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arXiv 2402.15734cs.LGstat.ML
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通过无监督预训练和上下文学习实现数据高效的算子学习

Data-Efficient Operator Learning via Unsupervised Pretraining and In-Context Learning

Simon Fraser University(西蒙弗雷泽大学);Lawrence Berkeley National Laboratory(伯克利国家实验室);International Computer Science Institute(国际计算机科学研究所);University of California, Berkeley(加州大学伯克利分校)

Wuyang Chen, Jialin Song, Pu Ren, Shashank Subramanian, Dmitriy Morozov, Michael W. Mahoney

AI总结:

本文提出一种用于偏微分方程算子学习的无监督预训练与上下文学习方法,通过挖掘无标签数据并利用物理启发代理任务预训练神经算子,显著提升了数据效率与分布外泛化能力。

摘要:

近年来,将机器学习方法与物理领域特定洞察相结合,在求解基于偏微分方程(PDEs)的科学问题方面展现出了巨大潜力。然而,由于这些方法对数据需求量大,仍然需要大量的PDE数据。这重新引入了对昂贵数值PDE求解的需求,在一定程度上破坏了避免这些昂贵模拟的初衷。在本研究中,为了寻求数据效率,我们为PDE算子学习设计了无监督预训练。为了减少对具有高昂模拟成本的训练数据的需求,我们挖掘了没有模拟解的无标签PDE数据,并使用受物理启发且基于重建的代理任务来预训练神经算子。为了提高分布外性能,我们进一步协助神经算子灵活利用一种基于相似度且能从上下文示例中学习的方法,而不会产生额外的训练成本或设计开销。在多种不同的PDE数据集上进行的广泛实证评估表明,我们的方法具有极高的数据效率,泛化能力更强,甚至优于传统的视觉预训练模型。我们在 https://github.com/delta-lab-ai/data_efficient_nopt 提供了代码。

英文摘要:

Recent years have witnessed the promise of coupling machine learning methods and physical domain-specific insights for solving scientific problems based on partial differential equations (PDEs). However, being data-intensive, these methods still require a large amount of PDE data. This reintroduces the need for expensive numerical PDE solutions, partially undermining the original goal of avoiding these expensive simulations. In this work, seeking data efficiency, we design unsupervised pretraining for PDE operator learning. To reduce the need for training data with heavy simulation costs, we mine unlabeled PDE data without simulated solutions, and we pretrain neural operators with physics-inspired reconstruction-based proxy tasks. To improve out-of-distribution performance, we further assist neural operators in flexibly leveraging a similarity-based method that learns in-context examples, without incurring extra training costs or designs. Extensive empirical evaluations on a diverse set of PDEs demonstrate that our method is highly data-efficient, more generalizable, and even outperforms conventional vision-pretrained models. We provide our code at https://github.com/delta-lab-ai/data_efficient_nopt.

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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