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Abstract. This paper presents the results of the ensemble Riemannian data assimilation for relatively high-dimensional nonlinear dynamical systems, focusing on the chaotic Lorenz-96 model and a two-layer quasi-geostrophic (QG) model of atmospheric circulation. The analysis state in this approach is inferred from a joint distribution that optimally couples the background probability distribution and the likelihood function, enabling formal treatment of systematic biases without any Gaussian assumptions. Despite the risk of the curse of dimensionality in the computation of the coupling distribution, comparisons with the classic implementation of the particle filter and the stochastic ensemble Kalman filter demonstrate that, with the same ensemble size, the presented methodology could improve the predictability of dynamical systems. In particular, under systematic errors, the root mean squared error of the analysis state can be reduced by 20 % (30 %) in the Lorenz-96 (QG) model. 

Abstract Aims We sought to investigate whether artificial intelligence (AI) and specifically deep neural networks (NNs) for electrocardiogram (ECG) signal analysis can be explained using human-selected features. We also sought to quantify such explainability and test if the AI model learns features that are similar to a human expert. Methods and results We used a set of 100 000 ECGs that were annotated by human explainable features. We applied both linear and non-linear models to predict published ECG AI models output for the detection of patients’ age and sex. We further used canonical correlation analysis to quantify the amount of shared information between the NN features and human-selected features. We reconstructed single human-selected ECG features from the unexplained NN features using a simple linear model. We noticed a strong correlation between the simple models and the AI output (R2 of 0.49–0.57 for the linear models and R2 of 0.69–0.70 for the non-linear models). We found that the correlation of the human explainable features with either 13 of the strongest age AI features or 15 of the strongest sex AI features was above 0.85 (for comparison, the first 14 principal components explain 90% of the human feature variance). We linearly reconstructed single human-selected ECG features from the AI features with R2 up to 0.86. Conclusion This work shows that NNs for ECG signals extract features in a similar manner to human experts and that they also generate additional novel features that help achieve superior performance. 

Abstract. In this paper, we present an ensemble data assimilation paradigm over a Riemannian manifold equipped with the Wasserstein metric. Unlike the Euclidean distance used in classic data assimilation methodologies, the Wasserstein metric can capture the translation and difference between the shapes of square-integrable probability distributions of the background state and observations. This enables us to formally penalize geophysical biases in state space with non-Gaussian distributions. The new approach is applied to dissipative and chaotic evolutionary dynamics, and its potential advantages and limitations are highlighted compared to the classic ensemble data assimilation approaches under systematic errors. 

We propose a neural network for unsupervised anomaly detection with a novel robust subspace recovery layer (RSR layer). This layer seeks to extract the underlying subspace from a latent representation of the given data and removes outliers that lie away from this subspace. It is used within an autoencoder. The encoder maps the data into a latent space, from which the RSR layer extracts the subspace. The decoder then smoothly maps back the underlying subspace to a “manifold” close to the original inliers. Inliers and outliers are distinguished according to the distances between the original and mapped positions (small for inliers and large for outliers). Extensive numerical experiments with both image and document datasets demonstrate state-of-the-art precision and recall. 

Generative networks have made it possible to generate meaningful signals such as images and texts from simple noise. Recently, generative methods based on GAN and VAE were developed for graphs and graph signals. However, the mathematical properties of these methods are unclear, and training good generative models is difficult. This work proposes a graph generation model that uses a recent adaptation of Mallat's scattering transform to graphs. The proposed model is naturally composed of an encoder and a decoder. The encoder is a Gaussianized graph scattering transform, which is robust to signal and graph manipulation. The decoder is a simple fully connected network that is adapted to specific tasks, such as link prediction, signal generation on graphs and full graph and signal generation. The training of our proposed system is efficient since it is only applied to the decoder and the hardware requirements are moderate. Numerical results demonstrate state-of-the-art performance of the proposed system for both link prediction and graph and signal generation.