Ibrahim Hoteit

Loïc Giraldi, Olivier P. Le Maître, Ibrahim Hoteit et al.

Optimal dimensionality reduction methods are proposed for the Bayesian inference of a Gaussian linear model with additive noise in presence of overabundant data. Three different optimal projections of the observations are proposed based on information theory: the projection that minimizes the Kullback-Leibler divergence between the posterior distributions of the original and the projected models, the one that minimizes the expected Kullback-Leibler divergence between the same distributions, and the one that maximizes the mutual information between the parameter of interest and the projected observations. The first two optimization problems are formulated as the determination of an optimal subspace and therefore the solution is computed using Riemannian optimization algorithms on the Grassmann manifold. Regarding the maximization of the mutual information, it is shown that there exists an optimal subspace that minimizes the entropy of the posterior distribution of the reduced model; a basis of the subspace can be computed as the solution to a generalized eigenvalue problem; an a priori error estimate on the mutual information is available for this particular solution; and that the dimensionality of the subspace to exactly conserve the mutual information between the input and the output of the models is less than the number of parameters to be inferred. Numerical applications to linear and nonlinear models are used to assess the efficiency of the proposed approaches, and to highlight their advantages compared to standard approaches based on the principal component analysis of the observations.

Mohamad Abed El Rahman Hammoud, Naila Raboudi, Edriss S. Titi et al.

Data assimilation (DA) plays a pivotal role in diverse applications, ranging from climate predictions and weather forecasts to trajectory planning for autonomous vehicles. A prime example is the widely used ensemble Kalman filter (EnKF), which relies on linear updates to minimize variance among the ensemble of forecast states. Recent advancements have seen the emergence of deep learning approaches in this domain, primarily within a supervised learning framework. However, the adaptability of such models to untrained scenarios remains a challenge. In this study, we introduce a novel DA strategy that utilizes reinforcement learning (RL) to apply state corrections using full or partial observations of the state variables. Our investigation focuses on demonstrating this approach to the chaotic Lorenz '63 system, where the agent's objective is to minimize the root-mean-squared error between the observations and corresponding forecast states. Consequently, the agent develops a correction strategy, enhancing model forecasts based on available system state observations. Our strategy employs a stochastic action policy, enabling a Monte Carlo-based DA framework that relies on randomly sampling the policy to generate an ensemble of assimilated realizations. Results demonstrate that the developed RL algorithm performs favorably when compared to the EnKF. Additionally, we illustrate the agent's capability to assimilate non-Gaussian data, addressing a significant limitation of the EnKF.

Guozhong Li, Muhannad Alhumaidi, Spiros Skiadopoulos et al.

The generation of voluminous scientific data poses significant challenges for efficient storage, transfer, and analysis. Recently, error-bounded lossy compression methods emerged due to their ability to achieve high compression ratios while controlling data distortion. However, they often overlook the inherent spatial and temporal correlations within scientific data, thus missing opportunities for higher compression. In this paper we propose GRAPHCOMP, a novel graph-based method for error-bounded lossy compression of scientific data. We perform irregular segmentation of the original grid data and generate a graph representation that preserves the spatial and temporal correlations. Inspired by Graph Neural Networks (GNNs), we then propose a temporal graph autoencoder to learn latent representations that significantly reduce the size of the graph, effectively compressing the original data. Decompression reverses the process and utilizes the learnt graph model together with the latent representation to reconstruct an approximation of the original data. The decompressed data are guaranteed to satisfy a user-defined point-wise error bound. We compare our method against the state-of-the-art error-bounded lossy methods (i.e., HPEZ, SZ3.1, SPERR, and ZFP) on large-scale real and synthetic data. GRAPHCOMP consistently achieves the highest compression ratio across most datasets, outperforming the second-best method by margins ranging from 22% to 50%.

Shehzad Afzal, Sohaib Ghani, Hank C. Jenkins-Smith et al.

Public health officials dealing with pandemics like COVID-19 have to evaluate and prepare response plans. This planning phase requires not only looking into the spatiotemporal dynamics and impact of the pandemic using simulation models, but they also need to plan and ensure the availability of resources under different spread scenarios. To this end, we have developed a visual analytics environment that enables public health officials to model, simulate, and explore the spread of COVID-19 by supplying county-level information such as population, demographics, and hospital beds. This environment facilitates users to explore spatiotemporal model simulation data relevant to COVID-19 through a geospatial map with linked statistical views, apply different decision measures at different points in time, and understand their potential impact. Users can drill-down to county-level details such as the number of sicknesses, deaths, needs for hospitalization, and variations in these statistics over time. We demonstrate the usefulness of this environment through a use case study and also provide feedback from domain experts. We also provide details about future extensions and potential applications of this work.