONET spectra agree to within a few per cent of those generated by CAMB parallelized over four CPUs, but are obtained two to three times faster on just a single processor. Furthermore, posteriors generated directly via COSMONET likelihoods can be obtained in less than 30 min on a single processor, corresponding to a speed up of a factor of similar to 32. We also demonstrate the capabilities of COSMONET by extending the CMB power spectra and matter transfer function training to a more generic 10 parameter cosmological model, including tensor modes, a varying equation of state of dark energy and massive neutrinos. Finally, we demonstrate that using COSMONET likelihoods directly, the sampling strategy adopted by COSMOMC is highly suboptimal. We find the generic BAYESYS sampler to be a further similar to 10 times faster, yielding 20 000 post burn-in samples in our seven parameter model in just 3 min on a single CPU. COSMONET and interfaces to both COSMOMC and BAYESYS are publically available at http://www.mrao.cam.ac.uk/software/cosmonet.