论文标题
具有低维流量表示的非线性动力学的稀疏鉴定
Sparse identification of nonlinear dynamics with low-dimensionalized flow representations
论文作者
论文摘要
我们对低维复合流现象的非线性动力学（SINDY）进行稀疏鉴定。 We first apply the SINDy with two regression methods, the thresholded least square algorithm (TLSA) and the adaptive Lasso (Alasso) which show reasonable ability with a wide range of sparsity constant in our preliminary tests, to a two-dimensional single cylinder wake at $Re_D=100$, its transient process, and a wake of two-parallel cylinders, as examples of high-dimensional fluid 数据。为了使用Sindy处理这些高维数据，其库矩阵适合低维变量组合，使用了基于卷积的神经网络自动编码器（CNN-AE）。 CNN-AE被用来将高维动力学映射到低维的潜在空间中。然后，信德（Sindy）寻求映射的低维潜在载体的管理方程。可以通过将Sindy与CNN解码器组合预测的潜在向量来提供高维动力学的时间演变，该解码器可以将低维的潜在矢量改造为原始尺寸。 Sindy可以提供稳定的解决方案，因为潜在动力学的管理方程和基于CNN的基于CNN-SINDY的建模可以成功地重现高维流场，尽管需要更多的术语来代表瞬态流动和两平行的圆柱唤醒。最终考虑了九个方程式湍流模型，以检查信德对湍流的适用性，尽管不使用CNN-AE。目前的结果表明，具有适当参数选择的提议方案使我们能够分析具有可解释的低维歧管的高维非线性动力学。
We perform a sparse identification of nonlinear dynamics (SINDy) for low-dimensionalized complex flow phenomena. We first apply the SINDy with two regression methods, the thresholded least square algorithm (TLSA) and the adaptive Lasso (Alasso) which show reasonable ability with a wide range of sparsity constant in our preliminary tests, to a two-dimensional single cylinder wake at $Re_D=100$, its transient process, and a wake of two-parallel cylinders, as examples of high-dimensional fluid data. To handle these high dimensional data with SINDy whose library matrix is suitable for low-dimensional variable combinations, a convolutional neural network-based autoencoder (CNN-AE) is utilized. The CNN-AE is employed to map a high-dimensional dynamics into a low-dimensional latent space. The SINDy then seeks a governing equation of the mapped low-dimensional latent vector. Temporal evolution of high-dimensional dynamics can be provided by combining the predicted latent vector by SINDy with the CNN decoder which can remap the low-dimensional latent vector to the original dimension. The SINDy can provide a stable solution as the governing equation of the latent dynamics and the CNN-SINDy based modeling can reproduce high-dimensional flow fields successfully, although more terms are required to represent the transient flow and the two-parallel cylinder wake than the periodic shedding. A nine-equation turbulent shear flow model is finally considered to examine the applicability of SINDy to turbulence, although without using CNN-AE. The present results suggest that the proposed scheme with an appropriate parameter choice enables us to analyze high-dimensional nonlinear dynamics with interpretable low-dimensional manifolds.
