arXivDaily arXiv每日学术速递 周一至周五更新
arXiv周末暂无论文更新,休息一下吧,周末愉快~~
arXiv 2602.18679cs.LGnlin.CD
收藏

用于动力系统变换器学习上下文转移算子

Transformers for dynamical systems learn transfer operators in-context

The Oden Institute, The University of Texas at Austin(德克萨斯大学奥斯汀分校奥登研究所);Department of Physics, The University of Texas at Austin(德克萨斯大学奥斯汀分校物理系)

Anthony Bao, Jeffrey Lai, William Gilpin

AI总结:

研究发现变换器在上下文学习中通过延迟嵌入和不变集预测来学习转移算子,揭示了预训练模型如何无需重新训练即可预测未见过的物理系统。

摘要:

大规模科学机器学习基础模型适应于训练期间未见过的物理环境,如湍流尺度的零样本迁移。这种现象,即上下文学习,挑战了传统物理系统学习和适应的理解。本文在最小设置中研究了动力系统上下文学习:训练一个小型双层单头变换器预测一个动力系统,然后评估其在不重新训练的情况下预测不同动力系统的能力。我们发现训练中存在分布内与分布外性能之间的早期权衡,表现为二次双下降现象。我们发现基于注意力的模型在上下文中应用转移算子预测策略:(1) 使用延迟嵌入提升低维时间序列,以检测系统的高维动态流形;(2) 识别并预测长寿命不变集,以表征该流形上的全局流动。我们的结果阐明了预训练模型如何在测试时无需重新训练即可预测未见过的物理系统,并展示了基于注意力的模型利用全局吸引子信息服务于短期预测的独特能力。

英文摘要:

Large-scale foundation models for scientific machine learning adapt to physical settings unseen during training, such as zero-shot transfer between turbulent scales. This phenomenon, in-context learning, challenges conventional understanding of learning and adaptation in physical systems. Here, we study in-context learning of dynamical systems in a minimal setting: we train a small two-layer, single-head transformer to forecast one dynamical system, and then evaluate its ability to forecast a different dynamical system without retraining. We discover an early tradeoff in training between in-distribution and out-of-distribution performance, which manifests as a secondary double descent phenomenon. We discover that attention-based models apply a transfer-operator forecasting strategy in-context. They (1) lift low-dimensional time series using delay embedding, to detect the system's higher-dimensional dynamical manifold, and (2) identify and forecast long-lived invariant sets that characterize the global flow on this manifold. Our results clarify the mechanism enabling large pretrained models to forecast unseen physical systems at test time without retraining, and they illustrate the unique ability of attention-based models to leverage global attractor information in service of short-term forecasts.

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。

↑