Bi-fidelity modeling of uncertain and partially unknown systems using DeepONets

De, Subhayan; Reynolds, Matthew; Hassanaly, Malik; King, Ruth; Doostan, Alireza

doi:10.1007/s00466-023-02272-4

Cited by 15 publications

(4 citation statements)

References 45 publications

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“…The underlying idea that motivates the algorithm is that is it easier to learn a correction to the density than the full density itself. Similar methods have been developed in the context of multifidelity methods (De et al, 2023). The predictor-corrector is summarized in Algorithm 2.…”

Section: Accommodating For Rare Observations: the Predictor-corrector...mentioning

confidence: 99%

Uniform-in-phase-space data selection with iterative normalizing flows

Hassanaly

Perry

Müeller

et al. 2023

DCE

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Improvements in computational and experimental capabilities are rapidly increasing the amount of scientific data that are routinely generated. In applications that are constrained by memory and computational intensity, excessively large datasets may hinder scientific discovery, making data reduction a critical component of data-driven methods. Datasets are growing in two directions: the number of data points and their dimensionality. Whereas dimension reduction typically aims at describing each data sample on lower-dimensional space, the focus here is on reducing the number of data points. A strategy is proposed to select data points such that they uniformly span the phase-space of the data. The algorithm proposed relies on estimating the probability map of the data and using it to construct an acceptance probability. An iterative method is used to accurately estimate the probability of the rare data points when only a small subset of the dataset is used to construct the probability map. Instead of binning the phase-space to estimate the probability map, its functional form is approximated with a normalizing flow. Therefore, the method naturally extends to high-dimensional datasets. The proposed framework is demonstrated as a viable pathway to enable data-efficient machine learning when abundant data are available.

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Section: Accommodating For Rare Observations: the Predictor-corrector...mentioning

confidence: 99%

Uniform-in-phase-space data selection with iterative normalizing flows

Hassanaly

Perry

Müeller

et al. 2023

DCE

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“…Moreover, the research outlined in Ahmed and Stinis (2023) [2] underscores the efficacy of multi-fidelity data in ensuring robust and efficient approximation of operators, especially in scenarios where high-fidelity data is either sparse or expensive to procure. Additionally, techniques like those presented in De et al ( 2023) [48] emphasize the cohesive integration of data from varying fidelities, ensuring that the neural operator captures the intricate dynamics and characteristics inherent in the high-fidelity data while also benefiting from the broader coverage and insights offered by the low-fidelity data. The confluence of neural operators and MFMs unveils novel research avenues poised to significantly influence future computational methodologies in diverse domains.…”

Section: Property Value Commentsmentioning

confidence: 99%

Review of multi-fidelity models

Giselle Fernández-Godino

2023

ACSE

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Multi-fidelity models provide a framework for integrating computational models of varying complexity, allowing for accurate predictions while optimizing computational resources. These models are especially beneficial when acquiring high-accuracy data is costly or computationally intensive. This review offers a comprehensive analysis of multi-fidelity models, focusing on their applications in scientific and engineering fields, particularly in optimization and uncertainty quantification. It classifies publications on multi-fidelity modeling according to several criteria, including application area, surrogate model selection, types of fidelity, combination methods and year of publication. The study investigates techniques for combining different fidelity levels, with an emphasis on multi-fidelity surrogate models. This work discusses reproducibility, open-sourcing methodologies and benchmarking procedures to promote transparency. The manuscript also includes educational toy problems to enhance understanding. Additionally, this paper outlines best practices for presenting multi-fidelity-related savings in a standardized, succinct and yet thorough manner. The review concludes by examining current trends in multifidelity modeling, including emerging techniques, recent advancements, and promising research directions.

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“…Many works [28][29][30][31][32][33][34] have proposed scientific machine-learning-based solutions for the multi-fidelity problem. For instance, in [28], a novel approach called the deep operator network (DeepONet) integrated a multi-fidelity neural network model to reduce the desired high-fidelity data and attained an error one order of magnitude smaller.…”

Section: Introductionmentioning

confidence: 99%

“…This approach was implemented to compute the Boltzmann transport equation (BTE) and proposed a fast solver for the inverse design of BTE problems. To reduce computational costs for complex physical problems involving parametric uncertainty and partial unknowns, a bi-fidelity modeling approach utilizing a deep operator network was introduced in [30]. This approach was applied to three problems: a nonlinear oscillator, heat transfer, and wind farm system.…”

Section: Introductionmentioning

confidence: 99%

A Physics-Guided Bi-Fidelity Fourier-Featured Operator Learning Framework for Predicting Time Evolution of Drag and Lift Coefficients

Mollaali,

Sahin,

Raza

et al. 2023

Fluids

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In the pursuit of accurate experimental and computational data while minimizing effort, there is a constant need for high-fidelity results. However, achieving such results often requires significant computational resources. To address this challenge, this paper proposes a deep operator learning-based framework that requires a limited high-fidelity dataset for training. We introduce a novel physics-guided, bi-fidelity, Fourier-featured deep operator network (DeepONet) framework that effectively combines low- and high-fidelity datasets, leveraging the strengths of each. In our methodology, we begin by designing a physics-guided Fourier-featured DeepONet, drawing inspiration from the intrinsic physical behavior of the target solution. Subsequently, we train this network to primarily learn the low-fidelity solution, utilizing an extensive dataset. This process ensures a comprehensive grasp of the foundational solution patterns. Following this foundational learning, the low-fidelity deep operator network’s output is enhanced using a physics-guided Fourier-featured residual deep operator network. This network refines the initial low-fidelity output, achieving the high-fidelity solution by employing a small high-fidelity dataset for training. Notably, in our framework, we employ the Fourier feature network as the trunk network for the DeepONets, given its proficiency in capturing and learning the oscillatory nature of the target solution with high precision. We validate our approach using a well-known 2D benchmark cylinder problem, which aims to predict the time trajectories of lift and drag coefficients. The results highlight that the physics-guided Fourier-featured deep operator network, serving as a foundational building block of our framework, possesses superior predictive capability for the lift and drag coefficients compared to its data-driven counterparts. The bi-fidelity learning framework, built upon the physics-guided Fourier-featured deep operator, accurately forecasts the time trajectories of lift and drag coefficients. A thorough evaluation of the proposed bi-fidelity framework confirms that our approach closely matches the high-fidelity solution, with an error rate under 2%. This confirms the effectiveness and reliability of our framework, particularly given the limited high-fidelity dataset used during training.

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Bi-fidelity modeling of uncertain and partially unknown systems using DeepONets

Cited by 15 publications

References 45 publications

Uniform-in-phase-space data selection with iterative normalizing flows

Uniform-in-phase-space data selection with iterative normalizing flows

Review of multi-fidelity models

A Physics-Guided Bi-Fidelity Fourier-Featured Operator Learning Framework for Predicting Time Evolution of Drag and Lift Coefficients

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