Optimal criteria and their asymptotic form for data selection in data-driven reduced-order modelling with Gaussian process regression

Sapsis, Themistoklis P.; Blanchard, Antoine

doi:10.1098/rsta.2021.0197

Cited by 4 publications

(1 citation statement)

References 24 publications

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“…This fundamental information in complex systems is provided by data, which is often expensive. Sapsis & Blanchard [ 188 ] introduce a criterion based on a Gaussian process regression (GPR) for the most effective selection of data or the associated experiments to generate this data to perform data-driven reduced-order modelling. In particular, an optimality condition for the selection of a new input is defined as the minimizer of the distance between the approximated output probability density function of the reduced-order model and the exact one, which is defined as the supremum over the unit sphere of the native Hilbert space for the GPR.…”

Section: The General Content Of the Issuementioning

confidence: 99%

Data-driven prediction in dynamical systems: recent developments

Ghadami

Epureanu

2022

Phil. Trans. R. Soc. A.

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In recent years, we have witnessed a significant shift toward ever-more complex and ever-larger-scale systems in the majority of the grand societal challenges tackled in applied sciences. The need to comprehend and predict the dynamics of complex systems have spurred developments in large-scale simulations and a multitude of methods across several disciplines. The goals of understanding and prediction in complex dynamical systems, however, have been hindered by high dimensionality, complexity and chaotic behaviours. Recent advances in data-driven techniques and machine-learning approaches have revolutionized how we model and analyse complex systems. The integration of these techniques with dynamical systems theory opens up opportunities to tackle previously unattainable challenges in modelling and prediction of dynamical systems. While data-driven prediction methods have made great strides in recent years, it is still necessary to develop new techniques to improve their applicability to a wider range of complex systems in science and engineering. This focus issue shares recent developments in the field of complex dynamical systems with emphasis on data-driven, data-assisted and artificial intelligence-based discovery of dynamical systems. This article is part of the theme issue 'Data-driven prediction in dynamical systems'.

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Section: The General Content Of the Issuementioning

confidence: 99%

Data-driven prediction in dynamical systems: recent developments

Ghadami

Epureanu

2022

Phil. Trans. R. Soc. A.

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Discovering and forecasting extreme events via active learning in neural operators

Pickering

Guth²,

Karniadakis³

et al. 2022

Nat Comput Sci

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Extreme events in society and nature, such as pandemic spikes or rogue waves, can have catastrophic consequences. Characterizing extremes is difficult as they occur rarely, arise from seemingly benign conditions, and belong to complex and often unknown infinite-dimensional systems. Such challenges render attempts at characterizing them as moot. We address each of these difficulties by combining novel training schemes in Bayesian experimental design (BED) with an ensemble of deep neural operators (DNOs). This model-agnostic framework pairs a BED scheme that actively selects data for quantifying extreme events with an ensemble of DNOs that approximate infinite-dimensional nonlinear operators.We find that not only does this framework clearly beat Gaussian processes (GPs) but that 1) shallow ensembles of just two members perform best; 2) extremes are uncovered regardless of the state of initial data (i.e. with or without extremes); 3) our method eliminates "double-descent" phenomena; 4) the use of batches of suboptimal acquisition points compared to step-by-step global optima does not hinder BED performance; and 5) Monte Carlo acquisition outperforms standard minimizers in high-dimensions.Together these conclusions form the foundation of an AI-assisted experimental infrastructure that can efficiently infer and pinpoint critical situations across many domains, from physical to societal systems.

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Output-weighted sampling for multi-armed bandits with extreme payoffs

et al. 2022

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We present a new type of acquisition function 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 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 attention mechanism that promotes exploration of extreme rewards. Our formulation is supported by asymptotic zero-regret guarantees, and its performance is demonstrated across several synthetic benchmarks, as well as two realistic examples involving noisy sensor network data. Finally, we provide a JAX library for efficient bandit optimization using Gaussian processes.

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Optimal criteria and their asymptotic form for data selection in data-driven reduced-order modelling with Gaussian process regression

Cited by 4 publications

References 24 publications

Data-driven prediction in dynamical systems: recent developments

Data-driven prediction in dynamical systems: recent developments

Discovering and forecasting extreme events via active learning in neural operators

Output-weighted sampling for multi-armed bandits with extreme payoffs

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