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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 595 records · Page 33
All sourcesNASA NTRSDOE OSTI
DOE OSTI2013

Theoretical formulation of finite-dimensional discrete phase spaces: II. On the uncertainty principle for Schwinger unitary operators

We introduce a self-consistent theoretical framework associated with the Schwinger unitary operators whose basic mathematical rules embrace a new uncertainty principle that generalizes and strengthens the Massar–Spindel inequality. Among other remarkable virtues, this quantum-algebraic approach exhibits a sound connection with the Wiener–Khinchin theorem for signal processing, which permits us to determine an effective tighter bound that not only imposes a new subtle set of restrictions upon the selective process of signals and wavelet bases, but also represents an important complement for property testing of unitary operators. Moreover, we establish a hierarchy of tighter bounds, which interpolates between the tightest bound and the Massar–Spindel inequality, as well as its respective link with the discrete Weyl function and tomographic reconstructions of finite quantum states. We also show how the Harper Hamiltonian and discrete Fourier operators can be combined to construct finite ground states which yield the tightest bound of a given finite-dimensional state vector space. Such results touch on some fundamental questions inherent to quantum mechanics and their implications in quantum information theory. -- Highlights: •Conception of a quantum-algebraic framework embracing a new uncertainty principle for unitary operators. •Determination of new restrictions upon the selective process of signals and wavelet bases. •Demonstration of looser bounds interpolating between the tightest bound and the Massar–Spindel inequality. •Construction of finite ground states properly describing the tightest bound. •Establishment of an important connection with the discrete Weyl function.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

NEML2: An efficient and modular multiphysics constitutive modeling library for hybrid computing environments

This paper presents NEML2, an open-source, high-performance library developed for constitutive material modeling, designed to support the flexible and modular development of models for complex material behavior. Building on the foundational structure of its predecessor, NEML, the NEML2 library introduces significant improvements, including enhanced vectorization, automatic differentiation, and seamless integration with PyTorch, facilitating the application of machine learning techniques in material simulations. NEML2 provides a C++ backend with Python bindings, enabling users to create custom material models that can be executed efficiently on both CPU and GPU platforms. The library also supports coupling with Multiphysics simulation frameworks like MOOSE, making it suitable for realistic simulations involving coupled physical processes. Rigorous quality assurance through unit and regression testing ensures the reliability of results, while the extensible, user-friendly design encourages collaboration and reproducibility across the scientific community. This paper provides an overview of NEML2’s architecture, core features, and applications, highlighting its impact on accelerating material qualification and advancing computational methods in materials science.

GPU↗
DOE OSTI2024

E(n)-Equivariant cartesian tensor message passing interatomic potential

Machine learning potential (MLP) has been a popular topic in recent years for its capability to replace expensive first-principles calculations in some large systems. Meanwhile, message passing networks have gained significant attention due to their remarkable accuracy, and a wave of message passing networks based on Cartesian coordinates has emerged. However, the information of the node in these models is usually limited to scalars, and vectors. In this work, we propose High-order Tensor message Passing interatomic Potential (HotPP), an E(n) equivariant message passing neural network that extends the node embedding and message to an arbitrary order tensor. By performing some basic equivariant operations, high order tensors can be coupled very simply and thus the model can make direct predictions of high-order tensors such as dipole moments and polarizabilities without any modifications. The tests in several datasets show that HotPP not only achieves high accuracy in predicting target properties, but also successfully performs tasks such as calculating phonon spectra, infrared spectra, and Raman spectra, demonstrating its potential as a tool for future research.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Development and Application of TK6-derived Cells Expressing Human Cytochrome P450s for Genotoxicity Testing

Abstract Metabolism plays a key role in chemical genotoxicity; however, most mammalian cells used for in vitro genotoxicity testing lack effective metabolizing enzymes. We recently developed a battery of TK6-derived cell lines that individually overexpress 1 of 8 cytochrome P450s (CYP1A1, 1A2, 1B1, 2A6, 2B6, 2C9, 2C19, and 3A4) using a lentiviral expression system. The increased expression and metabolic function of each individual CYP in each established cell line were confirmed using real-time PCR, Western blotting, and mass spectrometry analysis; the parental TK6 cells and empty vector (EV) transduced cells had negligible CYP levels. Subsequently, we evaluated these cell lines using 2 prototypical polyaromatic hydrocarbon mutagens, 7,12-dimethylbenz[a]anthracene (DMBA) and benzo[a]pyrene (B[a]P), that require metabolic activation to exert their genotoxicity. DMBA-induced cytotoxicity, phosphorylation of histone H2A.X, and micronucleus formation were significantly increased in TK6 cells with CYP1A1, 1B1, 2B6, and 2C19 expression as compared with EV controls. B[a]P significantly increased cytotoxicity, DNA damage, and chromosomal damage in TK6 cells overexpressing CYP1A1 and 1B1 when compared with EV controls. B[a]P also induced micronucleus formation in TK6 cells expressing CYP1A2. These results suggest that our CYP-expressing TK6 cell system can be used to detect the genotoxicity of compounds requiring metabolic transformation.

Li, Xilin↗
DOE OSTI2019

SUNDIALS Multiphysics+MPIManyVector Performance Testing

In this report we document performance test results on a SUNDIALS-based multiphysics demonstration application. We aim to assess the large-scale parallel performance of new capabilities that have been added to the SUNDIALS suite of time integrators and nonlinear solvers in recent years under funding from both the Exascale Computing Project (ECP) and the Scientific Discovery through Advanced Scientific (SciDAC) program, specifically: 1. SUNDIALS’ new MPIManyVector module, that allows extreme flexibility in how a solution "vector" is staged on computational resources. 2. ARKode’s new multirate integration module, MRIStep, allowing high-order accurate calculations that subcycle "fast" processes within "slow" ones. 3. SUNDIALS’ new flexible linear solver interfaces, that allow streamlined specification of problem-specific linear solvers. 4. SUNDIALS’ new N_Vector additions of "fused" vector operations (to increase arithmetic intensity) and separation of reduction operations into "local" and "global" versions (to reduce latency by combining multiple reductions into a single MPI_Allreduce call). We anticipate that subsequent reports will extend this work to investigate a variety of other new features, including SUNDIALS’ generic SUNNonlinearSolver interface and accelerator-enabled N Vector modules, and upcoming MRIStep extensions to support custom "fast" integrators (that leverage problem structure) and IMEX integration of the "slow" time scale (to add diffusion).

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Three-dimensional Boltzmann-Hydro Code for Core-collapse in Massive Stars. II. The Implementation of Moving-mesh for Neutron Star Kicks

We present a newly developed moving-mesh technique for the multi-dimensional Boltzmann-Hydro code for the simulation of core-collapse supernovae (CCSNe). What makes this technique different from others is the fact that it treats not only hydrodynamics but also neutrino transfer in the language of the 3 + 1 formalism of general relativity (GR), making use of the shift vector to specify the time evolution of the coordinate system. This means that the transport part of our code is essentially general relativistic, although in this paper it is applied only to the moving curvilinear coordinates in the flat Minknowski spacetime, since the gravity part is still Newtonian. The numerical aspect of the implementation is also described in detail. Employing the axisymmetric two-dimensional version of the code, we conduct two test computations: oscillations and runaways of proto-neutron star (PNS). We show that our new method works fine, tracking the motions of PNS correctly. We believe that this is a major advancement toward the realistic simulation of CCSNe.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Modeling freight mode choice using machine learning classifiers: a comparative study using Commodity Flow Survey (CFS) data

This study explores the usefulness of machine learning classifiers for modeling freight mode choice. We investigate eight commonly used machine learning classifiers, namely Naïve Bayes, Support Vector Machine, Artificial Neural Network, K-Nearest Neighbors, Classification and Regression Tree, Random Forest, Boosting and Bagging, along with the classical Multinomial Logit model. US 2012 Commodity Flow Survey data are used as the primary data source; we augment it with spatial attributes from secondary data sources. The performance of the classifiers is compared based on prediction accuracy results. The current research also examines the role of sample size and training-testing data split ratios on the predictive ability of the various approaches. In addition, the importance of variables is estimated to determine how the variables influence freight mode choice. The results show that the tree-based ensemble classifiers perform the best. Specifically, Random Forest produces the most accurate predictions, closely followed by Boosting and Bagging. With regard to variable importance, shipment characteristics, such as shipment distance, industry classification of the shipper and shipment size, are the most significant factors for freight mode choice decisions.

42 ENGINEERING↗
DOE OSTI2025

Application of Machine Learning and Data Augmentation Algorithms in the Discovery of Metal Hydrides for Hydrogen Storage

The development of efficient and sustainable hydrogen storage materials is a key challenge for realizing hydrogen as a clean and flexible energy carrier. Among various options, metal hydrides offer high volumetric storage density and operational safety, yet their application is limited by thermodynamic, kinetic, and compositional constraints. In this work, we investigate the potential of machine learning (ML) to predict key thermodynamic properties—equilibrium plateau pressure, enthalpy, and entropy of hydride formation—based solely on alloy composition using Magpie-generated descriptors. We significantly expand an existing experimental dataset from ~400 to 806 entries and assess the impact of dataset size and data augmentation, using the PADRE algorithm, on model performance. Models including Support Vector Machines and Gradient Boosted Random Forests were trained and optimized via grid search and cross-validation. Results show a marked improvement in predictive accuracy with increased dataset size, while data augmentation benefits are limited to smaller datasets and do not improve accuracy in underrepresented pressure regimes. Furthermore, clustering and cross-validation analyses highlight the limited generalizability of models across different material classes, though high accuracy is achieved when training and testing within a single hydride family (e.g., AB2). The study demonstrates the viability and limitations of ML for accelerating hydride discovery, emphasizing the importance of dataset diversity and representation for robust property prediction.

augmentation↗
DOE OSTI2022

Behavior and mechanisms of Doppler wind lidar error in varying stability regimes

Abstract. Wind lidars are widespread and important tools in atmospheric observations. An intrinsic part of lidar measurement error is due to atmospheric variability in the remote-sensing scan volume. This study describes and quantifies the distribution of measurement error due to turbulence in varying atmospheric stability. While the lidar error model is general, we demonstrate the approach using large ensembles of virtual WindCube V2 lidar performing a profiling Doppler-beam-swinging scan in quasi-stationary large-eddy simulations (LESs) of convective and stable boundary layers. Error trends vary with the stability regime, time averaging of results, and observation height. A systematic analysis of the observation error explains dominant mechanisms and supports the findings of the empirical results. Treating the error under a random variable framework allows for informed predictions about the effect of different configurations or conditions on lidar performance. Convective conditions are most prone to large errors (up to 1.5 m s−1 in 1 Hz wind speed in strong convection), driven by the large vertical velocity variances in convective conditions and the high elevation angle of the scanning beams (62∘). Range-gate weighting induces a negative bias into the horizontal wind speeds near the surface shear layer (−0.2 m s−1 in the stable test case). Errors in the horizontal wind speed and direction computed from the wind components are sensitive to the background wind speed but have negligible dependence on the relative orientation of the instrument. Especially during low winds and in the presence of large errors in the horizontal velocity estimates, the reported wind speed is subject to a systematic positive bias (up to 0.4 m s−1 in 1 Hz measurements in strong convection). Vector time-averaged measurements can improve the behavior of the error distributions (reducing the 10 min wind speed error standard deviation to <0.3 m s−1 and the bias to <0.1 m s−1 in strong convection) with a predictable effectiveness related to the number of decorrelated samples in the time window. Hybrid schemes weighting the 10 min scalar- and vector-averaged lidar measurements are shown to be effective at reducing the wind speed biases compared to cup measurements in most of the simulated conditions, with time averages longer than 10 min recommended for best use in some unstable conditions. The approach in decomposing the error mechanisms with the help of the LES flow field could be extended to more complex measurement scenarios and scans.

17 WIND ENERGY↗
DOE OSTI2021

Precision test of the muon-Higgs coupling at a high-energy muon collider

We explore the sensitivity of directly testing the muon-Higgs coupling at a high-energy muon collider. This is strongly motivated if there exists new physics that is not aligned with the Standard Model Yukawa interactions which are responsible for the fermion mass generation. We illustrate a few such examples for physics beyond the Standard Model. With the accidentally small value of the muon Yukawa coupling and its subtle role in the high-energy production of multiple (vector and Higgs) bosons, we show that it is possible to measure the muon-Higgs coupling to an accuracy of ten percent for a 10 TeV muon collider and a few percent for a 30 TeV machine by utilizing the three boson production, potentially sensitive to a new physics scale about Λ ~ 30 - 100 TeV.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Diffraction pattern simulation of cellulose fibrils using distributed and quantized pair distances

Intensity simulation of X-ray scattering from large twisted cellulose molecular fibrils is important in understanding the impact of chemical or physical treatments on structural properties such as twisting or coiling. This paper describes a highly efficient method for the simulation of X-ray diffraction patterns from complex fibrils using atom-type-specific pair-distance quantization. Pair distances are sorted into arrays which are labelled by atom type. Histograms of pair distances in each array are computed and binned and the resulting population distributions are used to represent the whole pair-distance data set. These quantized pair-distance arrays are used with a modified and vectorized Debye formula to simulate diffraction patterns. This approach utilizes fewer pair distances in each iteration, and atomic scattering factors are moved outside the iteration since the arrays are labelled by atom type. As a result, this algorithm significantly reduces the computation time while maintaining the accuracy of diffraction pattern simulation, making possible the simulation of diffraction patterns from large twisted fibrils in a relatively short period of time, as is required for model testing and refinement.

09 BIOMASS FUELS↗
DOE OSTI2015

SU-E-T-01: (In)dependence of Plan Quality On Treatment Modalities and Target-To-Critical Structure Geometry for Brain Tumor

Purpose: To evaluate and test the hypothesis that plan quality may be systematically affected by treatment delivery techniques and target-tocritical structure geometric relationship in radiotherapy for brain tumor. Methods: Thirty-four consecutive brain tumor patients treated between 2011–2014 were analyzed. Among this cohort, 10 were planned with 3DCRT, 11 with RadipArc, and 13 with helical IMRT on TomoTherapy. The selected dosimetric endpoints (i.e., PTV V100, maximum brainstem/chiasm/ optic nerve doses) were considered as a vector in a highdimensional space. A Pareto analysis was performed to identify the subset of Pareto-efficient plans.The geometric relationships, specifically the overlapping volume and centroid-of-mass distance between each critical structure to the PTV were extracted as potential geometric features. The classification-tree analyses were repeated using these geometric features with and without the treatment modality as an additional categorical predictor. In both scenarios, the dominant features to prognosticate the Pareto membership were identified and the tree structures to provide optimal inference were recorded. The classification performance was further analyzed to determine the role of treatment modality in affecting plan quality. Results: Seven Pareto-efficient plans were identified based on dosimetric endpoints (3 from 3DCRT, 3 from RapicArc, 1 from Tomo), which implies that the evaluated treatment modality may have a minor influence on plan quality. Classification trees with/without the treatment modality as a predictor both achieved accuracy of 88.2%: with 100% sensitivity and 87.1% specificity for the former, and 66.7% sensitivity and 96.0% specificity for the latter. The coincidence of accuracy from both analyses further indicates no-to-weak dependence of plan quality on treatment modality. Both analyses have identified the brainstem to PTV distance as the primary predictive feature for Pareto-efficiency. Conclusion: Pareto evaluation and classification-tree analyses have indicated that plan quality depends strongly on geometry for brain tumor, specifically PTV-tobrain-stem-distance but minimally on treatment modality.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2013

Multi-Gene Detection and Identification of Mosquito-Borne RNA Viruses Using an Oligonucleotide Microarray

Background: Arthropod-borne viruses are important emerging pathogens world-wide. Viruses transmitted by mosquitoes, such as dengue, yellow fever, and Japanese encephalitis viruses, infect hundreds of millions of people and animals each year. Global surveillance of these viruses in mosquito vectors using molecular based assays is critical for prevention and control of the associated diseases. Here, we report an oligonucleotide DNA microarray design, termed ArboChip5.1, for multi-gene detection and identification of mosquito-borne RNA viruses from the genera Flavivirus (family Flaviviridae), Alphavirus (Togaviridae), Orthobunyavirus (Bunyaviridae), and Phlebovirus (Bunyaviridae). Methodology/Principal Findings: The assay utilizes targeted PCR amplification of three genes from each virus genus for electrochemical detection on a portable, field-tested microarray platform. Fifty-two viruses propagated in cell-culture were used to evaluate the specificity of the PCR primer sets and the ArboChip5.1 microarray capture probes. The microarray detected all of the tested viruses and differentiated between many closely related viruses such as members of the dengue, Japanese encephalitis, and Semliki Forest virus clades. Laboratory infected mosquitoes were used to simulate field samples and to determine the limits of detection. Additionally, we identified dengue virus type 3, Japanese encephalitis virus, Tembusu virus, Culex flavivirus, and a Quang Binh-like virus from mosquitoes collected in Thailand in 2011 and 2012. Conclusions/Significance: We demonstrated that the described assay can be utilized in a comprehensive field surveillance program by the broad-range amplification and specific identification of arboviruses from infected mosquitoes. Furthermore, the microarray platform can be deployed in the field and viral RNA extraction to data analysis can occur in as little as 12 h. The information derived from the ArboChip5.1 microarray can help to establish public health priorities, detect disease outbreaks, and evaluate control programs.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2023

Piperitone ( p -Menth-1-En-3-One): A New Repellent for Tea Shot Hole Borer (Coleoptera: Curculionidae) in Florida Avocado Groves

The tea shot hole borer, Euwallacea perbrevis, has been recently established in Florida, USA, where it vectors fungal pathogens that cause Fusarium dieback in avocado. Pest monitoring uses a two-component lure containing quercivorol and α-copaene. Incorporation of a repellent into IPM programs may reduce the incidence of dieback in avocado groves, particularly if combined with lures in a push–pull system. This study evaluated piperitone and α-farnesene as potential repellents for E. perbrevis, comparing their efficacy to that of verbenone. Replicate 12-week field tests were conducted in commercial avocado groves. Each test compared beetle captures in traps baited with two-component lures versus captures in traps containing lures plus repellent. To complement field trials, Super-Q collections followed by GC analyses were performed to quantify emissions from repellent dispensers field-aged for 12 weeks. Electroantennography (EAG) was also used to measure beetle olfactory response to each repellent. Results indicated that α-farnesene was ineffective; however, piperitone and verbenone were comparable in repellency, achieving 50–70% reduction in captures, with longevity of 10–12 weeks. EAG responses to piperitone and verbenone were equivalent, and significantly greater than response to α-farnesene. Since piperitone is less expensive than verbenone, this study identifies a potential new E. perbrevis repellent.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2021

A Method of Ground-Based Cloud Motion Predict: CCLSTM + SR-Net

Ground-based cloud images can provide information on weather and cloud conditions, which play an important role in cloud cover monitoring and photovoltaic power generation forecasting. However, the cloud motion prediction of ground-based cloud images still lacks advanced and complete methods, and traditional technologies based on image processing and motion vector calculation are difficult to predict cloud morphological changes. In this paper, we propose a cloud motion prediction method based on Cascade Causal Long Short-Term Memory (CCLSTM) and Super-Resolution Network (SR-Net). Firstly, CCLSTM is used to estimate the shape and speed of cloud motion. Secondly, the Super-Resolution Network is built based on perceptual losses to reconstruct the result of CCLSTM and, finally, make it clearer. We tested our method on Atmospheric Radiation Measurement (ARM) Climate Research Facility TSI (total sky imager) images. The experiments showed that the method is able to predict the sky cloud changes in the next few steps.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Detecting Process Equipment Failures Using Acoustic Data and Machine Learning

Nuclear power plant (NPP) process equipment such as fans, motors, valves, and pumps generate frequent or continuous noise, and deviations from the normal operational sounds made by this equipment can indicate potential issues. These deviations can be identified via automated acoustic anomaly detection, which involves using acoustic sensors (i.e., microphones) alongside detection algorithms to continuously monitor for changes in acoustic signatures. This task is made challenging by the substantial background noise that exists, such as operators opening and closing doors, manipulating valves, and conversing—in addition to typical plant noises. In collaboration with a nuclear power utility partner, this effort assessed the efficacy of acoustic anomaly detection when using a specific acoustic sensor that compresses data into a fixed set of features that are transferable over a standard Internet of Things communication protocol, thereby improving usability but potentially degrading detection performance. Two methods of performing automated acoustic anomaly detection were evaluated: one-class support vector machine (OC-SVM) and isolation forest (iForest). To enable the use of high-quality acoustic data encompassing both normal and anomalous conditions, the study utilized the publicly available Malfunctioning Industrial Machine Investigation and Inspection dataset, which includes real measured acoustic sensor data for a range of equipment types, model numbers, and signal-to-noise ratios (SNRs), along with a benchmark set of detection results. Using this dataset, the methods were tested and then compared against the benchmark results. The results indicated that although the specific acoustic sensor did not enable as rich a feature set extraction, the proposed methods with the limited feature set performed just as well. This provides solid justification for both the methods and the use of the proposed acoustic sensor.

46 - INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AN↗
DOE OSTI2024

A research program to measure the lifetime of spin polarized fuel

The use of spin polarized fuel could increase the deuterium-tritium (D-T) fusion cross section by a factor of 1.5 and, owing to alpha heating, increase the fusion power by an even larger factor. Issues associated with the use of polarized fuel in a reactor are identified. Theoretically, nuclei remain polarized in a hot fusion plasma. The similarity between the Lorentz force law and the Bloch equations suggests polarization can be preserved despite the rich electromagnetic spectrum present in a magnetic fusion device. The most important depolarization mechanisms can be tested in existing devices. The use of polarized deuterium and 3 He in an experiment avoids the complexities of handling tritium, while encompassing the same nuclear reaction spin-physics, making it a useful proxy to study issues associated with full D-T implementation. 3 He fuel with 65% polarization can be prepared by permeating optically-pumped 3 He into a shell pellet. Dynamically polarized 7 Li-D pellets can achieve 70% vector polarization for the deuterium. Cryogenically-frozen pellets can be injected into fusion facilities by special injectors that minimize depolarizing field gradients. Alternatively, polarized nuclei could be injected as a neutral beam. Once injected, the lifetime of the polarized fuel is monitored through measurements of escaping charged fusion products. Multiple experimental scenarios to measure the polarization lifetime in the DIII-D tokamak and other magnetic-confinement facilities are discussed, followed by outstanding issues that warrant further study.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

MimicGAN: Robust Projection onto Image Manifolds with Corruption Mimicking

In the past few years, Generative Adversarial Networks (GANs) have dramatically advanced our ability to represent and parameterize high-dimensional, non-linear image manifolds. As a result, they have been widely adopted across a variety of applications, ranging from challenging inverse problems like image completion, to problems such as anomaly detection and adversarial defense. A recurring theme in many of these applications is the notion of projecting an image observation onto the manifold that is inferred by the generator. In this context, Projected Gradient Descent (PGD) has been the most popular approach, which essentially optimizes for a latent vector that minimizes the discrepancy between a generated image and the given observation. However, PGD is a brittle optimization technique that fails to identify the right projection (or latent vector) when the observation is corrupted, or perturbed even by a small amount. Such corruptions are common in the real world, for example images in the wild come with unknown crops, rotations, missing pixels, or other kinds of non-linear distributional shifts which break current encoding methods, rendering downstream applications unusable. To address this, we propose corruption mimicking—a new robust projection technique, that utilizes a surrogate network to approximate the unknown corruption directly at test time, without the need for additional supervision or data augmentation. The proposed method is significantly more robust than PGD and other competing methods under a wide variety of corruptions, thereby enabling a more effective use of GANs in real-world applications. Finally, more importantly, we show that our approach produces state-of-the-art performance in several GAN-based applications—anomaly detection, domain adaptation, and adversarial defense, that benefit from an accurate projection.

97 MATHEMATICS AND COMPUTING↗