Related papers: Adversarial Autoencoders in Operator Learning

Hyperparameters searches are computationally expensive. This paper studies some general choices of hyperparameters and training methods specifically for operator learning. It considers the architectures DeepONets, Fourier neural operators…

Koopman autoencoders are a prevalent architecture in operator learning. But, the loss functions and the form of the operator vary significantly in the literature. This paper presents a fair and systemic study of these options. Furthermore,…

To combat against adversarial attacks, autoencoder structure is widely used to perform denoising which is regarded as gradient masking. In this paper, we revisit the role of autoencoders in adversarial settings. Through the comprehensive…

Operator learning provides methods to approximate mappings between infinite-dimensional function spaces. Deep operator networks (DeepONets) are a notable architecture in this field. Recently, an extension of DeepONet based on model…

Recent research showed that deep neural networks are highly sensitive to so-called adversarial perturbations, which are tiny perturbations of the input data purposely designed to fool a machine learning classifier. Most classification…

Deep learning models, while achieving state-of-the-art performance on many tasks, are susceptible to adversarial attacks that exploit inherent vulnerabilities in their architectures. Adversarial attacks manipulate the input data with…

This paper explores a simple question: can we model the internal transformations of a neural network using dynamical systems theory? We introduce Koopman autoencoders to capture how neural representations evolve through network layers,…

Reduced order modelling relies on representing complex dynamical systems using simplified modes, which can be achieved through Koopman operator analysis. However, computing Koopman eigen pairs for high-dimensional observable data can be…

Adversarial attack methods have demonstrated the fragility of deep neural networks. Their imperceptible perturbations are frequently able fool classifiers into potentially dangerous misclassifications. We propose a novel way to interpret…

Defending against physical adversarial attacks is a rapidly growing topic in deep learning and computer vision. Prominent forms of physical adversarial attacks, such as overlaid adversarial patches and objects, share similarities with…

Autonomous driving technologies have received notable attention in the past decades. In autonomous driving systems, identifying a precise dynamical model for motion control is nontrivial due to the strong nonlinearity and uncertainty in…

A new data-driven method for operator learning of stochastic differential equations(SDE) is proposed in this paper. The central goal is to solve forward and inverse stochastic problems more effectively using limited data. Deep operator…

Koopman operator theory, a powerful framework for discovering the underlying dynamics of nonlinear dynamical systems, was recently shown to be intimately connected with neural network training. In this work, we take the first steps in…

We investigate adversarial attacks for autoencoders. We propose a procedure that distorts the input image to mislead the autoencoder in reconstructing a completely different target image. We attack the internal latent representations,…

Reliably detecting anomalies in a given set of images is a task of high practical relevance for visual quality inspection, surveillance, or medical image analysis. Autoencoder neural networks learn to reconstruct normal images, and hence…

We present a mechanism for detecting adversarial examples based on data representations taken from the hidden layers of the target network. For this purpose, we train individual autoencoders at intermediate layers of the target network.…

Anomaly detection is a challenging task for machine learning algorithms due to the inherent class imbalance. It is costly and time-demanding to manually analyse the observed data, thus usually only few known anomalies if any are available.…

Machine Learning models are vulnerable to adversarial attacks that rely on perturbing the input data. This work proposes a novel strategy using Autoencoder Deep Neural Networks to defend a machine learning model against two gradient-based…

Operator learning techniques have recently emerged as a powerful tool for learning maps between infinite-dimensional Banach spaces. Trained under appropriate constraints, they can also be effective in learning the solution operator of…

Deep neural networks are vulnerable to small input perturbations known as adversarial attacks. Inspired by the fact that these adversaries are constructed by iteratively minimizing the confidence of a network for the true class label, we…