A Tailored Convolutional Neural Network for Nonlinear Manifold Learning of Computational Physics Data Using Unstructured Spatial Discretizations

We propose a nonlinear manifold learning technique based on deep convolutional autoencoders that is appropriate for model order reduction of physical systems in complex geometries. Convolutional neural networks have proven to be highly advantageous compressing data arising from demonstrating slow-decaying Kolmogorov n-width. However, these are restricted structured meshes. Unstructured meshes often required performing analyses real with geometry. Our custom graph convolution operators the available differential given spatial discretization effectively extend application space arbitrarily geometry typically discretized using unstructured sets derivative underlying discretization, making method particularly well suited solution partial equations. demonstrate examples heat transfer and fluid mechanics show better than an magnitude improvement accuracy over linear methods.