Beecroft Institute for Particle Astrophysics and Cosmology

Abstract:

<jats:p><jats:italic>Context.N</jats:italic>-body simulations are computationally expensive and machine learning (ML) based emulation techniques have thus emerged as a way to increase their speed. Surrogate models are indeed fast, however, they are limited in terms of their trustworthiness due to potentially substantial emulation errors that current approaches are not equipped to correct.</jats:p> <jats:p><jats:italic>Aims.</jats:italic> To alleviate this problem, we have introduced COmoving Computer Acceleration (COCA), a hybrid framework interfacing ML algorithm with an <jats:italic>N</jats:italic>-body simulator. The correct physical equations of motion are solved in an emulated frame of reference, so that any emulation error is corrected by design. Thus, we are able to find a solution for the perturbation of particle trajectories around the ML solution. This approach is computationally cheaper than obtaining the full solution and it is guaranteed to converge to the truth as the number of force evaluations is increased.</jats:p> <jats:p><jats:italic>Methods.</jats:italic> Even though it is applicable to any ML algorithm and <jats:italic>N</jats:italic>-body simulator, we assessed this approach in the particular case of particle-mesh (PM) cosmological simulations in a frame of reference predicted by a convolutional neural network. In such cases, the time dependence is encoded as an additional input parameter to the network.</jats:p> <jats:p><jats:italic>Results.</jats:italic> We find that COCA efficiently reduces emulation errors in particle trajectories, requiring far fewer force evaluations than running the corresponding simulation without ML. As a consequence, we were able to obtain accurate final density and velocity fields for a reduced computational budget. We demonstrate that this method exhibits robustness when applied to examples outside the range of the training data. When compared to the direct emulation of the Lagrangian displacement field using the same training resources, COCA’s ability to correct emulation errors results in more accurate predictions.</jats:p> <jats:p><jats:italic>Conclusions.</jats:italic> Therefore, COCA makes <jats:italic>N</jats:italic>-body simulations cheaper by skipping unnecessary force evaluations, while still solving the correct equations of motion and correcting for emulation errors made by ML.</jats:p>

Abstract:

We implement a simple, main beam correction in the maximum-likelihood, parametric component separation approach, which allows on accounting for different beam widths of input maps at different frequencies without any preprocessing. We validate the approach on full-sky and cut-sky simulations and discuss the importance and impact of the assumptions and simplifications. We find that, in the cases when the underlying sky model is indeed parametric, the method successfully recovers component spectral parameters and component maps at the predefined resolution. The improvement on the precision of the estimated spectral parameters is found to be minor due to the redness of the foreground angular spectra, however the method is potentially more accurate, in particular if the foreground properties display strong, spatial variability, as it does not assume commutation of the beam smoothing and mixing matrix operators. The method permits a reconstruction of the cosmic microwave background map with a resolution significantly superior to that of the lowest resolution map used in the analysis and with the nearly optimal noise level, facilitating exploitation of the cosmological information contained on angular scales, which would be otherwise inaccessible. The method preserves all the advantages of a pixel-domain implementation of the parametric approach, and, as it deals with the beams in the harmonic domain, it can also straightforwardly account for spatially stationary map-domain noise correlations.