Explainable Binary Classification of Separable Shape Ensembles

Materials scientists utilize image segmentation of micrographs to create large curve ensembles representing grain boundaries of material microstructures. Observations of these collections of shapes can facilitate inferences about material properties and manufacturing processes. We seek to bolster this application, and related engineering/scientific tasks, using novel pattern recognition formalisms and inference over large ensembles of segmented curves -- i.e., facilitate principled assessments for quantifying differences in distributions of shapes. To this end, we apply a composite integral operator to motivate accurate and efficient numerical representations of discrete planar curves over matrix manifolds. The main result is a rigid-invariant orthonormal decomposition of curve component functions into separable forms of scale variations and complementary features of undulation. We demonstrate how these separable shape tensors -- given thousands of curves in an ensemble -- can inform explainable binary classification of segmented images by utilizing a product maximum mean discrepancy to distinguish the shape distributions; absent labelled data, building interpretable feature spaces in seconds without high performance computation, and detecting discrepancies below cursory visual inspections.

Super Resolution for Renewable Energy Resource Data With Wind From Reanalysis Data (Sup3rWind) and Application to Ukraine

With an increasing share of the electricity grid relying on wind to provide generating capacity and energy, there is an expanding global need for historically accurate high-resolution wind data. Conventional downscaling methods for generating these data have a high computational burden and require extensive tuning for historical accuracy. In this work, we present a novel deep learning-based spatiotemporal downscaling method, using generative adversarial networks (GANs), for generating historically accurate high-resolution wind resource data from the European Centre for Medium-Range Weather Forecasting Reanalysis version 5 data (ERA5). We achieve results comparable in historical accuracy and spatiotemporal variability to conventional downscaling by training a GAN model with ERA5 low-resolution input and high-resolution targets from the Wind Integration National Dataset, while reducing computational costs over dynamical downscaling by two orders of magnitude. Spatiotemporal cross-validation shows low error and high correlations with observations and excellent agreement with holdout data across distributions of physical metrics. We apply this approach to downscale 30-km hourly ERA5 data to 2-km 5-minute wind data for January 2000 through December 2023 at multiple hub heights over Eastern Europe. Uncertainty is estimated over the period with observational data by additionally downscaling the members of the European Centre for Medium-Range Weather Forecasting Ensemble of Data Assimilations. Comparisons against observational data from the Meteorological Assimilation Data Ingest System and multiple wind farms show comparable performance to the CONUS validation. This 24-year data record is the first member of the super resolution for renewable energy resource data with wind from reanalysis data dataset (Sup3rWind).

GANISP: a GAN-assisted Importance SPlitting Probability Estimator

Designing manufacturing processes with high yield and strong reliability relies on effective methods for rare event estimation. Genealogical importance splitting reduces the variance of rare event probability estimators by iteratively selecting and replicating realizations that are headed towards a rare event. The replication step is difficult when applied to deterministic systems where the initial conditions of the offspring realizations need to be modified. Typically, a random perturbation is applied to the offspring to differentiate their trajectory from the parent realization. However, this random perturbation strategy may be effective for some systems while failing for others, preventing variance reduction in the probability estimate. This work seeks to address this limitation using a generative model such as a Generative Adversarial Network (GAN) to generate perturbations that are consistent with the attractor of the dynamical system. The proposed GAN-assisted Importance SPlitting method (GANISP) improves the variance reduction for the system targeted. An implementation of the method is available in a companion repository (https://github.com/NREL/GANISP).

Adversarial sampling of unknown and high-dimensional conditional distributions

Many engineering problems require the prediction of realization-to-realization variability or a refined description of modeled quantities. In that case, it is necessary to sample elements from unknown high-dimensional spaces with possibly millions of degrees of freedom. While there exist methods able to sample elements from probability density functions (PDF) with known shapes, several approximations need to be made when the distribution is unknown. In this paper the sampling method, as well as the inference of the underlying distribution, are both handled with a data-driven method known as generative adversarial networks (GAN), which trains two competing neural networks to produce a network that can effectively generate samples from the training set distribution. In practice, it is often necessary to draw samples from conditional distributions. When the conditional variables are continuous, only one (if any) data point corresponding to a particular value of a conditioning variable may be available, which is not sufficient to estimate the conditional distribution. This work handles this problem using an a priori estimation of the conditional moments of a PDF. Two approaches, stochastic estimation, and an external neural network are compared here for computing these moments; however, any preferred method can be used. The algorithm is demonstrated in the case of the deconvolution of a filtered turbulent flow field. It is shown that all the versions of the proposed algorithm effectively sample the target conditional distribution with minimal impact on the quality of the samples compared to state-of-the-art methods. Additionally, the procedure can be used as a metric for the diversity of samples generated by a conditional GAN (cGAN) conditioned with continuous variables.