A representation learning approach to probe for dynamical dark energy in matter power spectra

• URL: http://arxiv.org/abs/2310.10717v2
• Date: Tue, 9 Jul 2024 16:30:26 GMT
• Title: A representation learning approach to probe for dynamical dark energy in matter power spectra
• Authors: Davide Piras, Lucas Lombriser,
• Abstract summary: We present DE-VAE, a variational autoencoder architecture to search for a compressed representation of dynamical dark energy (DE) models. We find that a single latent parameter is sufficient to predict 95% (99%) of DE power spectra generated over a broad range of cosmological parameters.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We present DE-VAE, a variational autoencoder (VAE) architecture to search for a compressed representation of dynamical dark energy (DE) models in observational studies of the cosmic large-scale structure. DE-VAE is trained on matter power spectra boosts generated at wavenumbers $k\in(0.01-2.5) \ h/\rm{Mpc}$ and at four redshift values $z\in(0.1,0.48,0.78,1.5)$ for the most typical dynamical DE parametrization with two extra parameters describing an evolving DE equation of state. The boosts are compressed to a lower-dimensional representation, which is concatenated with standard cold dark matter (CDM) parameters and then mapped back to reconstructed boosts; both the compression and the reconstruction components are parametrized as neural networks. Remarkably, we find that a single latent parameter is sufficient to predict 95% (99%) of DE power spectra generated over a broad range of cosmological parameters within $1\sigma$ ($2\sigma$) of a Gaussian error which includes cosmic variance, shot noise and systematic effects for a Stage IV-like survey. This single parameter shows a high mutual information with the two DE parameters, and these three variables can be linked together with an explicit equation through symbolic regression. Considering a model with two latent variables only marginally improves the accuracy of the predictions, and adding a third latent variable has no significant impact on the model's performance. We discuss how the DE-VAE architecture can be extended from a proof of concept to a general framework to be employed in the search for a common lower-dimensional parametrization of a wide range of beyond-$\Lambda$CDM models and for different cosmological datasets. Such a framework could then both inform the development of cosmological surveys by targeting optimal probes, and provide theoretical insight into the common phenomenological aspects of beyond-$\Lambda$CDM models.

Related papers

• Scaling Exponents Across Parameterizations and Optimizers [94.54718325264218]
  We propose a new perspective on parameterization by investigating a key assumption in prior work. Our empirical investigation includes tens of thousands of models trained with all combinations of threes. We find that the best learning rate scaling prescription would often have been excluded by the assumptions in prior work.
  arXiv  Detail & Related papers  (2024-07-08T12:32:51Z)
• Cosmological Field Emulation and Parameter Inference with Diffusion Models [2.3020018305241337]
  We leverage diffusion generative models to address two tasks of importance to cosmology. We show that the model is able to generate fields with power spectra consistent with those of the simulated target distribution. We additionally explore their utility as parameter inference models and find that we can obtain tight constraints on cosmological parameters.
  arXiv  Detail & Related papers  (2023-12-12T18:58:42Z)
• Towards Convergence Rates for Parameter Estimation in Gaussian-gated Mixture of Experts [40.24720443257405]
  We provide a convergence analysis for maximum likelihood estimation (MLE) in the Gaussian-gated MoE model. Our findings reveal that the MLE has distinct behaviors under two complement settings of location parameters of the Gaussian gating functions. Notably, these behaviors can be characterized by the solvability of two different systems of equations.
  arXiv  Detail & Related papers  (2023-05-12T16:02:19Z)
• Modeling the space-time correlation of pulsed twin beams [68.8204255655161]
  Entangled twin-beams generated by parametric down-conversion are among the favorite sources for imaging-oriented applications. We propose a semi-analytic model which aims to bridge the gap between time-consuming numerical simulations and the unrealistic plane-wave pump theory.
  arXiv  Detail & Related papers  (2023-01-18T11:29:49Z)
• On the influence of over-parameterization in manifold based surrogates and deep neural operators [0.0]
  We show two approaches for constructing accurate and generalizable approximators for complex physico-chemical processes. We first propose an extension of the m-PCE, constructing a mapping between latent spaces formed by two separate embeddings of input functions and output QoIs. We demonstrate that performance m-PCE and DeepONet is comparable for cases of relatively output mappings. When highly non-smooth dynamics is considered, DeepONet shows higher accuracy.
  arXiv  Detail & Related papers  (2022-03-09T22:27:46Z)
• Post-mortem on a deep learning contest: a Simpson's paradox and the complementary roles of scale metrics versus shape metrics [61.49826776409194]
  We analyze a corpus of models made publicly-available for a contest to predict the generalization accuracy of neural network (NN) models. We identify what amounts to a Simpson's paradox: where "scale" metrics perform well overall but perform poorly on sub partitions of the data. We present two novel shape metrics, one data-independent, and the other data-dependent, which can predict trends in the test accuracy of a series of NNs.
  arXiv  Detail & Related papers  (2021-06-01T19:19:49Z)
• Understanding Overparameterization in Generative Adversarial Networks [56.57403335510056]
  Generative Adversarial Networks (GANs) are used to train non- concave mini-max optimization problems. A theory has shown the importance of the gradient descent (GD) to globally optimal solutions. We show that in an overized GAN with a $1$-layer neural network generator and a linear discriminator, the GDA converges to a global saddle point of the underlying non- concave min-max problem.
  arXiv  Detail & Related papers  (2021-04-12T16:23:37Z)
• Quaternion Factorization Machines: A Lightweight Solution to Intricate Feature Interaction Modelling [76.89779231460193]
  factorization machine (FM) is capable of automatically learning high-order interactions among features to make predictions without the need for manual feature engineering. We propose the quaternion factorization machine (QFM) and quaternion neural factorization machine (QNFM) for sparse predictive analytics.
  arXiv  Detail & Related papers  (2021-04-05T00:02:36Z)
• Bayesian multiscale deep generative model for the solution of high-dimensional inverse problems [0.0]
  A novel multiscale Bayesian inference approach is introduced based on deep probabilistic generative models. The method allows high-dimensional parameter estimation while exhibiting stability, efficiency and accuracy.
  arXiv  Detail & Related papers  (2021-02-04T11:47:21Z)
• On the Sparsity of Neural Machine Translation Models [65.49762428553345]
  We investigate whether redundant parameters can be reused to achieve better performance. Experiments and analyses are systematically conducted on different datasets and NMT architectures.
  arXiv  Detail & Related papers  (2020-10-06T11:47:20Z)
• Gravitational-wave parameter estimation with autoregressive neural network flows [0.0]
  We introduce the use of autoregressive normalizing flows for rapid likelihood-free inference of binary black hole system parameters from gravitational-wave data with deep neural networks. A normalizing flow is an invertible mapping on a sample space that can be used to induce a transformation from a simple probability distribution to a more complex one. We build a more powerful latent variable model by incorporating autoregressive flows within the variational autoencoder framework.
  arXiv  Detail & Related papers  (2020-02-18T15:44:04Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.