Neural Fields for Interactive Visualization of Statistical Dependencies in 3D Simulation Ensembles

We present the first neural network that has learned to compactly represent and can efficiently reconstruct the statistical dependencies between the values of physical variables at different spatial locations in large 3D simulation ensembles. Going beyond linear dependencies, we consider mutual information as a measure of non-linear dependence. We demonstrate learning and reconstruction with a large weather forecast ensemble comprising 1000 members, each storing multiple physical variables at a 250 x 352 x 20 simulation grid. By circumventing compute-intensive statistical estimators at runtime, we demonstrate significantly reduced memory and computation requirements for reconstructing the major dependence structures. This enables embedding the estimator into a GPU-accelerated direct volume renderer and interactively visualizing all mutual dependencies for a selected domain point

Postprocessing of Ensemble Weather Forecasts Using Permutation-invariant Neural Networks

Statistical postprocessing is used to translate ensembles of raw numerical weather forecasts into reliable probabilistic forecast distributions. In this study, we examine the use of permutation-invariant neural networks for this task. In contrast to previous approaches, which often operate on ensemble summary statistics and dismiss details of the ensemble distribution, we propose networks which treat forecast ensembles as a set of unordered member forecasts and learn link functions that are by design invariant to permutations of the member ordering. We evaluate the quality of the obtained forecast distributions in terms of calibration and sharpness, and compare the models against classical and neural network-based benchmark methods. In case studies addressing the postprocessing of surface temperature and wind gust forecasts, we demonstrate state-of-the-art prediction quality. To deepen the understanding of the learned inference process, we further propose a permutation-based importance analysis for ensemble-valued predictors, which highlights specific aspects of the ensemble forecast that are considered important by the trained postprocessing models. Our results suggest that most of the relevant information is contained in few ensemble-internal degrees of freedom, which may impact the design of future ensemble forecasting and postprocessing systems.Comment: Submitted to Artificial Intelligence for the Earth System

An Emergent Space for Distributed Data with Hidden Internal Order through Manifold Learning

Manifold-learning techniques are routinely used in mining complex spatiotemporal data to extract useful, parsimonious data representations/parametrizations; these are, in turn, useful in nonlinear model identification tasks. We focus here on the case of time series data that can ultimately be modelled as a spatially distributed system (e.g. a partial differential equation, PDE), but where we do not know the space in which this PDE should be formulated. Hence, even the spatial coordinates for the distributed system themselves need to be identified - to emerge from - the data mining process. We will first validate this emergent space reconstruction for time series sampled without space labels in known PDEs; this brings up the issue of observability of physical space from temporal observation data, and the transition from spatially resolved to lumped (order-parameter-based) representations by tuning the scale of the data mining kernels. We will then present actual emergent space discovery illustrations. Our illustrative examples include chimera states (states of coexisting coherent and incoherent dynamics), and chaotic as well as quasiperiodic spatiotemporal dynamics, arising in partial differential equations and/or in heterogeneous networks. We also discuss how data-driven spatial coordinates can be extracted in ways invariant to the nature of the measuring instrument. Such gauge-invariant data mining can go beyond the fusion of heterogeneous observations of the same system, to the possible matching of apparently different systems