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Time resolution independent operator learning

delete2025-12-04
delete0
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OA
AI
D
Diab Abueidda
M
Mbebo Nonna
P
Panos Pantidis
M
Mostafa E. Mobasher
DOI：10.1016/j.cma.2025.118586delete
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摘要

摘要

En 中文
从稀疏和不规则数据中精确学习时变偏微分方程（PDEs）的解算子仍然是一项具有挑战性的任务。循环DeepONet扩展继承了序列到序列（seq2seq）RNN架构的离散时间局限性，而神经ODE代理模型在初始化后无法引入新的输入。我们引入了NCDE-DeepONet，一种连续时间算子网络，它将神经受控微分方程（NCDE）嵌入到分支网络中，并通过显式空间-时间坐标增强主干网络。NCDE将整个载荷历史编码为受样条插值输入路径驱动的受控ODE的解，使得该表示与输入分辨率无关：它编码观测样本的不同输入信号离散化方式。主干网络随后在任意空间位置和时间点上探测该潜在路径，从而使整体映射输出分辨率无关：预测可以在训练期间未见的网格和时间步长上查询，无需重新训练或插值。瞬态泊松、弹性动力学和热弹性问题的基准测试验证了该框架的鲁棒性和准确性，实现了近乎瞬时的解预测。这些发现表明，受控动力学为瞬态力学中的高保真算子学习提供了原理上正确且高效的基石。
Keyword:
Neural differential equations
Ordinary differential equations
Operator learning
Thermoelasticity
Elastodynamics
AI总结

AI总结

对已上传原文的论文进行重点信息的提取，主要内容包括：简要概述、研究摘要、背景介绍、关键亮点、图文解析、展望与总结。

期刊

Computer Methods in Applied Mechanics and Engineering 封面图
Computer Methods in Applied Mechanics and Engineering
IF:
7.3
论文数:
1.3W
被引数:
5.6W

机构

N
New York University
学者数:
4.4W
论文数: 3.9W
被引数: 5.8W
引用论文

引用论文

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