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We develop Riemannian approaches to variational autoencoders (VAEs) for PDE-type ambient data with regularizing geometric latent dynamics, which we refer to as VAE-DLM, or VAEs with dynamical latent manifolds. We redevelop the VAE framework…

The use of machine learning to generate synthetic data has grown in popularity with the proliferation of text-to-image models and especially large language models. The core methodology these models use is to learn the distribution of the…

Variational Autoencoders (VAEs) are expressive latent variable models that can be used to learn complex probability distributions from training data. However, the quality of the resulting model crucially relies on the expressiveness of the…

Variational Autoencoders (VAE) are probabilistic deep generative models underpinned by elegant theory, stable training processes, and meaningful manifold representations. However, they produce blurry images due to a lack of explicit…

We present a generative AI algorithm for addressing the pressing task of fast, accurate, and robust statistical computation of three-dimensional turbulent fluid flows. Our algorithm, termed as GenCFD, is based on an end-to-end conditional…

We use a data-driven approach to model a three-dimensional turbulent flow using cutting-edge Deep Learning techniques. The deep learning framework incorporates physical constraints on the flow, such as preserving incompressibility and…

Variational Autoencoders (VAEs) have been a pioneering force in the realm of deep generative models. Amongst its legions of progenies, Wasserstein Autoencoders (WAEs) stand out in particular due to the dual offering of heightened generative…

Complex turbulent flow simulations are an integral aspect of the engineering design process. The mainstay of these simulations is represented by eddy viscosity based turbulence models. Eddy viscosity models are computationally cheap due to…

Variational autoencoders (VAEs) are essential tools in end-to-end representation learning. However, the sequential text generation common pitfall with VAEs is that the model tends to ignore latent variables with a strong auto-regressive…

The Reynolds-averaged Navier-Stokes (RANS) equations are widely used in turbulence applications. They require accurately modeling the anisotropic Reynolds stress tensor, for which traditional Reynolds stress closure models only yield…

The use of Variational Autoencoders in different Machine Learning tasks has drastically increased in the last years. They have been developed as denoising, clustering and generative tools, highlighting a large potential in a wide range of…

Variational autoencoders (VAE) represent a popular, flexible form of deep generative model that can be stochastically fit to samples from a given random process using an information-theoretic variational bound on the true underlying…

Recently, deep generative models have become increasingly popular in unsupervised anomaly detection. However, deep generative models aim at recovering the data distribution rather than detecting anomalies. Besides, deep generative models…

Physics-integrated generative modeling is a class of hybrid or grey-box modeling in which we augment the the data-driven model with the physics knowledge governing the data distribution. The use of physics knowledge allows the generative…

Generative Adversarial Networks (GANs) have experienced a recent surge in popularity, performing competitively in a variety of tasks, especially in computer vision. However, GAN training has shown limited success in natural language…

The generative autoencoders, such as the variational autoencoders or the adversarial autoencoders, have achieved great success in lots of real-world applications, including image generation, and signal communication. However, little concern…

A long-standing question for urban and regional planners pertains to the ability to describe urban patterns quantitatively. Cities' transport infrastructure, particularly street networks, provides an invaluable source of information about…

Developing reduced-order models applicable to fluid-dynamics problems involving complex geometries and different flow conditions remains a critical challenge for turbulent flows. This study introduces VIVALDy, a novel machine-learning…

Generative adversarial networks (GANs) were initially proposed to generate images by learning from a large number of samples. Recently, GANs have been used to emulate complex physical systems such as turbulent flows. However, a critical…

Noting the importance of the latent variables in inference and learning, we propose a novel framework for autoencoders based on the homeomorphic transformation of latent variables, which could reduce the distance between vectors in the…