一种用于降阶建模中残差学习的 DeepONet 多保真度方法
A DeepONet multi-fidelity approach for residual learning in reduced order modeling
AI总结：
本文提出一种结合多保真度视角与 DeepONet 的残差学习方法，通过神经网络学习降阶模型引入的误差，以提升新预测的精度，并利用 POD 与 gappy POD 集成验证了其有效性。
摘要：
在本文中，我们提出了一种新方法，通过利用多保真度视角和 DeepONets 来提高降阶模型的精度。降阶模型通过简化原始模型提供实时数值近似。为了达到快速计算的目的，该操作引入的误差通常被忽略和牺牲。我们建议将模型降阶与机器学习残差学习相耦合，使得上述误差能够被神经网络学习并用于新预测的推断。我们强调，该框架最大限度地利用了高保真度信息，将其用于构建降阶模型和学习残差。在本研究中，我们探讨了本征正交分解（POD）、用于传感器数据的 gappy POD 与最新的 DeepONet 架构的集成。展示了针对参数化基准函数和非线性参数化 Navier-Stokes 问题的数值研究。
英文摘要：
In the present work, we introduce a novel approach to enhance the precision of reduced order models by exploiting a multi-fidelity perspective and DeepONets. Reduced models provide a real-time numerical approximation by simplifying the original model. The error introduced by the such operation is usually neglected and sacrificed in order to reach a fast computation. We propose to couple the model reduction to a machine learning residual learning, such that the above-mentioned error can be learned by a neural network and inferred for new predictions. We emphasize that the framework maximizes the exploitation of high-fidelity information, using it for building the reduced order model and for learning the residual. In this work, we explore the integration of proper orthogonal decomposition (POD), and gappy POD for sensors data, with the recent DeepONet architecture. Numerical investigations for a parametric benchmark function and a nonlinear parametric Navier-Stokes problem are presented.
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。
