Computer simulation often is used to study complex physical and engineering processes. Although a computer simulator often can be viewed as an inexpensive way to gain insight into a system, it still can be computationally costly. Much of the recent work on the design and analysis of computer experiments has focused on scenarios where the goal is to fit a response surface or process optimization. In this article we develop a sequential methodology for estimating a contour from a complex computer code. The approach uses a stochastic process model as a surrogate for the computer simulator. The surrogate model and associated uncertainty are key components in a new criterion used to identify the computer trials aimed specifically at improving the contour estimate. The proposed approach is applied to exploration of a contour for a network queuing system. Issues related to practical implementation of the proposed approach also are addressed.

We introduce a new cosmic emulator for the matter power spectrum covering eight cosmological parameters. Targeted at optical surveys, the emulator provides accurate predictions out to a wavenumber k ∼ 5Mpc −1 and redshift z ≤ 2. Besides covering the standard set of ΛCDM parameters, massive neutrinos and a dynamical dark energy of state are included. The emulator is built on a sample set of 36 cosmological models, carefully chosen to provide accurate predictions over the wide and large parameter space. For each model, we have performed a high-resolution simulation, augmented with sixteen medium-resolution simulations and TimeRG perturbation theory results to provide accurate coverage of a wide k-range; the dataset generated as part of this project is more than 1.2Pbyte. With the current set of simulated models, we achieve an accuracy of approximately 4%. Because the sampling approach used here has established convergence and error-control properties, follow-on results with more than a hundred cosmological models will soon achieve ∼ 1% accuracy. We compare our approach with other prediction schemes that are based on halo model ideas and remapping approaches. The new emulator code is publicly available. Subject headings: methods: statistical -cosmology: large-scale structure of the universe

Ground and space-based sky surveys enable powerful cosmological probes based on measurements of galaxy properties and the distribution of galaxies in the Universe. These probes include weak lensing, baryon acoustic oscillations, abundance of galaxy clusters, and redshift space distortions; they are essential to improving our knowledge of the nature of dark energy. On the theory and modeling front, large-scale simulations of cosmic structure formation play an important role in interpreting the observations and in the challenging task of extracting cosmological physics at the needed precision. These simulations must cover a parameter range beyond the standard six cosmological parameters and need to be run at high mass and force resolution. One key simulationbased task is the generation of accurate theoretical predictions for observables, via the method of emulation. Using a new sampling technique, we explore an 8-dimensional parameter space including massive neutrinos and a variable dark energy equation of state. We construct trial emulators using two surrogate models (the linear power spectrum and an approximate halo mass function). The new sampling method allows us to build precision emulators from just 26 cosmological models and to increase the emulator accuracy by adding new sets of simulations in a prescribed way. This allows emulator fidelity to be systematically improved as new observational data becomes available and higher accuracy is required. Finally, using one ΛCDM cosmology as an example, we study the demands imposed on a simulation campaign to achieve the required statistics and accuracy when building emulators for dark energy investigations. Subject headings: methods: statistical -cosmology: large-scale structure of the universe

No abstract

Statistical emulators of computer simulators have proven to be useful in a variety of applications. The widely adopted model for emulator building, using a Gaussian process model with strictly positive correlation function, is computationally intractable when the number of simulator evaluations is large. We propose a new model that uses a combination of low-order regression terms and compactly supported correlation functions to recreate the desired predictive behavior of the emulator at a fraction of the computational cost. Following the usual approach of taking the correlation to be a product of correlations in each input dimension, we show how to impose restrictions on the ranges of the correlations, giving sparsity, while also allowing the ranges to trade off against one another, thereby giving good predictive performance. We illustrate the method using data from a computer simulator of photometric redshift with 20,000 simulator evaluations and 80,000 predictions.Simulation of complex systems has become commonplace in scientific studies. Frequently, simulators (or computer models) are computationally demanding, and relatively few evaluations can be performed. In other cases, the computer models are fast to evaluate but are not readily available to all