论文标题
使用深空和时间卷积自动编码器的随机大规模和时间依赖性问题的降低订购建模
Reduced-order modeling for stochastic large-scale and time-dependent problems using deep spatial and temporal convolutional autoencoders
论文作者
论文摘要
提出了一种基于卷积自动编码器（NIROM-CAE）的非侵入性降低订单模型，作为数据驱动的工具，以构建有效的非线性降低级模型，以用于随机时空大规模的大规模物理问题。该方法使用两个1D横向倾斜自动编码器（CAE）来减少从高保真数字求解器收集的一组高保真快照中的空间和时间尺寸。然后，使用基于回归的多层感知器（MLP）将来自两个压缩水平生成的编码潜在向量映射到输入参数。将提出方法的准确性与通过两种基准基于线性降序技术的人工神经网络（POD-ANN）进行了比较，这是通过两个基准测试（一维汉堡和Stoker的解决方案）和一个假设的大坝爆破流量问题，带有一个非结构化的网状网格和一条复杂的小型河流。数值结果表明，提出的非线性框架具有强大的预测能力，可以准确近似于复杂随机的大规模和时间依赖性问题的输出的统计矩，并且在预测在线阶段的计算成本较低。
A non-intrusive reduced order model based on convolutional autoencoders (NIROM-CAEs) is proposed as a data-driven tool to build an efficient nonlinear reduced-order model for stochastic spatio-temporal large-scale physical problems. The method uses two 1d-convolutional autoencoders (CAEs) to reduce the spatial and temporal dimensions from a set of high-fidelity snapshots collected from the high-fidelity numerical solver. The encoded latent vectors, generated from two compression levels, are then mapped to the input parameters using a regression-based multilayer perceptron (MLP). The accuracy of the proposed approach is compared to that of the linear reduced-order technique-based artificial neural network (POD-ANN) through two benchmark tests (the one-dimensional Burgers and Stoker's solutions) and a hypothetical dam-break flow problem, with an unstructured mesh and over a complex bathymetry river. The numerical results show that the proposed nonlinear framework presents strong predictive abilities to accurately approximate the statistical moments of the outputs for complex stochastic large-scale and time-dependent problems, with low computational cost during the predictive online stage.
