W. L. Kimmy Wu

Bio: W. L. Kimmy Wu is an academic researcher. The author has contributed to research in topics: Cosmic microwave background & Estimation theory. The author has an hindex of 1, co-authored 2 publications receiving 51 citations.

DeepCMB: Lensing Reconstruction of the Cosmic Microwave Background with Deep Neural Networks

Abstract: Next-generation cosmic microwave background (CMB) experiments will have lower noise and therefore increased sensitivity, enabling improved constraints on fundamental physics parameters such as the sum of neutrino masses and the tensor-to-scalar ratio r. Achieving competitive constraints on these parameters requires high signal-to-noise extraction of the projected gravitational potential from the CMB maps. Standard methods for reconstructing the lensing potential employ the quadratic estimator (QE). However, the QE performs suboptimally at the low noise levels expected in upcoming experiments. Other methods, like maximum likelihood estimators (MLE), are under active development. In this work, we demonstrate reconstruction of the CMB lensing potential with deep convolutional neural networks (CNN) - ie, a ResUNet. The network is trained and tested on simulated data, and otherwise has no physical parametrization related to the physical processes of the CMB and gravitational lensing. We show that, over a wide range of angular scales, ResUNets recover the input gravitational potential with a higher signal-to-noise ratio than the QE method, reaching levels comparable to analytic approximations of MLE methods. We demonstrate that the network outputs quantifiably different lensing maps when given input CMB maps generated with different cosmologies. We also show we can use the reconstructed lensing map for cosmological parameter estimation. This application of CNN provides a few innovations at the intersection of cosmology and machine learning. First, while training and regressing on images, we predict a continuous-variable field rather than discrete classes. Second, we are able to establish uncertainty measures for the network output that are analogous to standard methods. We expect this approach to excel in capturing hard-to-model non-Gaussian astrophysical foreground and noise contributions.

CMB-S4 Science Case, Reference Design, and Project Plan

Abstract: We present the science case, reference design, and project plan for the Stage-4 ground-based cosmic microwave background experiment CMB-S4.

Learning to predict the cosmological structure formation.

Abstract: Matter evolved under the influence of gravity from minuscule density fluctuations. Nonperturbative structure formed hierarchically over all scales and developed non-Gaussian features in the Universe, known as the cosmic web. To fully understand the structure formation of the Universe is one of the holy grails of modern astrophysics. Astrophysicists survey large volumes of the Universe and use a large ensemble of computer simulations to compare with the observed data to extract the full information of our own Universe. However, to evolve billions of particles over billions of years, even with the simplest physics, is a daunting task. We build a deep neural network, the Deep Density Displacement Model ([Formula: see text]), which learns from a set of prerun numerical simulations, to predict the nonlinear large-scale structure of the Universe with the Zel'dovich Approximation (ZA), an analytical approximation based on perturbation theory, as the input. Our extensive analysis demonstrates that [Formula: see text] outperforms the second-order perturbation theory (2LPT), the commonly used fast-approximate simulation method, in predicting cosmic structure in the nonlinear regime. We also show that [Formula: see text] is able to accurately extrapolate far beyond its training data and predict structure formation for significantly different cosmological parameters. Our study proves that deep learning is a practical and accurate alternative to approximate 3D simulations of the gravitational structure formation of the Universe.

What can machine learning tell us about the background expansion of the Universe

Abstract: Machine learning (ML) algorithms have revolutionized the way we interpret data in astronomy, particle physics, biology, and even economics, since they can remove biases due to a priori chosen models. Here we apply a particular ML method, the genetic algorithms (GA), to cosmological data that describes the background expansion of the Universe, namely the pantheon Type Ia supernovae and the Hubble expansion history $H(z)$ datasets. We obtain model independent and nonparametric reconstructions of the luminosity distance ${d}_{L}(z)$ and Hubble parameter $H(z)$ without assuming any dark energy model or a flat Universe. We then estimate the deceleration parameter $q(z)$, a measure of the acceleration of the Universe, and we make a $\ensuremath{\sim}4.5\ensuremath{\sigma}$ model independent detection of the accelerated expansion, but we also place constraints on the transition redshift of the acceleration phase $({z}_{\mathrm{tr}}=0.662\ifmmode\pm\else\textpm\fi{}0.027)$. We also find a deviation from $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ at high redshifts, albeit within the errors, hinting toward the recently alleged tension between the SnIa/quasar data and the cosmological constant $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ model at high redshifts ($z\ensuremath{\gtrsim}1.5$). Finally, we show the GA can be used in complementary null tests of the $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ via reconstructions of the Hubble parameter and the luminosity distance.

Convolutional neural networks on the HEALPix sphere: a pixel-based algorithm and its application to CMB data analysis

Abstract: We describe a novel method for the application of convolutional neural networks (CNNs) to fields defined on the sphere, using the Hierarchical Equal Area Latitude Pixelization scheme (HEALPix). Specifically, we have developed a pixel-based approach to implement convolutional and pooling layers on the spherical surface, similarly to what is commonly done for CNNs applied to Euclidean space. The main advantage of our algorithm is to be fully integrable with existing, highly optimized libraries for NNs (e.g., PyTorch, TensorFlow, etc.). We present two applications of our method: (i) recognition of handwritten digits projected on the sphere; (ii) estimation of cosmological parameter from simulated maps of the cosmic microwave background (CMB). The latter represents the main target of this exploratory work, whose goal is to show the applicability of our CNN to CMB parameter estimation. We have built a simple NN architecture, consisting of four convolutional and pooling layers, and we have used it for all the applications explored herein. Concerning the recognition of handwritten digits, our CNN reaches an accuracy of ∼95%, comparable with other existing spherical CNNs, and this is true regardless of the position and orientation of the image on the sphere. For CMB-related applications, we tested the CNN on the estimation of a mock cosmological parameter, defining the angular scale at which the power spectrum of a Gaussian field projected on the sphere peaks. We estimated the value of this parameter directly from simulated maps, in several cases: temperature and polarization maps, presence of white noise, and partially covered maps. For temperature maps, the NN performances are comparable with those from standard spectrum-based Bayesian methods. For polarization, CNNs perform about a factor four worse than standard algorithms. Nonetheless, our results demonstrate, for the first time, that CNNs are able to extract information from polarization fields, both in full-sky and masked maps, and to distinguish between E and B -modes in pixel space. Lastly, we have applied our CNN to the estimation of the Thomson scattering optical depth at reionization (τ ) from simulated CMB maps. Even without any specific optimization of the NN architecture, we reach an accuracy comparable with standard Bayesian methods. This work represents a first step towards the exploitation of NNs in CMB parameter estimation and demonstrates the feasibility of our approach.