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We propose a new approach to Generative Adversarial Networks (GANs) to achieve an improved performance with additional robustness to its so-called and well recognized mode collapse. We first proceed by mapping the desired data onto a…

We developed a new class of physics-informed generative adversarial networks (PI-GANs) to solve in a unified manner forward, inverse and mixed stochastic problems based on a limited number of scattered measurements. Unlike standard GANs…

Generative Adversarial Networks (GANs) have gained momentum for their ability to model image distributions. They learn to emulate the training set and that enables sampling from that domain and using the knowledge learned for useful…

Generative adversarial networks (GANs) are a novel approach to generative modelling, a task whose goal it is to learn a distribution of real data points. They have often proved difficult to train: GANs are unlike many techniques in machine…

Current Generative Adversarial Network (GAN)-based approaches for time series generation face challenges such as suboptimal convergence, information loss in embedding spaces, and instability. To overcome these challenges, we introduce an…

Vision-Language Latent Diffusion Models (LDMs) (Rombach et al., 2022) provide powerful generative priors for inverse problems. However, existing LDM-based inverse solvers typically require a large number of neural function evaluations…

This paper studies how well generative adversarial networks (GANs) learn probability distributions from finite samples. Our main results establish the convergence rates of GANs under a collection of integral probability metrics defined…

We investigate the impact of the input dimension on the generalization error in generative adversarial networks (GANs). In particular, we first provide both theoretical and practical evidence to validate the existence of an optimal input…

Inverse scattering problems are inherently challenging, given the fact they are ill-posed and nonlinear. This paper presents a powerful deep learning-based approach that relies on generative adversarial networks to accurately and…

Achievement of solutions in Navier-Stokes equation is one of challenging quests, especially for its closure problem. For achievement of particular solutions, there are variety of numerical simulations including Direct Numerical Simulation…

Implicit generative models have the capability to learn arbitrary complex data distributions. On the downside, training requires telling apart real data from artificially-generated ones using adversarial discriminators, leading to unstable…

In generative modeling, numerous successful approaches leverage a low-dimensional latent space, e.g., Stable Diffusion models the latent space induced by an encoder and generates images through a paired decoder. Although the selection of…

The field of image generation through generative modelling is abundantly discussed nowadays. It can be used for various applications, such as up-scaling existing images, creating non-existing objects, such as interior design scenes,…

Generative adversarial networks (GANs) have proven effective in modeling distributions of high-dimensional data. However, their training instability is a well-known hindrance to convergence, which results in practical challenges in their…

Image generation has been heavily investigated in computer vision, where one core research challenge is to generate images from arbitrarily complex distributions with little supervision. Generative Adversarial Networks (GANs) as an implicit…

Generative Adversarial Networks (GANs) have been impactful on many problems and applications but suffer from unstable training. The Wasserstein GAN (WGAN) leverages the Wasserstein distance to avoid the caveats in the minmax two-player…

Generative learning generates high dimensional data based on low dimensional conditions, also called prompts. Therefore, generative learning algorithms are eligible for solving (Bayesian) inverse problems. In this article we compare a…

Generative adversarial networks (GANs) are a machine learning framework comprising a generative model for sampling from a target distribution and a discriminative model for evaluating the proximity of a sample to the target distribution.…

Bayesian Generative AI (BayesGen-AI) methods are developed and applied to Bayesian computation. BayesGen-AI reconstructs the posterior distribution by directly modeling the parameter of interest as a mapping (a.k.a. deep learner) from a…

Inferring the latent variable generating a given test sample is a challenging problem in Generative Adversarial Networks (GANs). In this paper, we propose InvGAN - a novel framework for solving the inference problem in GANs, which involves…