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Generative adversarial networks (GANs) have emerged as a powerful tool for generating high-fidelity data. However, the main bottleneck of existing approaches is the lack of supervision on the generator training, which often results in…
Operator learning offers a robust framework for approximating mappings between infinite-dimensional function spaces. It has also become a powerful tool for solving inverse problems in the computational sciences. This chapter surveys…
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…
The generative adversarial network (GAN) aims to approximate an unknown distribution via a parameterized neural network (NN). While GANs have been widely applied in reinforcement and semi-supervised learning as well as computer vision…
We introduce Kernel Density Discrimination GAN (KDD GAN), a novel method for generative adversarial learning. KDD GAN formulates the training as a likelihood ratio optimization problem where the data distributions are written explicitly via…
We propose a framework of generative adversarial networks with multiple discriminators, which collaborate to represent a real dataset more effectively. Our approach facilitates learning a generator consistent with the underlying data…
Generative adversarial networks (GANs) have emerged as a powerful unsupervised method to model the statistical patterns of real-world data sets, such as natural images. These networks are trained to map random inputs in their latent space…
Generative Adversarial Networks (GANs) have made great progress in synthesizing realistic images in recent years. However, they are often trained on image datasets with either too few samples or too many classes belonging to different data…
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…
Deep generative models have achieved impressive success in recent years. Generative Adversarial Networks (GANs) and Variational Autoencoders (VAEs), as emerging families for generative model learning, have largely been considered as two…
Neural network based data-driven operator learning schemes have shown tremendous potential in computational mechanics. DeepONet is one such neural network architecture which has gained widespread appreciation owing to its excellent…
Generative adversarial networks (GANs) have given us a great tool to fit implicit generative models to data. Implicit distributions are ones we can sample from easily, and take derivatives of samples with respect to model parameters. These…
The goal of anomaly detection is to identify anomalous samples from normal ones. In this paper, a small number of anomalies are assumed to be available at the training stage, but they are assumed to be collected only from several anomaly…
Deep neural networks have been successful in diverse discriminative classification tasks, although, they are poorly calibrated often assigning high probability to misclassified predictions. Potential consequences could lead to…
We investigate the problem of sampling from posterior distributions with intractable normalizing constants in Bayesian inference. Our solution is a new generative modeling approach based on optimal transport (OT) that learns a deterministic…
Generative adversarial networks (GANs) are a method based on the training of two neural networks, one called generator and the other discriminator, competing with each other to generate new instances that resemble those of the probability…
Image-to-image translation is an ill-posed problem as unique one-to-one mapping may not exist between the source and target images. Learning-based methods proposed in this context often evaluate the performance on test data that is similar…
Characterizing statistical properties of solutions of inverse problems is essential for decision making. Bayesian inversion offers a tractable framework for this purpose, but current approaches are computationally unfeasible for most…
Network embedding has become a hot research topic recently which can provide low-dimensional feature representations for many machine learning applications. Current work focuses on either (1) whether the embedding is designed as an…
Inverting a Generative Adversarial Network (GAN) facilitates a wide range of image editing tasks using pre-trained generators. Existing methods typically employ the latent space of GANs as the inversion space yet observe the insufficient…