Disentangled Latent Spaces for Reduced Order Models using Deterministic Autoencoders

Data-driven reduced-order models based on autoencoders generally lack interpretability compared to classical methods such as the proper orthogonal decomposition. More interpretability can be gained by disentangling the latent variables and analyzing the resulting modes. For this purpose, probabilistic $\beta$-variational autoencoders ($\beta$-VAEs) are frequently used in computational fluid dynamics and other simulation sciences. Using a benchmark periodic flow dataset, we show that competitive results can be achieved using non-probabilistic autoencoder approaches that either promote orthogonality or penalize correlation between latent variables. Compared to probabilistic autoencoders, these approaches offer more robustness with respect to the choice of hyperparameters entering the loss function. We further demonstrate the ability of a non-probabilistic approach to identify a reduced number of active latent variables by introducing a correlation penalty, a function also known from the use of $\beta$-VAE. The investigated probabilistic and non-probabilistic autoencoder models are finally used for the dimensionality reduction of aircraft ditching loads, which serves as an industrial application in this work.

Machine Learning based Prediction of Ditching Loads

We present approaches to predict dynamic ditching loads on aircraft fuselages using machine learning. The employed learning procedure is structured into two parts, the reconstruction of the spatial loads using a convolutional autoencoder (CAE) and the transient evolution of these loads in a subsequent part. Different CAE strategies are assessed and combined with either long short-term memory (LSTM) networks or Koopman-operator based methods to predict the transient behaviour. The training data is compiled by an extension of the momentum method of von-Karman and Wagner and the rationale of the training approach is briefly summarised. The application included refers to a full-scale fuselage of a DLR-D150 aircraft for a range of horizontal and vertical approach velocities at 6{\deg} incidence. Results indicate a satisfactory level of predictive agreement for all four investigated surrogate models examined, with the combination of an LSTM and a deep decoder CAE showing the best performance.