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arXiv 2304.07599cs.LGcs.NAmath.DSmath.NA
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在潜在空间中学习可提高深度神经算子的预测精度

Learning in latent spaces improves the predictive accuracy of deep neural operators

Johns Hopkins University(约翰斯·霍普金斯大学);Brown University(布朗大学)

Katiana Kontolati, Somdatta Goswami, George Em Karniadakis, Michael D. Shields

AI总结:

本文提出L-DeepONet,通过自编码器将高维PDE输入输出映射到低维潜在空间,在多种时间相关PDE上相比标准DeepONet提升了预测精度和计算效率。

摘要:

算子回归为描述物理系统的偏微分方程(PDEs)提供了一种强大的构造离散化不变仿真器的方法。神经算子特别采用深度神经网络来近似无穷维Banach空间之间的映射。作为数据驱动模型,神经算子需要生成带标签的观测数据,而在复杂高保真模型的情况下,这会产生包含冗余和噪声特征的高维数据集,从而阻碍基于梯度的优化。将这些高维数据集映射到显著特征的低维潜在空间,可以使数据处理更加容易,并增强学习效果。在这项工作中,我们研究了潜在深度算子网络(L-DeepONet),它是标准DeepONet的扩展,利用通过合适的自编码器识别出的高维PDE输入和输出函数的潜在表示。我们证明,L-DeepONet在精度和计算效率方面均优于标准方法,适用于多种时间相关的PDE,例如脆性材料中裂缝扩展的建模、对流流体流动以及表现出多尺度动力学特征的大尺度大气流动。

英文摘要:

Operator regression provides a powerful means of constructing discretization-invariant emulators for partial-differential equations (PDEs) describing physical systems. Neural operators specifically employ deep neural networks to approximate mappings between infinite-dimensional Banach spaces. As data-driven models, neural operators require the generation of labeled observations, which in cases of complex high-fidelity models result in high-dimensional datasets containing redundant and noisy features, which can hinder gradient-based optimization. Mapping these high-dimensional datasets to a low-dimensional latent space of salient features can make it easier to work with the data and also enhance learning. In this work, we investigate the latent deep operator network (L-DeepONet), an extension of standard DeepONet, which leverages latent representations of high-dimensional PDE input and output functions identified with suitable autoencoders. We illustrate that L-DeepONet outperforms the standard approach in terms of both accuracy and computational efficiency across diverse time-dependent PDEs, e.g., modeling the growth of fracture in brittle materials, convective fluid flows, and large-scale atmospheric flows exhibiting multiscale dynamical features.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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