Multi-fidelity wavelet neural operator surrogate model for time-independent and time-dependent reliability analysis

IF 3 3区 工程技术 Q2 ENGINEERING, MECHANICAL Probabilistic Engineering Mechanics Pub Date : 2024-07-01 DOI:10.1016/j.probengmech.2024.103672
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Abstract

Operator learning frameworks have recently emerged as an effective scientific machine learning tool for learning complex nonlinear operators of differential equations. Since neural operators learn an infinite-dimensional functional mapping, it is useful in applications requiring rapid prediction of solutions for a wide range of input functions. A task of a similar nature arises in many applications of uncertainty quantification, including reliability estimation and design under uncertainty, each of which demands thousands of samples subjected to a wide range of possible input conditions, an aspect to which neural operators are specialized. Although the neural operators are capable of learning complex nonlinear solution operators, they require an extensive amount of data for successful training. Unlike the applications in computer vision, the computational complexity of the numerical simulations and the cost of physical experiments contributing to the synthetic and real training data compromise the performance of the trained neural operator model, thereby directly impacting the accuracy of uncertainty quantification results. We aim to alleviate the data bottleneck by using multi-fidelity learning in neural operators, where a neural operator is trained by using a large amount of inexpensive low-fidelity data along with a small amount of expensive high-fidelity data. We propose the multi-fidelity wavelet neural operator, capable of learning solution operators from a multi-fidelity dataset, for efficient and effective data-driven reliability analysis of dynamical systems. We illustrate the performance of the proposed framework on bi-fidelity data simulated on coarse and refined grids for spatial and spatiotemporal systems.

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用于与时间无关和与时间有关的可靠性分析的多保真小波神经算子代用模型
近来,算子学习框架已成为一种有效的科学机器学习工具,可用于学习微分方程的复杂非线性算子。由于神经算子学习的是无限维函数映射,因此在需要快速预测各种输入函数解的应用中非常有用。在不确定性量化的许多应用中都会出现类似的任务,包括可靠性估计和不确定性条件下的设计,每种应用都需要在各种可能的输入条件下采集数千个样本,而这正是神经算子所擅长的方面。虽然神经算子能够学习复杂的非线性解算子,但它们需要大量数据才能成功训练。与计算机视觉中的应用不同,数值模拟的计算复杂性以及合成和真实训练数据所需的物理实验成本会影响训练后神经算子模型的性能,从而直接影响不确定性量化结果的准确性。我们的目标是通过在神经算子中使用多保真度学习来缓解数据瓶颈,即通过使用大量廉价的低保真度数据和少量昂贵的高保真度数据来训练神经算子。我们提出了多保真度小波神经算子,它能够从多保真度数据集中学习解算子,用于对动态系统进行高效、有效的数据驱动可靠性分析。我们对空间和时空系统在粗网格和细网格上模拟的双保真数据说明了所提框架的性能。
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来源期刊
Probabilistic Engineering Mechanics
Probabilistic Engineering Mechanics 工程技术-工程:机械
CiteScore
3.80
自引率
15.40%
发文量
98
审稿时长
13.5 months
期刊介绍: This journal provides a forum for scholarly work dealing primarily with probabilistic and statistical approaches to contemporary solid/structural and fluid mechanics problems encountered in diverse technical disciplines such as aerospace, civil, marine, mechanical, and nuclear engineering. The journal aims to maintain a healthy balance between general solution techniques and problem-specific results, encouraging a fruitful exchange of ideas among disparate engineering specialities.
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