Uncertainty quantification is a rapidly growing field in computer simulation-based scientific applications. The UQLab project aims at the development of a Matlab-based software framework for uncertainty quantification. It is designed to encourage both academic researchers and field engineers to use and develop advanced and innovative algorithms for uncertainty quantification, possibly exploiting modern distributed computing facilities. Ease of use, extendibility and handling of non-intrusive stochastic methods are core elements of its development philosophy. The modular platform comprises a highly optimized core probabilistic modelling engine and a simple programming interface that provides unified access to heterogeneous high performance computing resources. Finally, it provides a content-management system that allows users to easily develop additional custom modules within the framework. In this contribution, we intend to demonstrate the features of the platform at its current development stage.

Sparse polynomial chaos expansions (PCE) are a popular surrogate modelling method that takes advantage of the properties of PCE, the sparsity-of-effects principle, and powerful sparse regression so...

We present a new power spectrum emulator named EuclidEmulator that estimates the nonlinear correction to the linear dark matter power spectrum depending on the six cosmological parameters ω_b, ω_m, n_s, h, w₀ and σ₈. It is constructed using the uncertainty quantification software UQLab using a spectral decomposition method called polynomial chaos expansion. All steps in its construction have been tested and optimized: the large high-resolution N-body simulations carried out with PKDGRAV3 were validated using a simulation from the Euclid Flagship campaign and demonstrated to have converged up to wavenumbers k ≈ 5 h Mpc⁻¹ for redshifts z ≤ 5. The emulator is based on 100 input cosmologies simulated in boxes of (1250Mpc/h)³ using 2048³ particles. We show that by creating mock emulators it is possible to successfully predict and optimize the performance of the final emulator prior to performing any N-body simulations. The absolute accuracy of the final nonlinear power spectrum is as good as one obtained with N-body simulations, conservatively, ∼1% for k ≲ 1 h Mpc⁻¹ and z ≲ 1. This enables efficient forward modeling in the nonlinear regime allowing for estimation of cosmological parameters using Markov Chain Monte Carlo (MCMC) methods. EuclidEmulator has been compared to HALOFIT, CosmicEmu and NGenHalofit, and shown to be more accurate than these other approaches. This work paves a new way for optimal construction of future emulators that also consider other cosmological observables, use higher resolution input simulations and investigate higher dimensional cosmological parameter spaces.

We present a new, updated version of the EuclidEmulator (called EuclidEmulator2), a fast and accurate predictor for the nonlinear correction of the matter power spectrum. 2 per cent level accurate emulation is now supported in the eight-dimensional parameter space of w₀w_aCDM+∑m_ν models between redshift z = 0 and z = 3 for spatial scales within the range |$0.01 \, h\, {\rm Mpc}^{-1}\le k \le 10\, h\, {\rm Mpc}^{-1}$|⁠. In order to achieve this level of accuracy, we have had to improve the quality of the underlying N-body simulations used as training data: (i) we use self-consistent linear evolution of non-dark matter species such as massive neutrinos, photons, dark energy, and the metric field, (ii) we perform the simulations in the so-called N-body gauge, which allows one to interpret the results in the framework of general relativity, (iii) we run over 250 high-resolution simulations with 3000³ particles in boxes of 1(h⁻¹ Gpc)³ volumes based on paired-and-fixed initial conditions, and (iv) we provide a resolution correction that can be applied to emulated results as a post-processing step in order to drastically reduce systematic biases on small scales due to residual resolution effects in the simulations. We find that the inclusion of the dynamical dark energy parameter w_a significantly increases the complexity and expense of creating the emulator. The high fidelity of EuclidEmulator2 is tested in various comparisons against N-body simulations as well as alternative fast predictors such as HALOFIT, HMCode, and CosmicEmu. A blind test is successfully performed against the Euclid Flagship v2.0 simulation. Nonlinear correction factors emulated with EuclidEmulator2 are accurate at the level of |$1{{\ \rm per\ cent}}$| or better for |$0.01 \, h\, {\rm Mpc}^{-1}\le k \le 10\, h\, {\rm Mpc}^{-1}$| and z ≤ 3 compared to high-resolution dark-matter-only simulations. EuclidEmulator2 is publicly available at https://github.com/miknab/EuclidEmulator2.