Multi-level convolutional autoencoder networks for parametric prediction of spatio-temporal dynamics
Multi-level convolutional autoencoder networks for parametric prediction of spatio-temporal dynamics
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DOI：
10.1016/j.cma.2020.113379
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发表时间：
2020-12-01
影响因子：
7.2
通讯作者：
Duraisamy, Karthik
中科院分区：
文献类型：
--
作者：
Xu, Jiayang;Duraisamy, Karthik
在复杂时空动力学的预测建模结束时，提出了一个数据驱动的框架，利用嵌套的非线性流形。使用三个级别的神经网络，目的是预测参数设置中感兴趣的系统的未来状态。卷积自动编码器用作顶层，将高维输入数据沿空间维度编码为潜在变量序列。时间卷积自动编码器（TCAE）作为第二层，进一步沿时间维度对第一层的输出序列进行编码，并输出一组封装动态时空演化的潜在变量。扩张时间卷积的使用使感受野随着网络深度呈指数增长，从而可以有效处理科学计算中典型的长时间序列。全连接网络用作第三层，从训练数据中学习这些潜在变量与全局参数之间的映射，并预测新参数。对于未来状态预测，第二层使用时间卷积网络来预测顶层输出序列的后续步骤。对最底层的潜在变量进行解码，以获得新的全局参数和/或未来时间的物理空间的动态。预测能力是针对一系列涉及不连续性、波传播、强瞬态和相干结构的问题进行评估的。评估结果对不同模型选择的敏感性。结果表明，只要有足够的数据和仔细的训练，就可以构建有效的数据驱动的预测模型。提供了对当前方法及其在模型简化领域中的地位的看法。 (c) 2020 Elsevier B.V. 保留所有权利。
A data-driven framework is proposed towards the end of predictive modeling of complex spatio-temporal dynamics, leveraging nested non-linear manifolds. Three levels of neural networks are used, with the goal of predicting the future state of a system of interest in a parametric setting. A convolutional autoencoder is used as the top level to encode the high dimensional input data along spatial dimensions into a sequence of latent variables. A temporal convolutional autoencoder (TCAE) serves as the second level, which further encodes the output sequence from the first level along the temporal dimension, and outputs a set of latent variables that encapsulate the spatio-temporal evolution of the dynamics. The use of dilated temporal convolutions grows the receptive field exponentially with network depth, allowing for efficient processing of long temporal sequences typical of scientific computations. A fully-connected network is used as the third level to learn the mapping between these latent variables and the global parameters from training data, and predict them for new parameters. For future state predictions, the second level uses a temporal convolutional network to predict subsequent steps of the output sequence from the top level. Latent variables at the bottom-most level are decoded to obtain the dynamics in physical space at new global parameters and/or at a future time. Predictive capabilities are evaluated on a range of problems involving discontinuities, wave propagation, strong transients, and coherent structures. The sensitivity of the results to different modeling choices is assessed. The results suggest that given adequate data and careful training, effective data-driven predictive models can be constructed. Perspectives are provided on the present approach and its place in the landscape of model reduction. (c) 2020 Elsevier B.V. All rights reserved.