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Recently, researchers have utilized neural networks to accurately solve partial differential equations (PDEs), enabling the mesh-free method for scientific computation. Unfortunately, the network performance drops when encountering a high…

Generative Adversarial Networks (GANs) have been shown to be powerful and flexible priors when solving inverse problems. One challenge of using them is overcoming representation error, the fundamental limitation of the network in…

Generative adversarial networks (GANs) have made impressive advances in image generation, but they often require large-scale training data to avoid degradation caused by discriminator overfitting. To tackle this issue, we investigate the…

The control of nonlinear systems with unknown dynamics has been a significant field of research for many years. This paper presents a novel data-driven optimal adaptive control structure with less control effort and faster adaptation than…

Recent years have witnessed the rapid progress of generative adversarial networks (GANs). However, the success of the GAN models hinges on a large amount of training data. This work proposes a regularization approach for training robust GAN…

This study delves into the application of Generative Adversarial Networks (GANs) within the context of imbalanced datasets. Our primary aim is to enhance the performance and stability of GANs in such datasets. In pursuit of this objective,…

While Generative Adversarial Networks (GANs) achieve spectacular results on unstructured data like images, there is still a gap on tabular data, data for which state of the art supervised learning still favours to a large extent decision…

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…

Generative adversarial networks (GANs) have shown promising results when applied on partial differential equations and financial time series generation. We investigate if GANs can also be used to approximate one-dimensional Ito stochastic…

Deep neural networks (DNN) have been used to model nonlinear relations between physical quantities. Those DNNs are embedded in physical systems described by partial differential equations (PDE) and trained by minimizing a loss function that…

This work addresses the accurate and efficient simulation of physical phenomena governed by parametric Partial Differential Equations (PDEs) characterized by varying boundary conditions, where parametric instances modify not only the…

Deep learning models are increasingly deployed in safety-critical tasks where predictions must satisfy hard constraints, such as physical laws, fairness requirements, or safety limits. However, standard architectures lack built-in…

In this paper, we study the generative models of sequential discrete data. To tackle the exposure bias problem inherent in maximum likelihood estimation (MLE), generative adversarial networks (GANs) are introduced to penalize the…

Generative adversarial networks (GANs) have shown great success in applications such as image generation and inpainting. However, they typically require large datasets, which are often not available, especially in the context of prediction…

We propose Graphical Generative Adversarial Networks (Graphical-GAN) to model structured data. Graphical-GAN conjoins the power of Bayesian networks on compactly representing the dependency structures among random variables and that of…

The instability of Generative Adversarial Network (GAN) training has frequently been attributed to gradient descent. Consequently, recent methods have aimed to tailor the models and training procedures to stabilise the discrete updates. In…

Solving inverse problems in scientific and engineering fields has long been intriguing and holds great potential for many applications, yet most techniques still struggle to address issues such as high dimensionality, nonlinearity and model…

We propose Unbalanced GANs, which pre-trains the generator of the generative adversarial network (GAN) using variational autoencoder (VAE). We guarantee the stable training of the generator by preventing the faster convergence of the…

Recently a type of neural networks called Generative Adversarial Networks (GANs) has been proposed as a solution for fast generation of simulation-like datasets, in an attempt to bypass heavy computations and expensive cosmological…

Modelling dependencies between climate extremes is important for climate risk assessment, for instance when allocating emergency management funds. In statistics, multivariate extreme value theory is often used to model spatial extremes.…