A long short-term memory embedding for hybrid uplifted reduced order models
A long short-term memory embedding for hybrid uplifted reduced order models
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DOI：
10.1016/j.physd.2020.132471
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发表时间：
2020-08-01
影响因子：
4
通讯作者：
Iliescu, Traian
中科院分区：
文献类型：
--
作者：
Ahmed, Shady E.;San, Omer;Iliescu, Traian
本文通过将基于标准投影的方法与长短期记忆（LSTM）嵌入相结合，提出了一种提升降阶建模（UROM）方法。我们的方法有三个建模层或组件。在第一层，我们利用侵入式投影方法对最大模态所代表的动态建模。第二层由LSTM模型组成，用于计算超出该截断的残差。这个闭合层是指将丢弃模态的残余效应纳入最大尺度动力学的过程。然而，由于潜在的非线性过程，对于高Kolmogorov n-width系统，产生低秩近似的可行性逐渐减弱。第三个提升层，称为超分辨率，通过利用LSTM的多功能性将跨度扩展到更多的模式来解决这个有限的表示问题。因此，我们的模型集成了基于物理的投影模型和基于内存的LSTM闭包，以及基于LSTM的超分辨率模型。在一些应用中，我们利用格拉斯曼流形来构造未知条件下的rom。利用二次非线性的Burgers方程和Navier-Stokes方程进行了数值实验。我们的结果表明，所提出的方法在建立参数化系统的降阶模型方面具有鲁棒性，并证实了精度和效率之间的改进权衡。(C) 2020 Elsevier B.V.版权所有
In this paper, we introduce an uplifted reduced order modeling (UROM) approach through the integration of standard projection based methods with long short-term memory (LSTM) embedding. Our approach has three modeling layers or components. In the first layer, we utilize an intrusive projection approach to model the dynamics represented by the largest modes. The second layer consists of an LSTM model to account for residuals beyond this truncation. This closure layer refers to the process of including the residual effect of the discarded modes into the dynamics of the largest scales. However, the feasibility of generating a low rank approximation tails off for higher Kolmogorov n-width systems due to the underlying nonlinear processes. The third uplifting layer, called super-resolution, addresses this limited representation issue by expanding the span into a larger number of modes utilizing the versatility of LSTM. Therefore, our model integrates a physics-based projection model with a memory embedded LSTM closure and an LSTM based super-resolution model. In several applications, we exploit the use of Grassmann manifold to construct UROM for unseen conditions. We perform numerical experiments by using the Burgers and Navier-Stokes equations with quadratic nonlinearity. Our results show the robustness of the proposed approach in building reduced order models for parameterized systems and confirm the improved trade-off between accuracy and efficiency. (C) 2020 Elsevier B.V. All rights reserved.