16 research outputs found
Multifidelity Information Fusion Algorithms for High-Dimensional Systems and Massive Data sets
We develop a framework for multifidelity information fusion and predictive inference in high-dimensional input spaces and in the presence of massive data sets. Hence, we tackle simultaneously the “big N" problem for big data and the curse of dimensionality in multivariate parametric problems. The proposed methodology establishes a new paradigm for constructing response surfaces of high-dimensional stochastic dynamical systems, simultaneously accounting for multifidelity in physical models as well as multifidelity in probability space. Scaling to high dimensions is achieved by data-driven dimensionality reduction techniques based on hierarchical functional decompositions and a graph-theoretic approach for encoding custom autocorrelation structure in Gaussian process priors. Multifidelity information fusion is facilitated through stochastic autoregressive schemes and frequency-domain machine learning algorithms that scale linearly with the data. Taking together these new developments leads to linear complexity algorithms as demonstrated in benchmark problems involving deterministic and stochastic fields in up to 10⁵ input dimensions and 10⁵ training points on a standard desktop computer
Output-Weighted Sampling for Multi-Armed Bandits with Extreme Payoffs
We present a new type of acquisition functions for online decision making in
multi-armed and contextual bandit problems with extreme payoffs. Specifically,
we model the payoff function as a Gaussian process and formulate a novel type
of upper confidence bound (UCB) acquisition function that guides exploration
towards the bandits that are deemed most relevant according to the variability
of the observed rewards. This is achieved by computing a tractable likelihood
ratio that quantifies the importance of the output relative to the inputs and
essentially acts as an \textit{attention mechanism} that promotes exploration
of extreme rewards. We demonstrate the benefits of the proposed methodology
across several synthetic benchmarks, as well as a realistic example involving
noisy sensor network data. Finally, we provide a JAX library for efficient
bandit optimization using Gaussian processes.Comment: 10 pages, 4 figures, 1 tabl
Machine Learning for Fluid Mechanics
The field of fluid mechanics is rapidly advancing, driven by unprecedented
volumes of data from field measurements, experiments and large-scale
simulations at multiple spatiotemporal scales. Machine learning offers a wealth
of techniques to extract information from data that could be translated into
knowledge about the underlying fluid mechanics. Moreover, machine learning
algorithms can augment domain knowledge and automate tasks related to flow
control and optimization. This article presents an overview of past history,
current developments, and emerging opportunities of machine learning for fluid
mechanics. It outlines fundamental machine learning methodologies and discusses
their uses for understanding, modeling, optimizing, and controlling fluid
flows. The strengths and limitations of these methods are addressed from the
perspective of scientific inquiry that considers data as an inherent part of
modeling, experimentation, and simulation. Machine learning provides a powerful
information processing framework that can enrich, and possibly even transform,
current lines of fluid mechanics research and industrial applications.Comment: To appear in the Annual Reviews of Fluid Mechanics, 202