Autoencoder embeddings: latent manifold investigation in Aerodynamics
Please login to view abstract download link
Autoencoders demonstrated a great potential in Fluid Dynamics due to the possibility to construct very accurate surrogate reduced order models. High compression rates are achieved by a non-linear dimensionality reduction into a low-dimensional non-linear space (the latent space). To deploy the trained decoder as a generative model, the latent space can be sampled in a parametric way to perform predictions of new unseen cases [1]. However, the latent space produced by the encoder is a manifold, where the tools of Euclidean geometry cannot be applied. If the training dataset is dense, simply interpolating the latent space for inference already leads to accurate predictions. However, if the dataset is sparse or the manifold has a strong curvature, high errors can be faced if standard interpolation tools are applied. In this presentation, the geometry of the latent manifold of different datasets will be analyzed (airfoils and wings flows), looking for insights provided by the shape of the latent space. Based on the Jacobian J of the Decoder transformation, it is possible to compute the Magnification Factor: $MF = \sqrt{\mathrm{det}(J^TJ)}$, which provides stretching and compressions within the latent space (Fig. 1) [2]. A method for regularizing the latent space during training will be shown, leading to a more regular space and reducing the prediction errors during inference. In addition, a metric informed method will be presented for navigating in the latent space.
