Predictive uncertainty on astrophysics recovery from multifield cosmology

Abstract

We investigate how the constraints on the density parameter (Ωm), the power spectrum amplitude (σ 8) and the supernova feedback parameters (A SN1 and A SN2) vary when exploiting information from multiple fields in cosmology. We make use of a convolutional neural network to retrieve the salient features from different combinations of field maps from IllustrisTNG in the CAMELS project. The fields considered are neutral hydrogen (HI), gas density (Mgas), magnetic fields (B) and gas metallicity (Z). We estimate the predictive uncertainty — sum of the squares of aleatoric and epistemic uncertainties — of the parameters inferred by our model by using Monte Carlo dropout, a Bayesian approximation. Results show that in general, the performance of the model improves as the number of channels of its input is increased. In the best setup which includes all fields (four channel input, Mgas-HI-B-Z) the model achieves R 2 > 0.96 on all parameters. Similarly, we find that the predictive uncertainty, which is dominated by the aleatoric uncertainty, decreases as more fields are used to train the model in general. The uncertainties obtained by dropout variational inference are overestimated on all parameters in our case, in that the predictive uncertainty is much larger than the actual squared error, which is the square of the difference between the ground truth and prediction. After calibration, which consists of a simple σ scaling method, the average deviation of the predictive uncertainty from the actual error goes down to 25% at most (on A SN1).