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ABSTRACT We present a coherent, re-usable python framework building on the CosmoPower emulator code for high-accuracy calculations of cosmological observables with Einstein–Boltzmann codes. For detailed statistical analyses, such codes require high computing power, making parameter space exploration costly, especially for beyond-$$\Lambda$$CDM analyses. Machine learning-enabled emulators of Einstein–Boltzmann codes are becoming an increasingly popular solution to this problem. To enable generation, sharing, and use of emulators for inference, we define standards for robustly describing, packaging, and distributing them. We present software for easily performing these tasks in an automated and replicable manner and provide examples and guidelines for generating emulators and wrappers for using them in popular cosmological inference codes. We demonstrate our framework with a suite of high-accuracy emulators for the CAMB code’s calculations of CMB $$C_\ell$$, $P(k)$, background evolution, and derived parameter quantities. We show these emulators are accurate enough for analysing both $$\Lambda$$CDM and a set of extension models ($$N_{\rm eff}$$, $$\sum m_\nu$$, $$w_0 w_a$$) with stage-IV observatories, recovering the original high-accuracy spectra to tolerances well within the cosmic variance uncertainties. We show our emulators also recover cosmological parameters in a simulated cosmic-variance limited experiment, finding results well within $$0.1 \sigma$$ of the input cosmology, while requiring $$\lesssim 1/50$$ of the evaluation time.
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A surrogate-based approach to nonlinear, non-Gaussian joint state-parameter data assimilation
Many recent advances in sequential assimilation of data into nonlinear high-dimensional models are modifications to particle filters which employ efficient searches of a high-dimensional state space. In this work, we present a complementary strategy that combines statistical emulators and particle filters. The emulators are used to learn and offer a computationally cheap approximation to the forward dynamic mapping. This emulator-particle filter (Emu-PF) approach requires a modest number of forward-model runs, but yields well-resolved posterior distributions even in non-Gaussian cases. We explore several modifications to the Emu-PF that utilize mechanisms for dimension reduction to efficiently fit the statistical emulator, and present a series of simulation experiments on an atypical Lorenz-96 system to demonstrate their performance. We conclude with a discussion on how the Emu-PF can be paired with modern particle filtering algorithms.
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- Award ID(s):
- 1821338
- PAR ID:
- 10289563
- Date Published:
- Journal Name:
- Foundations of Data Science
- Volume:
- 0
- Issue:
- 0
- ISSN:
- 2639-8001
- Page Range / eLocation ID:
- 0
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.3934/fods.2021019
