Collaborative Research: Particles and Proxies for Sampling

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This project addresses sampling in high dimensions which is important for a variety of disciplines, including computational chemistry, materials science, and molecular dynamics simulations for climate models, power network, traffic models, or the study of viruses and pandemics. The project will develop new simulation algorithms as well as improvements of existing algorithms. The outcomes will benefit these disciplines in several ways. First, the algorithmic optimizations will provide new tools that practitioners could use to accelerate their computations. Second, rigorous results on these methods will provide practitioners with confidence in their predictions. Finally, open source software will be developed. Students will be involved and receive interdisciplinary training. The project addresses challenges in sampling and related problems arising from complex energy landscapes such as in potential energy in an atomistic system; the negative log-likelihood in a Bayesian inference problem; or the loss function in a machine learning problem. In Markov Chain Monte Carlo methods, these landscapes often define the evolution of a Markov chain that samples some target distribution. This project will develop efficient computations of ergodic averages over Markov chains and methods that reduce the computational cost of ergodic averages, by either reducing the number of required iterations or reducing the per-iterate cost. The new techniques and analyses will be based on proxy landscapes and interacting particle systems. Proxies can reduce per-iterate cost or lead to faster convergence, while interacting particle systems can reduce the bias from proxies or cut down on variance. The project includes a study of how parameter choices affect the variance of the weighted ensemble particle method at finite particle number; the development of a weight-corrected particle system to account for bias from proxies; and an analysis of methods for overcoming sampling difficulties associated with rough landscapes.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.