Abstract 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.

中文翻译：

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用于时空动态参数预测的多级卷积自编码器网络

摘要 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。使用了三级神经网络，目的是在参数设置中预测感兴趣系统的未来状态。卷积自编码器用作顶层，将沿空间维度的高维输入数据编码为潜在变量序列。时间卷积自动编码器 (TCAE) 作为第二层，它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，允许有效处理典型的科学计算的长时间序列。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从顶层预测输出序列的后续步骤。解码最底层的潜在变量以获得新的全局参数和/或未来时间的物理空间动态。对一系列问题的预测能力进行评估，包括不连续性、波传播、强瞬态和相干结构。评估结果对不同建模选择的敏感性。结果表明，如果有足够的数据和仔细的训练，可以构建有效的数据驱动的预测模型。提供了关于当前方法及其在模型简化领域中的地位的观点。