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Generative models of graphs are well-known, but many existing models are limited in scalability and expressivity. We present a novel sequential graphical variational autoencoder operating directly on graphical representations of data. In…

Deriving governing equations of complex physical systems based on first principles can be quite challenging when there are certain unknown terms and hidden physical mechanisms in the systems. In this work, we apply a deep learning…

We present an algorithm to learn the relevant latent variables of a large-scale discretized physical system and predict its time evolution using thermodynamically-consistent deep neural networks. Our method relies on sparse autoencoders,…

This work introduces a learning-enhanced observer (LEO) for linear time-invariant systems with uncertain dynamics. Rather than relying solely on nominal models, the proposed framework treats the system matrices as optimizable variables and…

Turbulent flow fields are characterized by extreme events that are statistically intermittent and carry a significant amount of energy and physical importance. To emulate these flows, we introduce the extreme variational Autoencoder (xVAE),…

This work studies a macroscopic traffic flow model driven by a system of nonlinear hyperbolic partial differential equations. Using Lie symmetry analysis, we determine the infinitesimal generators and construct an optimal system of…

Variational autoencoder (VAE) estimates the posterior parameters (mean and variance) of latent variables corresponding to each input data. While it is used for many tasks, the transparency of the model is still an underlying issue. This…

Latent diffusion models have established a new state-of-the-art in high-resolution visual generation. Integrating Vision Foundation Model priors improves generative efficiency, yet existing latent designs remain largely heuristic. These…

Variational autoencoders (VAE) are directed generative models that learn factorial latent variables. As noted by Burda et al. (2015), these models exhibit the problem of factor over-pruning where a significant number of stochastic factors…

In today's digital world, the generation of vast amounts of streaming data in various domains has become ubiquitous. However, many of these data are unlabeled, making it challenging to identify events, particularly anomalies. This task…

Flow-based models have proven successful for time-series generation, particularly when defined in lower-dimensional latent spaces that enable efficient sampling. However, how to design latent representations with desirable equivariance…

Fluid turbulence is characterized by strong coupling across a broad range of scales. Furthermore, besides the usual local cascades, such coupling may extend to interactions that are non-local in scale-space. As such the computational…

Modern visual world modeling systems increasingly rely on high-capacity architectures and large-scale data to produce plausible motion, yet they often fail to preserve underlying 3D geometry or physically consistent camera dynamics. A key…

The Variational Autoencoder (VAE) is a seminal approach in deep generative modeling with latent variables. Interpreting its reconstruction process as a nonlinear transformation of samples from the latent posterior distribution, we apply the…

Time-lagged autoencoders (TAEs) have been proposed as a deep learning regression-based approach to the discovery of slow modes in dynamical systems. However, a rigorous analysis of nonlinear TAEs remains lacking. In this work, we discuss…

We present a method for learning latent stochastic differential equations (SDEs) from high-dimensional time series data. Given a high-dimensional time series generated from a lower dimensional latent unknown It\^o process, the proposed…

A variational autoencoder (VAE) derived from Tsallis statistics called q-VAE is proposed. In the proposed method, a standard VAE is employed to statistically extract latent space hidden in sampled data, and this latent space helps make…

Reduced order models (ROMs) play a critical role in fluid mechanics by providing low-cost predictions, making them an attractive tool for engineering applications. However, for ROMs to be widely applicable, they must not only generalise…

Variational autoencoders (VAEs) are widely used deep generative models capable of learning unsupervised latent representations of data. Such representations are often difficult to interpret or control. We consider the problem of…

The linear part of transient evoked (TE) otoacoustic emission (OAE) is thought to be generated via coherent reflection near the characteristic place of constituent wave components. Because of the tonotopic organization of the cochlea, high…