Tim W. Reid

Christian Prothmann, Vijay Gadepally, Jeremy Kepner et al.

The DAF-MIT AI Accelerator is a collaboration between the United States Department of the Air Force (DAF) and the Massachusetts Institute of Technology (MIT). This program pioneers fundamental advances in artificial intelligence (AI) to expand the competitive advantage of the United States in the defense and civilian sectors. In recent years, AI Accelerator projects have developed and launched public challenge problems aimed at advancing AI research in priority areas. Hallmarks of AI Accelerator challenges include large, publicly available, and AI-ready datasets to stimulate open-source solutions and engage the wider academic and private sector AI ecosystem. This article supplements our previous publication, which introduced AI Accelerator challenges. We provide an update on how ongoing and new challenges have successfully contributed to AI research and applications of AI technologies.

Jon Cockayne, Ilse C. F. Ipsen, Chris J. Oates et al.

This paper presents a probabilistic perspective on iterative methods for approximating the solution $\mathbf{x}_* \in \mathbb{R}^d$ of a nonsingular linear system $\mathbf{A} \mathbf{x}_* = \mathbf{b}$. In the approach a standard iterative method on $\mathbb{R}^d$ is lifted to act on the space of probability distributions $\mathcal{P}(\mathbb{R}^d)$. Classically, an iterative method produces a sequence $\mathbf{x}_m$ of approximations that converge to $\mathbf{x}_*$. The output of the iterative methods proposed in this paper is, instead, a sequence of probability distributions $μ_m \in \mathcal{P}(\mathbb{R}^d)$. The distributional output both provides a "best guess" for $\mathbf{x}_*$, for example as the mean of $μ_m$, and also probabilistic uncertainty quantification for the value of $\mathbf{x}_*$ when it has not been exactly determined. Theoretical analysis is provided in the prototypical case of a stationary linear iterative method. In this setting we characterise both the rate of contraction of $μ_m$ to an atomic measure on $\mathbf{x}_*$ and the nature of the uncertainty quantification being provided. We conclude with an empirical illustration that highlights the insight into solution uncertainty that can be provided by probabilistic iterative methods.