Performing data assimilation (DA) at low cost is of prime concern in Earth system modeling, particularly in the era of Big Data, where huge quantities of observations are available. Capitalizing on the ability of neural network techniques to approximate the solution of partial differential equations (PDEs), we incorporate deep learning (DL) methods into a DA framework. More precisely, we exploit the latent structure provided by autoencoders (AEs) to design an ensemble transform Kalman filter with model error (ETKF‐Q) in the latent space. Model dynamics are also propagated within the latent space via a surrogate neural network. This novel ETKF‐Q‐Latent (ETKF‐Q‐L) algorithm is tested on a tailored instructional version of Lorenz 96 equations, named the augmented Lorenz 96 system, which possesses a latent structure that accurately represents the observed dynamics. Numerical experiments based on this particular system evidence that the ETKF‐Q‐L approach both reduces the computational cost and provides better accuracy than state‐of‐the‐art algorithms such as the ETKF‐Q.
Deep neural networks (DNNs) have proven to be powerful tools for processing unstructured data. However for high-dimensional data, like images, they are inherently vulnerable to adversarial attacks. Small almost invisible perturbations added to the input can be used to fool DNNs. Various attacks, hardening methods and detection methods have been introduced in recent years. Notoriously, Carlini-Wagner (CW) type attacks computed by iterative minimization belong to those that are most difficult to detect. In this work, we demonstrate that such iterative minimization attacks can by used as detectors themselves. Thus, in some sense we show that one can fight fire with fire. This work also outlines a mathematical proof that under certain assumptions this detector provides asymptotically optimal separation of original and attacked images. In numerical experiments, we obtain AUROC values up to 99.73% for our detection method. This distinctly surpasses state of the art detection rates for CW attacks from the literature. We also give numerical evidence that our method is robust against the attacker's choice of the method of attack.
Deep neural networks (DNNs) have proven to be powerful tools for processing unstructured data. However, for high-dimensional data, like images, they are inherently vulnerable to adversarial attacks. Small almost invisible perturbations added to the input can be used to fool DNNs. Various attacks, hardening methods and detection methods have been introduced in recent years. Notoriously, Carlini–Wagner (CW)-type attacks computed by iterative minimization belong to those that are most difficult to detect. In this work we outline a mathematical proof that the CW attack can be used as a detector itself. That is, under certain assumptions and in the limit of attack iterations this detector provides asymptotically optimal separation of original and attacked images. In numerical experiments, we experimentally validate this statement and furthermore obtain AUROC values up to $$99.73\%$$ 99.73 % on CIFAR10 and ImageNet. This is in the upper part of the spectrum of current state-of-the-art detection rates for CW attacks.
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