Model reduction for fluid flow simulation continues to be of great interest across a number of scientific and engineering fields. In a previous work [arXiv:2104.13962], we explored the use of Neural Ordinary Differential Equations (NODE) as a non-intrusive method for propagating the latent-space dynamics in reduced order models. Here, we investigate employing deep autoencoders for discovering the reduced basis representation, the dynamics of which are then approximated by NODE. The ability of deep autoencoders to represent the latent-space is compared to the traditional proper orthogonal decomposition (POD) approach, again in conjunction with NODE for capturing the dynamics. Additionally, we compare their behavior with two classical non-intrusive methods based on POD and radial basis function interpolation as well as dynamic mode decomposition. The test problems we consider include incompressible flow around a cylinder as well as a real-world application of shallow water hydrodynamics in an estuarine system. Our findings indicate that deep autoencoders can leverage nonlinear manifold learning to achieve a highly efficient compression of spatial information and define a latent-space that appears to be more suitable for capturing the temporal dynamics through the NODE framework.

翻译：在许多科学和工程领域,流体模拟模型的减少仍然具有极大的兴趣。在以前的一项工作[arXiv:2104.113962]中,我们探索了使用神经普通差异(NODE)作为非侵入性方法,在减少的顺序模型中传播潜空动态。在这里,我们调查了使用深自动代算器来发现基础代表器的缩小,其动态随后由 NODE 所近似。深自动代算器代表潜层空间的能力与传统的正确或地心分解法(POD)相比,再次与NODE结合,以捕捉动态。此外,我们将它们的行为与两种基于POD和辐射基的经典非侵入性方法相比较,这两种方法的功能是内插和动态模式分解。我们所考虑的测试问题包括气瓶周围的压流以及浅水体动力学在排卵系统中的实际应用。我们的研究结果表明,深自动代算器能够利用非线性多元性多元性学习实现高度高效的空间动态,通过空间信息定位框架来界定高度高效的潜测。