ACED: Multi-Fidelity Markov Chain Monte Carlo for Cosmology

Scientists and engineers build quantitative models of our natural and constructed world. Using the process of statistical inference, the models are tested against experimental data in order to constrain their underlying parameters, which leads to an improved understanding of the models and more accurate predictions for future data. Markov Chain Monte Carlo (MCMC) is the most popular algorithm for statistical inference because of its power and simplicity. The goal of this project is to develop a new MCMC inference method, Shrek, which exploits the fact that many models in science and engineering can be calculated using different time-accuracy trade-offs. By performing inference with a combination of low accuracy but computationally cheap models, with high accuracy but computationally expensive models, Shrek can achieve better performance than traditional MCMC algorithms. The project team aims to apply Shrek to the field of cosmology to answer questions about dark matter, galaxy formation, and the expansion rate of the Universe. Furthermore, the team is developing an open-source software package so that scientists across many fields may use the Shrek algorithm. This project exploits the multi-fidelity nature of many scientific and engineering models to help guide MCMC. Many simulations, including the Boltzmann codes ubiquitously used to model the cosmic microwave background, have tunable fidelities. This can be, for instance, a spatial or temporal resolution of the model, or an accuracy parameter for a differential equation solver. Using lower-fidelity models to guide the MCMC algorithm at the desired highest-fidelity model results in an MCMC method that converges to the true highest-fidelity posterior in fewer samples and less total computation time. The project team is developing a new recursive MCMC sampler (Shrek MCMC) that can exploit multiple fidelities for computational acceleration. Specifically, the plan is to (1) couple Shrek MCMC with neural network emulators, (2) prove convergence bounds and use these to guide automatic tuning of Shrek MCMC, and (3) develop a layered Multi-fidelity Hamiltonian Monte Carlo (Shrek HMC) sampler. The resulting algorithms will be made publicly available through open-source licenses and will be incorporated into popular existing sampling packages. In cosmology, this research allows for larger, more flexible, inference pipelines. The team will use the new Shrek algorithms to test proposed solutions to the cosmological H0 and S8 tensions simultaneously and to model the local dark matter density in order to answer questions about the formation and content of the Local Group of galaxies. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.