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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Revealing Decision Conservativeness Through Inverse Distributionally Robust Optimization

This paper introduces Inverse Distributionally Robust Optimization (I-DRO) as a method to infer the conservativeness level of a decision-maker, represented by the size of a Wasserstein metric-based ambiguity set, from the optimal decisions made using Forward Distributionally Robust Optimization (F-DRO). By leveraging the Karush-Kuhn-Tucker (KKT) conditions of the convex F-DRO model, we formulate I-DRO as a bi-linear program, which can be solved using off-the-shelf optimization solvers. Additionally, this formulation exhibits several advantageous properties. We demonstrate that I-DRO not only guarantees the existence and uniqueness of an optimal solution but also establishes the necessary and sufficient conditions for this optimal solution to accurately match the actual conservativeness level in F-DRO. Furthermore, we identify three extreme scenarios that may impact I-DRO effectiveness. Our case study applies F-DRO for power system scheduling under uncertainty and employs I-DRO to recover the conservativeness level of system operators. Numerical experiments based on an IEEE 5-bus system and a realistic NYISO 11-zone system demonstrate I-DRO performance in both normal and extreme scenarios. An extended version of this paper with additional analyses is available at li2024revealing.

distributionally robust optimization↗
DOE OSTI2024

Acoustic sensing and autoencoder approach for abnormal gas detection in a spent nuclear fuel canister mock-up

Currently, spent nuclear fuel (SNF) from commercial nuclear power plants is stored in stainless-steel canisters for interim dry storage. To provide an inert environment, these canisters are backfilled with helium after vacuum drying. However, the helium environment may be contaminated during extended storage because of the material degradation. For example, the heavier fission gas xenon may be released from the fuel rods into the canister cavity should the fuel cladding be breached. Other gases such as air and water vapor may also be present as a result of leakage caused by chloride-induced stress corrosion cracking on the canister walls or by insufficient vacuum drying. Therefore, monitoring the gas composition can provide critical information about the health of SNF canisters. In this study, noninvasive testing was conducted on a 2/3-scaled SNF canister mock-up using acoustic sensing. Ultrasonic transducers were placed on the exterior surface of the canister to probe the gas composition. A dataset was collected by sealing the canister mock-up and introducing up to 1.53% argon or 1.29% air into the helium background gas. Three methods were used to detect changes in the gas composition: the time-of-flight (TOF) method, the differential method, and the autoencoder method. Results showed that the TOF method had sufficient resolution to detect abnormal gas concentrations of less than 1.0%. The differential method demonstrated a periodic in-phase and out-of-phase behavior between the benchmark (i.e., pure helium) and abnormal (i.e., with argon or air) state signals. The variational autoencoder (VAE) and the Wasserstein autoencoder (WAE) were trained on the benchmark data and were applied directly to the abnormal state data. It was found that both the unsupervised VAE and the WAE were able to distinguish the benchmark and abnormal states of the canister mock-up based on the reconstruction error.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2022

Residuals-based distributionally robust optimization with covariate information

We consider data-driven approaches that integrate a machine learning prediction model within distributionally robust optimization (DRO) given limited joint observations of uncertain parameters and covariates. Our framework is flexible in the sense that it can accommodate a variety of regression setups and DRO ambiguity sets. We investigate asymptotic and finite sample properties of solutions obtained using Wasserstein, sample robust optimization, and phi-divergence-based ambiguity sets within our DRO formulations, and explore cross-validation approaches for sizing these ambiguity sets. Through numerical experiments, we validate our theoretical results, study the effectiveness of our approaches for sizing ambiguity sets, and illustrate the benefits of our DRO formulations in the limited data regime even when the prediction model is misspecified.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Persistent Homology Metrics Reveal Quantum Fluctuations and Reactive Atoms in Path Integral Dynamics

Nuclear quantum effects (NQEs) are known to impact a number of features associated with chemical reactivity and physicochemical properties, particularly for light atoms and at low temperatures. In the imaginary time path integral formalism, each atom is mapped onto a “ring polymer” whose spread is related to the quantum mechanical uncertainty in the particle’s position, i.e., its thermal wavelength. A number of metrics have previously been used to investigate and characterize this spread and explain effects arising from quantum delocalization, zero-point energy, and tunneling. Many of these shape metrics consider just the instantaneous structure of the ring polymers. However, given the significant interest in methods such as centroid molecular dynamics and ring polymer molecular dynamics that link the molecular dynamics of these ring polymers to real time properties, there exists significant opportunity to exploit metrics that also allow for the study of the fluctuations of the atom delocalization in time. Here we consider the ring polymer delocalization from the perspective of computational topology, specifically persistent homology, which describes the 3-dimensional arrangement of point cloud data, (i.e. atomic positions). We employ the Betti sequence probability distribution to define the ensemble of shapes adopted by the ring polymer. The Wasserstein distances of Betti sequences adjacent in time are used to characterize fluctuations in shape, where the Fourier transform and associated principal components provides added information differentiating atoms with different NQEs based on their dynamic properties. We demonstrate this methodology on two representative systems, a glassy system consisting of two atom types with dramatically different de Broglie thermal wavelengths, and ab initio molecular dynamics simulation of an aqueous 4 M HCl solution where the H-atoms are differentiated based on their participation in proton transfer reactions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Local Versus Global Distances for Zigzag and Multi-Parameter Persistence Modules

In this paper, we establish explicit and broadly applicable relationships between persistence-based distances computed locally and globally. In particular, we show that the bottleneck distance and the Wasserstein distance between two zigzag persistence modules restricted to an interval is always bounded above by the distance between the unrestricted versions. While this result is not surprising, it could have potential practical implications. We give two related applications for metric graph distances, as well as an extension for the matching distance between multi-parameter persistence modules.

persistent homology, metric graph, inequality↗
DOE OSTI2023

SHAPER: can you hear the shape of a jet?

The identification of interesting substructures within jets is an important tool for searching for new physics and probing the Standard Model at colliders. Many of these substructure tools have previously been shown to take the form of optimal transport problems, in particular the Energy Mover’s Distance (EMD). In this work, we show that the EMD is in fact the natural structure for comparing collider events, which accounts for its recent success in understanding event and jet substructure. We then present a Shape Hunting Algorithm using Parameterized Energy Reconstruction (SHAPER), which is a general framework for defining and computing shape-based observables. SHAPER generalizes N-jettiness from point clusters to any extended, parametrizable shape. This is accomplished by efficiently minimizing the EMD between events and parameterized manifolds of energy flows representing idealized shapes, implemented using the dual-potential Sinkhorn approximation of the Wasserstein metric. We show how the geometric language of observables as manifolds can be used to define novel observables with built-in infrared-and-collinear safety. We demonstrate the efficacy of the SHAPER framework by performing empirical jet substructure studies using several examples of new shape-based observables.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Measurements of multijet event isotropies using optimal transport with the ATLAS detector

A measurement of novel event shapes quantifying the isotropy of collider events is performed in 140 fb -1 of proton-proton collisions with $\sqrt{s}$ = 13 TeV centre-of-mass energy recorded with the ATLAS detector at CERN’s Large Hadron Collider. These event shapes are defined as the Wasserstein distance between collider events and isotropic reference geometries. This distance is evaluated by solving optimal transport problems, using the ‘Energy-Mover’s Distance’. Isotropic references with cylindrical and circular symmetries are studied, to probe the symmetries of interest at hadron colliders. The novel event-shape observables defined in this way are infrared- and collinear-safe, have improved dynamic range and have greater sensitivity to isotropic radiation patterns than other event shapes. The measured event-shape variables are corrected for detector effects, and presented in inclusive bins of jet multiplicity and the scalar sum of the two leading jets’ transverse momenta. The measured distributions are provided as inputs to future Monte Carlo tuning campaigns and other studies probing fundamental properties of QCD and the production of hadronic final states up to the TeV-scale.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Learning generative neural networks with physics knowledge

Deep generative neural networks have enabled modeling complex distributions, but incorporating physics knowledge into the neural networks is still challenging and is at the core of current physics-based machine learning research. To this end, we propose a physics generative neural network (PhysGNN), a new class of generative neural networks for learning unknown distributions in a physical system described by partial differential equations (PDE). PhysGNN couples PDE systems with generative neural networks. It is a fully differentiable model that allows back-propagation of gradients through both numerical PDE solvers and generative neural networks, and is trained by minimizing the discrete Wasserstein distance between generated and observed probability distributions of the PDE outputs using the stochastic gradient descent method. Moreover, PhysGNN does not require adversarial training like standard generative neural networks, which offers better stability than adversarial training. We show that PhysGNN can learn complex distributions in stochastic inverse problems, where conventional methods such as maximum likelihood estimation and momentum matching methods may be inapplicable when little knowledge is known about the form of unknown distributions or the physical model is too complex. Furthermore, our method allows physics-based generative neural network training for learning complex distributions in the context of differential equations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Towards inverse microstructure-centered materials design using generative phase-field modeling and deep variational autoencoders

The field of Integrated Computational Materials Engineering (ICME) combines a broad range of methods to study materials’ responses over a spectrum of length scales. A relatively unexplored aspect of microstructure-sensitive materials design is uncertainty propagation and quantification (UP/UQ) of materials’ microstructure, as well as establishing process-structure–property (PSP) relationships for inverse material design. In this study, an efficient UP technique built on the idea of changing probability measures and a deep generative unsupervised representative machine learning method for microstructure-based design of thermal conductivity of materials is proposed. Probability measures are used to represent microstructure space, and Wasserstein metrics are used to test the efficiency of the UP method. By using deep Variational AutoEncoder (VAE), we identify the correlations between the material/process parameters and the thermal conductivity of heterogeneous dual-phase microstructures. Through high-throughput screening, UP, and the deep-generative VAE method, PSP relationships that are too complex can be revealed by exploiting the materials’ design space with an emphasis on microstructures. As a last point, we demonstrate generative machine learning serves as a useful tool for inverse microstructure-centered materials design, and we demonstrate this by examining the inverse design of thermal conductivity in nano-structured materials. Here, the results reveal the effects of morphology, volume fraction, characteristic length scale, and the individual thermal diffusivity of phases on the thermal conductivity of dual-phase alloys. Our findings emphasize the advantages of high-throughput phase-field modeling and generative deep learning for linking PSP and inverse microstructure-centered materials design.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Stochastic Optimization and Uncertainty Quantification of Natrium-based Nuclear-Renewable Energy Systems for Flexible Power Applications in Deregulated Markets

Rapid integration of variable renewable energy sources (VRES) has made modeling and stochastic optimization of hybrid energy systems crucial for studying their long-term performance and viability. However, most studies have focused on just historical data, which may be unreliable for capturing short-term fluctuations, rare events, and long-term patterns of energy demand, price, and the variability of renewable energy sources. For this study, optimal synthetic time series models were developed using Wasserstein distance. The models were validated by comparing the key statistical measures against those of the historical data. They were then used to optimize the integrated Natrium-style advanced energy systems and their long-term (30 years) economics. The stochastic model performs bi-level optimization to find the optimal sizes for the balance of plant and thermal energy storage, while also optimizing energy dispatch to achieve the maximum net present value. In studies of two deregulated markets (California ISO and the Electric Reliability Council of Texas), the integrated Natrium-style system performed better in CAISO than in ERCOT, given higher and more consistent electricity prices during peak-demand periods. The potentially enlarged cost associated with the variable operation and maintenance of the TES system also plays a significant role in driving the system sizing, thus its impacts on the system are investigated in detail through comparison against a baseline case. The study also finds that the bi-level optimization results based on stochastic gradient descent closely match the grid search results. The uncertainty quantification of the stochastic signals provides further NPV-related insights and probability distributions for the case studies. The normal standard error of the mean of NPV for the case with and without TES VOM for CAISO were found to be 7.73M (plus-minus sign) 1.09M USD and 104.99M (plus-minus sign) 1.25M USD, respectively based on a 95% confidence. Given the relatively small NPV variance based on 150 samples, the analysis affords the most robust possible prediction of the techno-economic performance of the integrated Natrium-style energy systems.

25 ENERGY STORAGE↗
DOE OSTI2023

Reliable extrapolation of deep neural operators informed by physics or sparse observations

Deep neural operators can learn nonlinear mappings between infinite-dimensional function spaces via deep neural networks. As promising surrogate solvers of partial differential equations (PDEs) for real-time prediction, deep neural operators such as deep operator networks (DeepONets) provide a new simulation paradigm in science and engineering. Pure data-driven neural operators and deep learning models, in general, are usually limited to interpolation scenarios, where new predictions utilize inputs within the support of the training set. However, in the inference stage of real-world applications, the input may lie outside the support, i.e., extrapolation is required, which may result to large errors and unavoidable failure of deep learning models. Here, we address this challenge of extrapolation for deep neural operators. First, we systematically investigate the extrapolation behavior of DeepONets by quantifying the extrapolation complexity, via the 2-Wasserstein distance between two function spaces and propose a new strategy of bias–variance trade-off for extrapolation with respect to model capacity. Subsequently, we develop a complete workflow, including extrapolation determination, and we propose five reliable learning methods that guarantee a safe prediction under extrapolation by requiring additional information—the governing PDEs of the system or sparse new observations. The proposed methods are based on either fine-tuning a pre-trained DeepONet or multifidelity learning. We demonstrate the effectiveness of the proposed framework for various types of parametric PDEs. Furthermore, our systematic comparisons provide practical guidelines for selecting a proper extrapolation method depending on the available information, desired accuracy, and required inference speed.

42 ENGINEERING↗
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 OSTI2024

CO 2 storage site characterization using ensemble-based approaches with deep generative models

Estimating spatially distributed properties such as permeability from available sparse measurements is a great challenge in efficient subsurface CO 2 storage operations. In this paper, a deep generative model that can accurately capture complex subsurface structure is tested with an ensemble-based inversion method for accurate and accelerated characterization of CO 2 storage sites. We chose Wasserstein Generative Adversarial Network with Gradient Penalty (WGAN-GP) for its realistic reservoir property representation and Ensemble Smoother with Multiple Data Assimilation (ES-MDA) for its robust data fitting and uncertainty quantification capability. WGAN-GP are trained to generate high-dimensional permeability fields from a low-dimensional latent space and ES-MDA then updates the latent variables by assimilating available measurements. Several subsurface site characterization examples including Gaussian, channelized, and fractured reservoirs are used to evaluate the accuracy and computational efficiency of the proposed method and the main features of the unknown permeability fields are characterized accurately with reliable uncertainty quantification. Furthermore, the estimation performance is compared with a widely-used variational, i.e., optimization-based, inversion approach, and the proposed approach outperforms the variational inversion method in several benchmark cases. We explain such superior performance by visualizing the objective function in the latent space: because of nonlinear and aggressive dimension reduction via generative modeling, the objective function surface becomes extremely complex while the ensemble approximation can smooth out the multi-modal surface during the minimization. This suggests that the ensemble-based approach works well over the variational approach when combined with deep generative models at the cost of forward model runs unless convergence-ensuring modifications are implemented in the variational inversion.

42 ENGINEERING↗
DOE OSTI2020

Physics-informed semantic inpainting: Application to geostatistical modeling

A fundamental problem in geostatistical modeling is to infer the heterogeneous geological field based on limited measurements and some prior spatial statistics. Semantic inpainting, a technique for image processing using deep generative models, has been recently applied for this purpose, demonstrating its effectiveness in dealing with complex spatial patterns. However, the original semantic inpainting framework incorporates only information from direct measurements, while in geostatistics indirect measurements are often plentiful. In this work, to overcome this limitation, we propose a physics-informed semantic inpainting framework, employing the Wasserstein Generative Adversarial Network with Gradient Penalty (WGAN-GP) and jointly incorporating the direct and indirect measurements by exploiting the underlying physical laws. Our simulation results for a high-dimensional problem with 512 dimensions show that in the new method, the physical conservation laws are satisfied and contribute in enhancing the inpainting performance compared to using only the direct measurements.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Machine learning-based microstructure prediction during laser sintering of alumina

Abstract Predicting material’s microstructure under new processing conditions is essential in advanced manufacturing and materials science. This is because the material’s microstructure hugely influences the material’s properties. We demonstrate an elegant machine learning algorithm that faithfully predicts the microstructure under new conditions, without the need of knowing the governing laws. We name this algorithm, RCWGAN-GP, which is regression-based conditional generative adversarial networks with Wasserstein loss function and gradient penalty. This algorithm was trained with experimental SEM micrographs from laser-sintered alumina under various laser powers. The RCWGAN-GP realistically regenerates the SEM micrographs under the trained laser powers. Impressively, it also faithfully predicts the alumina’s microstructure under unexplored laser powers. The predicted microstructure features, including the morphology of the sintered particles and the pores, match the experimental SEM micrographs very well. We further quantitatively examined the prediction accuracy of the RCWGAN-GP. We trained the algorithm with computer-created micrograph datasets of secondary-phase growth governed by the well-known Johnson–Mehl–Avrami (JMA) equation. The RCWGAN-GP accurately regenerates the micrographs at the trained time series, in terms of the grains’ shapes, sizes, and spatial distributions. More importantly, the predicted secondary phase fraction accurately follows the JMA curve.

08 HYDROGEN↗
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 OSTI2023

Generative adversarial networks for scintillation signal simulation in EXO-200

Generative Adversarial Networks trained on samples of simulated or actual events have been proposed as a way of generating large simulated datasets at a reduced computational cost. In this work, a novel approach to perform the simulation of photodetector signals from the time projection chamber of the EXO-200 experiment is demonstrated. The method is based on a Wasserstein Generative Adversarial Network — a deep learning technique allowing for implicit non-parametric estimation of the population distribution for a given set of objects. Our network is trained on real calibration data using raw scintillation waveforms as input. We find that it is able to produce high-quality simulated waveforms an order of magnitude faster than the traditional simulation approach and, importantly, generalize from the training sample and discern salient high-level features of the data. In particular, the network correctly deduces position dependency of scintillation light response in the detector and correctly recognizes dead photodetector channels. Furthermore, the network output is then integrated into the EXO-200 analysis framework to show that the standard EXO-200 reconstruction routine processes the simulated waveforms to produce energy distributions comparable to that of real waveforms. Finally, the remaining discrepancies and potential ways to improve the approach further are highlighted.

47 OTHER INSTRUMENTATION↗
DOE OSTI2023

Generalizing to new geometries with Geometry-Aware Autoregressive Models (GAAMs) for fast calorimeter simulation

Generation of simulated detector response to collision products is crucial to data analysis in particle physics, but computationally very expensive. One subdetector, the calorimeter, dominates the computational time due to the high granularity of its cells and complexity of the interactions. Generative models can provide more rapid sample production, but currently require significant effort to optimize performance for specific detector geometries, often requiring many models to describe the varying cell sizes and arrangements, without the ability to generalize to other geometries. Here, we develop a geometry-aware autoregressive model, which learns how the calorimeter response varies with geometry, and is capable of generating simulated responses to unseen geometries without additional training. The geometry-aware model outperforms a baseline unaware model by over 50% in several metrics such as the Wasserstein distance between the generated and the true distributions of key quantities which summarize the simulated response. A single geometry-aware model could replace the hundreds of generative models currently designed for calorimeter simulation by physicists analyzing data collected at the Large Hadron Collider. This proof-of-concept study motivates the design of a foundational model that will be a crucial tool for the study of future detectors, dramatically reducing the large upfront investment usually needed to develop generative calorimeter models.

47 OTHER INSTRUMENTATION↗