Computational Fluid Dynamics (CFD) plays a pivotal role in fluid mechanics, enabling precise simulations of fluid behavior through partial differential equations (PDEs). However, traditional CFD methods are resource-intensive, particularly for high-fidelity simulations of complex flows, which are further complicated by high dimensionality, inherent stochasticity, and limited data availability. This paper addresses these challenges by proposing a data-driven approach that leverages a Gaussian Mixture Variational Autoencoder (GMVAE) to encode high-dimensional scientific data into low-dimensional, physically meaningful representations. The GMVAE learns a structured latent space where data can be categorized based on physical properties such as the Reynolds number while maintaining global physical consistency. To assess the interpretability of the learned representations, we introduce a novel metric based on graph spectral theory, quantifying the smoothness of physical quantities along the latent manifold. We validate our approach using 2D Navier-Stokes simulations of flow past a cylinder over a range of Reynolds numbers. Our results demonstrate that the GMVAE provides improved clustering, meaningful latent structure, and robust generative capabilities compared to baseline dimensionality reduction methods. This framework offers a promising direction for data-driven turbulence modeling and broader applications in computational fluid dynamics and engineering systems.

We present latent combinational game design -- an approach for generating playable games that blend a given set of games in a desired combination using deep generative latent variable models. We use Gaussian Mixture Variational Autoencoders (GMVAEs) which model the VAE latent space via a mixture of Gaussian components. Through supervised training, each component encodes levels from one game and lets us define blended games as linear combinations of these components. This enables generating new games that blend the input games as well as controlling the relative proportions of each game in the blend. We also extend prior blending work using conditional VAEs and compare against the GMVAE and additionally introduce a hybrid conditional GMVAE (CGMVAE) architecture which lets us generate whole blended levels and layouts. Results show that these approaches can generate playable games that blend the input games in specified combinations. We use both platformers and dungeon-based games to demonstrate our results.

Variational autoencoders (VAEs) have been shown to be able to generate game levels but require manual exploration of the learned latent space to generate outputs with desired attributes. While conditional VAEs address this by allowing generation to be conditioned on labels, such labels have to be provided during training and thus require prior knowledge which may not always be available. In this paper, we apply Gaussian Mixture VAEs (GMVAEs), a variant of the VAE which imposes a mixture of Gaussians (GM) on the latent space, unlike regular VAEs which impose a unimodal Gaussian. This allows GMVAEs to cluster levels in an unsupervised manner using the components of the GM and then generate new levels using the learned components. We demonstrate our approach with levels from Super Mario Bros., Kid Icarus and Mega Man. Our results show that the learned components discover and cluster level structures and patterns and can be used to generate levels with desired characteristics.

In inference, open-set classification is to either classify a sample into a known class from training or reject it as an unknown class. Existing deep open-set classifiers train explicit closed-set classifiers, in some cases disjointly utilizing reconstruction, which we find dilutes the latent representation's ability to distinguish unknown classes. In contrast, we train our model to cooperatively learn reconstruction and perform class-based clustering in the latent space. With this, our Gaussian mixture variational autoencoder (GMVAE) achieves more accurate and robust open-set classification results, with an average F1 improvement of 29.5%, through extensive experiments aided by analytical results.

We study a variant of the variational autoencoder model (VAE) with a Gaussian mixture as a prior distribution, with the goal of performing unsupervised clustering through deep generative models. We observe that the known problem of over-regularisation that has been shown to arise in regular VAEs also manifests itself in our model and leads to cluster degeneracy. We show that a heuristic called minimum information constraint that has been shown to mitigate this effect in VAEs can also be applied to improve unsupervised clustering performance with our model. Furthermore we analyse the effect of this heuristic and provide an intuition of the various processes with the help of visualizations. Finally, we demonstrate the performance of our model on synthetic data, MNIST and SVHN, showing that the obtained clusters are distinct, interpretable and result in achieving competitive performance on unsupervised clustering to the state-of-the-art results.