Multi-Fidelity Emulation for the Matter Power Spectrum using Gaussian Processes

Ho, Ming-Feng; Bird, Simeon; Shelton, Christian R.

doi:10.48550/arxiv.2105.01081

Cited by 5 publications

(6 citation statements)

References 53 publications

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“…This means that not only data has an uncertainty but so does the theoretical model, which propagates and could affect cosmological constraints. Although the uncertainty can be decreased in certain parts of the parameter space by iteratively adding new simulations (Rogers et al 2019;Pellejero-Ibañez et al 2020) (or by combining simulations of different quality (Ho et al 2021)), so that e.g. a high-likelihood region is better sampled than regions ruled out by data, this process depends on the summary statistic and scale in question.…”

Section: Emulators and Interpolatorsmentioning

confidence: 99%

Large-scale dark matter simulations

Angulo,

Hahn

2021

Preprint

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We review the field of collisionless numerical simulations for the large-scale structure of the Universe. We start by providing the main set of equations solved by these simulations and their connection with General Relativity. We then recap the relevant numerical approaches: discretization of the phase-space distribution (focusing on N -body but including alternatives, e.g., Lagrangian submanifold and Schrödinger-Poisson) and the respective techniques for their time evolution and force calculation (Direct summation, mesh techniques, and hierarchical tree methods). We pay attention to the creation of initial conditions and the connection with Lagrangian Perturbation Theory. We then discuss the possible alternatives in terms of the micro-physical properties of dark matter (e.g., neutralinos, warm dark matter, QCD axions, Bose-Einstein condensates, and primordial black holes), and extensions to account for multiple fluids (baryons and neutrinos), primordial non-Gaussianity and modified gravity. We continue by discussing challenges involved in achieving highly accurate predictions. A key aspect of cosmological simulations is the connection to cosmological observables, we discuss various techniques in this regard: structure finding, galaxy formation and baryonic modelling, the creation of emulators and light-cones, and the role of machine learning. We finalise with a recount of state-of-the-art large-scale simulations and conclude with an outlook for the next decade.

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Section: Emulators and Interpolatorsmentioning

confidence: 99%

Large-scale dark matter simulations

Angulo,

Hahn

2021

Preprint

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“…The choice of 𝑘 max is largely problem-dependent. For example, for cosmological constraints 𝑘 max ∼ 1 ℎ Mpc −1 may suffice, as the matter power spectrum is currently calibrated to about 1% precision to that scale and to 3% precision to 𝑘 max ∼ 5 ℎ Mpc −1 (Ho et al 2021;Aricò et al 2021, at 𝑧 = 0, but the accuracy at higher redshifts is expected to be comparable or even better due to weaker clustering on a given spatial scale). For other applications, pushing deeper into the non-linear regime may be desirable.…”

Section: Present Modelmentioning

confidence: 99%

Reconstruction of the Density Power Spectrum from Quasar Spectra using Machine Learning

Veiga¹,

Meng²,

Gnedin³

et al. 2021

Preprint

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We describe a novel end-to-end approach using Machine Learning to reconstruct the power spectrum of cosmological density perturbations at high redshift from observed quasar spectra. State-of-the-art cosmological simulations of structure formation are used to generate a large synthetic dataset of line-of-sight absorption spectra paired with 1-dimensional fluid quantities along the same line-of-sight, such as the total density of matter and the density of neutral atomic hydrogen. With this dataset, we build a series of data-driven models to predict the power spectrum of total matter density. We are able to produce models which yield reconstruction to accuracy of about 1% for wavelengths 𝑘 ≤ 2 ℎ Mpc −1 , while the error increases at larger 𝑘. We show the size of data sample required to reach a particular error rate, giving a sense of how much data is necessary to reach a desired accuracy. This work provides a foundation for developing methods to analyse very large upcoming datasets with the next-generation observational facilities.

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“…Here, the PRIYA simulations are used to build multi-fidelity emulators [52][53][54] for the flux power spectrum and the IGM temperature at mean density. Each emulator is a surrogate model, able to reproduce the 1D flux power spectrum or mean IGM temperature for cosmological parameters (within the prior simulation volume) to ∼ 1% accuracy.…”

Section: Introductionmentioning

confidence: 99%

Cosmological constraints from the eBOSS Lyman-α forest using the PRIYA simulations

Fernandez,

Bird,

2024

J. Cosmol. Astropart. Phys.

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We present new cosmological parameter constraints from the eBOSS Lyman-α forest survey. We use a new theoretical model and likelihood based on the PRIYA simulation suite. PRIYA is the first suite to resolve the Lyman-α forest in a (120 Mpc/h)3 volume, using a multi-fidelity emulation technique. We use PRIYA to predict Lyman-α forest observables with ≲ 1% interpolation error over an 11 dimensional (9 simulated, 2 in post-processing) parameter space. We identify an internal tension within the flux power spectrum data. Once the discrepant data is removed, we find the primeval scalar spectral index measured at a pivot scale of k 0 = 0.78 Mpc-1 to be nP = 1.009+0.027 -0.018 at 68% confidence. This measurement from the Lyman-α forest flux power spectrum alone is in reasonable agreement with Planck, and in tension with earlier eBOSS analyses. The amplitude of matter fluctuations is σ 8 = 0.733+0.026 -0.029 at 68% confidence, in agreement with Dark Energy Survey weak lensing measurements and other small-scale structure probes and in tension with CMB measurements from Planck and ACT. The effective optical depth to Lyman-α photons from our pipeline is in good agreement with earlier high resolution measurements. We find a linear power at z = 3 and k = 0.009 s/km of Δ2 L = 0.302+0.024 -0.027 with a slope n eff = -2.264+0.026 -0.018. Our flux power spectrum only chains prefer a low level of heating during helium reionization. When we add IGM temperature data we find nP = 0.983 ± 0.020 and σ 8 = 0.703+0.023 -0.027. Our chains prefer an early and long helium reionization event, as suggested by measurements from the helium Lyman-α forest. In the near future we will use our pipeline to infer cosmological parameters from the DESI Lyman-α data.

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Multi-Fidelity Emulation for the Matter Power Spectrum using Gaussian Processes

Cited by 5 publications

References 53 publications

Large-scale dark matter simulations

Large-scale dark matter simulations

Reconstruction of the Density Power Spectrum from Quasar Spectra using Machine Learning

Cosmological constraints from the eBOSS Lyman-α forest using the PRIYA simulations

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