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All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Wasserstein normalized autoencoder for anomaly detection

A novel anomaly detection algorithm is presented. The Wasserstein normalized autoencoder (WNAE) is a normalized probabilistic model that minimizes the Wasserstein distance between the learned probability distribution—a Boltzmann distribution where the energy is the reconstruction error of the autoencoder (AE)—and the distribution of the training data. This algorithm has been developed and applied to the identification of semivisible jets—conical sprays of visible standard model (SM) particles and invisible dark matter states—with the CMS experiment at the CERN LHC. Trained on jets of particles from simulated SM processes, the WNAE is shown to learn the probability distribution of the input data in a fully unsupervised fashion, such that it effectively identifies new physics jets as anomalies. The model exhibits stable, convergent training and recovers strong classification performance for a wide range of signals against the selected background process, for which a standard AE fails because of outlier reconstruction. In addition, the model improves upon standard normalized autoencoders while remaining fully agnostic to the signal. The WNAE directly tackles the problem of outlier reconstruction, a common failure mode of autoencoders in anomaly detection tasks.

Hayrapetyan, Aram [Yerevan Phys. Inst.]↗
DOE OSTI2026

Wasserstein Normalized Autoencoder for Anomaly Detection in ProtoDUNE Vertical-Drift Detector

ProtoDUNE Vertical Drift needs a selective triggering algorithm. The detector sits on Earth's surface, so cosmic activity dominates its data. Our goal in this paper is to trigger on neutrino events more robustly than the current deployed Analog-to-Digital Converter Simple Window (ADCSW) model and, eventually, search for signals of Beyond Standard Model (BSM) physics at DUNE as our ultimate North Star objective. As a step towards this goal, we evaluate a Wasserstein Normalized Autoencoder (WNAE) on simulated collection-plane only windows of shape $1\times10\times10$ where Neutrinos act as our BSM-proxy and Cosmic-ray Muons serve as our learned background. The network parameters are fitted using only cosmic-ray muon events as background in order to maintain an unsupervised pipeline. Training uses finite-step Langevin $x^-$ samples, positive-sample reconstruction energy, and an empirical sliced $2$-Wasserstein objective to learn a normalized Boltzmann energy model. We then calibrate on a nominal $5\,\mathrm{Hz}$ operating threshold calculated from cosmic validation data. Both WNAE and ADCSW accept 311 of 194,083 held-out cosmic background events at this $5\,\mathrm{Hz}$ threshold. We found that WNAE accepts 9,677 of 34,634 neutrino-proxy events $(27.9\pm0.24)\%$, compared with 10,076 $(29.1\pm0.24)\%$ for ADCSW, an observed WNAE-minus-ADCSW difference of $-1.15\%$. At another nominal $2\,\mathrm{Hz}$ target threshold, the corresponding efficiencies are $(20.5\pm0.22)\%$ and $(22.6\pm0.22)\%$, respectively. Of the WNAE-selected neutrino proxies at $5\,\mathrm{Hz}$, $(20.8\pm0.4)\%$ of the classified neutrino-proxy events are unique to WNAE, where the uncertainty is an absolute binomial standard error of $0.4\%$.

Zheng, Jake [U. Chicago (main)] (ORCID:00090002189↗
DOE OSTI2026

Wasserstein Normalized Autoencoder for Anomaly Detection in ProtoDUNE Vertical-Drift Detector

ProtoDUNE Vertical Drift needs a selective triggering algorithm. The detector sits on Earth's surface, so cosmic activity dominates its data. Our goal in this paper is to trigger on neutrino events more robustly than the current deployed Analog-to-Digital Converter Simple Window (ADCSW) model and, eventually, search for signals of Beyond Standard Model (BSM) physics at DUNE as our ultimate North Star objective. As a step towards this goal, we evaluate a Wasserstein Normalized Autoencoder (WNAE) on simulated collection-plane only windows of shape $1\times10\times10$ where Neutrinos act as our BSM-proxy and Cosmic-ray Muons serve as our learned background. The network parameters are fitted using only cosmic-ray muon events as background in order to maintain an unsupervised pipeline. Training uses finite-step Langevin $x^-$ samples, positive-sample reconstruction energy, and an empirical sliced $2$-Wasserstein objective to learn a normalized Boltzmann energy model. We then calibrate on a nominal $5\,\mathrm{Hz}$ operating threshold calculated from cosmic validation data. Both WNAE and ADCSW accept 311 of 194,083 held-out cosmic background events at this $5\,\mathrm{Hz}$ threshold. We found that WNAE accepts 9,677 of 34,634 neutrino-proxy events $(27.9\pm0.24)\%$, compared with 10,076 $(29.1\pm0.24)\%$ for ADCSW, an observed WNAE-minus-ADCSW difference of $-1.15\%$. At another nominal $2\,\mathrm{Hz}$ target threshold, the corresponding efficiencies are $(20.5\pm0.22)\%$ and $(22.6\pm0.22)\%$, respectively. Of the WNAE-selected neutrino proxies at $5\,\mathrm{Hz}$, $(20.8\pm0.4)\%$ of the classified neutrino-proxy events are unique to WNAE, where the uncertainty is an absolute binomial standard error of $0.4\%$.

Zheng, Jake [Chicago U.] (ORCID:0009000218901379)↗
DOE OSTI2025

Two-Stage Distributionally Robust Conic Linear Programming over 1-Wasserstein Balls

Here, this paper studies two-stage distributionally robust conic linear programming under constraint uncertainty over type-1 Wasserstein balls. We present optimality conditions for the dual of the worst-case expectation problem, which characterizes worst-case uncertain parameters for its inner maximization problem. This condition offers an alternative proof, a counterexample, and an extension to previous works. Additionally, the condition highlights the potential advantage of a specific distance metric for out-of-sample performance, as exemplified in a numerical study on a facility location problem with demand uncertainty. Furthermore, cutting-plane-based algorithms, equipped with a unified scenario generation framework, are proposed for addressing both unbounded support and second-stage dual feasible regions, with a finite convergence proof under less stringent assumptions.

Wasserstein↗
DOE OSTI2026

Neural Scaling Laws for Jet Generation

Recently observed empirical scaling laws describe the performance of foundation-type models as three independent key quantities -- dataset size, compute, and model parameters -- are modified. Extracting these scaling laws informs the training of large complex models for which the tuning of hyperparameters in traditional ways is not feasible. This work for the first time explores if scaling laws can also be observed for the task of particle jet generation -- both relevant as a pre-training objective for foundation models and as in-situ simulation by itself. We indeed replicate the key logarithmic scaling law behavior for model-size scaling. Beyond studying the next token prediction validation loss of the generative model, we also study the sliced Wasserstein distance of five physical quantities that are not immediately available to the model during training. Our study shows that this quantity is monotonically related to the next token prediction validation loss, meaning that this loss is indeed a good proxy for the physics performance. For the scaling with dataset size and compute, we observe substantially weaker scaling behavior of both the loss and the sliced Wasserstein distance. We analyze this behavior by introducing the concept of a learnable window, and argue that autoregressive next token prediction on jet constituents exhibits comparatively rapid saturation relative to language-model studies. We discuss possible origins of this behavior, including the stochastic nature of QCD radiation and differences between generative and supervised learning tasks in collider physics.

Amram, Oz [Fermilab]↗
DOE OSTI2025

Data efficiency assessment of generative adversarial networks in energy applications

This study investigates the data requirements of generative artificial intelligence (AI), particularly generative adversarial networks (GANs), for reliable data augmentation in energy applications. Generative AI, though seen as a solution to data limitations, requires substantial data to learn meaningful distributions—a challenge often overlooked. This study addresses the challenge through synthetic data generation for critical heat flux (CHF) and power grid demand, focusing on renewable and nuclear energy. Two variants of GAN employed are conditional GAN (cGAN) and Wasserstein GAN (wGAN). Our findings include the strong dependency of GAN on data size, with performance declining on smaller datasets and varying performance when generalizing to unseen experiments. Mass flux and heated length significantly influence CHF predictions. wGAN is more robust to feature exclusion, making it suitable for constrained synthetic data generation. In energy demand forecasting, wGAN performed well for solar, wind, and load predictions. Longer lookback hours and larger datasets improved predictions, especially for load power. Seasonal variations posed challenges, with wGAN achieving a relatively high error of Root Mean Squared Error (RMSE) of 0.32 for load power prediction, compared to RMSE of 0.07 under same-season conditions. Feature exclusions impacted cGAN the most, while wGAN showed greater robustness. This study concludes that, while generative AI is effective for data augmentation, it requires substantial data and careful training to generate realistic synthetic data and generalize to new experiments in engineering applications.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2026

Data-based filtered dissipation rate modelling for multi-modal turbulent combustion: evaluating a priori model generalizability

Manifold-based models offer a computationally efficient alternative to directly transporting the thermochemical state in computational simulations of turbulent reacting flows, projecting the high-dimensional thermochemical state-space onto a low-dimensional manifold. Recent efforts have yielded a manifold-based model applicable to multi-modal combustion, enabling reconstruction of the thermochemical state from solutions to two-dimensional manifold equations in mixture fraction and generalized progress variable that are parameterised by three scalar dissipation rates. In coarse-grained simulations such as Large Eddy Simulation (LES), closure of the multi-modal manifold equations and subfilter variances/covariance requires closure of three filtered scalar dissipation rates. Here, the present work adopts a data-based approach, providing closure for the three filtered scalar dissipation rates via deep neural networks (DNNs). High-fidelity datasets corresponding to an autoigniting n-dodecane jet flame and a bluff body swirl-stabilized confined lifted spray flame of two aviation fuels (Jet-A and C1) with different ignition propensities are leveraged to generate training data that spans a diverse range of thermodynamic conditions and combustion modes, including low- and high-temperature ignition regimes in addition to premixed and nonpremixed behaviour. A final DNN model is trained to enforce inherent physical constraints by learning nonlinear functional transformations of the three filtered scalar dissipation rates. The generalizability of this constrained DNN model is demonstrated a priori via conditional statistics evaluated on the lifted spray flame with C1–a configuration that had not been included in the training data. Excellent DNN agreement with conditional DNS statistics is observed, and integrated gradients are computed to identify the most sensitive input variables. The similarity of the marginal PDFs of the most informative input variables and outputs across configurations are quantified via the Wasserstein metric, demonstrating that data-based models may successfully generalize to unseen parametric conditions so long as the most informative input variables share similar distributions across training and testing datasets.

Data-based modelling↗
DOE OSTI2025

Learning with Adaptive Conservativeness for Distributionally Robust Optimization: Incentive Design for Voltage Regulation

Information asymmetry between the Distribution System Operator (DSO) and Distributed Energy Resource Aggregators (DERAs) obstructs designing effective incentives for voltage regulation. To capture this effect, we employ a Stackelberg game-theoretic framework, where the DSO seeks to overcome the information asymmetry and refine its incentive strategies by learning from DERA behavior over multiple iterations. We introduce a model-based online learning algorithm for the DSO, aimed at inferring the relationship between incentives and DERA responses. Given the uncertain nature of these responses, we also propose a distributionally robust incentive design model to control the probability of voltage regulation failure and then reformulate it into a convex problem. This model allows the DSO to periodically revise distribution assumptions on uncertain parameters in the decision model of the DERA. Finally, we present a gradient-based method that permits the DSO to adaptively modify its conservativeness level, measured by the size of a Wasserstein metric-based ambiguity set, according to historical voltage regulation performance. The effectiveness of our proposed method is demonstrated through numerical experiments.

adaptation models↗
DOE OSTI2026

Synthetic Atmospheric River Ensembles Generated by Deep-AR

This dataset contains 35,850 synthetic landfalling atmospheric river (AR) realizations generated by the Deep-AR two-stage deep-learning framework over the Northeast Pacific and U.S. West Coast. The archive contains 25 stochastic ensemble members for each of 1,434 held-out observed seed events. Each synthetic realization is initialized from conditions 48 hours before the corresponding observed AR landfall and is generated autoregressively at 6-hour intervals over a 144-hour period. Deep-AR combines a deterministic residual network (ResNet) that advances the large-scale atmospheric state with a Wasserstein generative adversarial network (WGAN) that produces stochastic, high-resolution fields. Each HDF5 file contains 0.25° gridded synthetic integrated vapor transport components (qu, qv), 10 m wind components (u10, v10), and 6-hour accumulated precipitation on a common 200 × 480 grid. The files also include coordinate and datetime arrays. This dataset supports AR hazard analysis, ensemble-based uncertainty characterization, precipitation-extremes research, and regional stress testing. Synthetic files follow the naming convention deepar.model.YYYYMMDD.HHMMSS.vNN.h5. YYYYMMDD.HHMMSS identifies the UTC initial-condition timestamp, which occurs 48 hours before the diagnosed observed landfall, and vNN identifies the zero-padded ensemble member, ranging from v01 through v25. Each synthetic file can be paired with its corresponding observed file by matching the initial-condition timestamp. The paired observed file follows the naming convention deepar.obs.YYYYMMDD.HHMMSS.h5 and is available in the separately registered oracle/deepar.obs dataset at https://wdh.energy.gov/ds/oracle/deepar.obs (DOI: https://doi.org/10.21947/3377671).

17 WIND ENERGY↗
DOE OSTI2025

GenAI-Based Digital Twins Aided Data Augmentation Increases Accuracy in Real-Time Cokurtosis-Based Anomaly Detection of Wearable Data

Early detection of potential infectious disease outbreaks is crucial for developing effective interventions. In this study, we introduce advanced anomaly detection methods tailored for health datasets collected from wearables, offering insights at both individual and population levels. Leveraging real-world physiological data from wearables, including heart rate and activity, we developed a framework for the early detection of infection in individuals. Despite the availability of data from recent pandemics, substantial gaps remain in data collection, hindering method development. To bridge this gap, we utilized Wasserstein Generative Adversarial Networks (WGANs) to generate realistic synthetic wearable data, augmenting our dataset for training. Subsequently, we use these augmented datasets to implement a cokurtosis-based technique for anomaly detection in multivariate time-series data. Our approach includes a comprehensive assessment of uncertainties in synthetic data compared to the actual data upon which it was modeled, as well as the uncertainty associated with fine-tuning anomaly detection thresholds in physiological measurements. Through our work, we present an enhanced method for early anomaly detection in multivariate datasets, with promising applications in healthcare and beyond. This framework could revolutionize early detection strategies and significantly impact public health response efforts in future pandemics.

Data-Driven Digital Twins↗
DOE OSTI2026

Score-based deterministic density sampling

We propose a deterministic sampling framework using Score-Based Transport Modeling for sampling an unnormalized target density π given only its score ∇ log π. Our method approximates the Wasserstein gradient flow on KL($f_t$∥π) by learning the time-varying score ∇ log $f_t$ on the fly using score matching. While having the same marginal distribution as Langevin dynamics, our method produces smooth deterministic trajectories, resulting in monotone noise-free convergence. We prove that our method dissipates relative entropy at the same rate as the exact gradient flow, provided sufficient training. Numerical experiments validate our theoretical findings: our method converges at the optimal rate, has smooth trajectories, and is often more sample efficient than its stochastic counterpart. Experiments on high-dimensional image data show that our method produces high-quality generations in as few as 15 steps and exhibits natural exploratory behavior. The memory and runtime scale linearly in the sample size.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Learning with Adaptive Conservativeness for Distributionally Robust Optimization: Incentive Design for Voltage Regulation: Preprint

Information asymmetry between the Distribution System Operator (DSO) and Distributed Energy Resource Aggregators (DERAs) obstructs designing effective incentives for voltage regulation. To capture this effect, we employ a Stackelberg game-theoretic framework, where the DSO seeks to overcome the information asymmetry and refine its incentive strategies by learning from DERA behavior over multiple iterations. We introduce a model-based online learning algorithm for the DSO, aimed at inferring the relationship between incentives and DERA responses. Given the uncertain nature of these responses, we also propose a distributionally robust incentive design model to control the probability of voltage regulation failure and then reformulate it into a convex problem. This model allows the DSO to periodically revise distribution assumptions on uncertain parameters in the decision model of the DERA. Finally, we present a gradient-based method that permits the DSO to adaptively modify its conservativeness level, measured by the size of a Wasserstein metric-based ambiguity set, according to historical voltage regulation performance. The effectiveness of our proposed method is demonstrated through numerical experiments.

distribution system operator↗