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At least 271 records · Page 15

Code Coverage Status of the ARC Code DASSH-F

The Argonne Reactor Code (ARC) software system supports users in their fast reactor design goals by providing neutronic, thermal-hydraulic, and structural analysis capabilities. DASSH-F serves as a steady state thermal hydraulic capability within the ARC system and replaces the SE2-ANL software that preceded it. This document identifies the set of test problems used to assess the code coverage for DASSH-F. The goal is to document what parts of the existing DASSH-F code are touched by the set of test problems and which are not. Because the verification work remains to be done on DASSH-F, one can assume that most of these issues will be resolved as part of that work. The code coverage analysis of DASSH-F was performed with the Code Coverage Tool of the Intel Fortran compiler which requires modifications to the compilation of DASSH-F. The code coverage tables are given for each submodule of DASSH-F. Because DASSH-F links to modules in DIF3D, some details on coverage changes to the DIF3D linked files is provided. As will be seen, most of the uncovered parts/files can be ignored because they are either for error message and debugging output or obviously not needed by DASSH-F today. Seven features of the DASSH-F code were identified to not be covered by the existing testing suite and thus additional verification test problems are suggested to fully cover these sections.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

The right conditions for high-precision dynamic temperature and heat capacity measurement via pyrometry and conductivity

The pursuit of accurate bulk temperature T under extreme conditions has been a long-standing goal of the high pressure science community, complicated by a lack of data to inform models. To reach these extremely high-pressure, high-temperature (high P − T) conditions, a combination of dynamic and heated static experiments (e.g., diamond or gem anvil cel experiments) are used. For example, in a diamond anvil cell (DAC) experiment, a sample placed in the DAC is first pressurized. Following pressurization, the sample T is increased either by heating the entire DAC (usually using resistive heating, and limited to ∼1000K) or by applying intense laser power to the sample surfaces. In a dynamic experiment, the process of pressurizing the sample also heats it. In the case of shock physics experiments, such heating is substantial, easily reaching thousands of Kelvin; in our work we have seen T ∼17000K. Most methods of measuring temperature at ambient are not compatible with experiments under these high-pressure, high-temperature conditions: thermocouples break, melt, or have conductivity properties that differ from ambient where they are calibrated; thermometers would melt; both are too slow. As a result most methods are based on non-contact techniques such as x-ray diffraction broadening, neutron scattering, or optical methods. Of these, optical methods using the visible and near-infrared region of the spectrum are the most commonly used as the sources and detectors are readily available. In the case of optical methods the optical depth, and therefore the measurement location, is limited to the surface. When a window or anvil material is used, heat flows from the sample into the window/anvil. Likewise, if the sample undergoes a change in thermodynamic state, such as expansion upon release, different T may be expected. As a result, the surface or apparent temperature T app measurement will differ from the bulk or interior temperature that is desired. This surface measurement must be related to the bulk measurement using thermal transport models and material models. While it is tempting to conclude that one should just use x-ray methods that directly probe the interior, even these methods have been shown to depend on thermal transport and material models. Regardless of the method used to create the high P − T condition, therefore, we must understand the role of thermal transport and material models upon our interpretation of the T measurement, as well as the errors and uncertainties associated with the choice of models used in the analysis. This is a substantial area of research and this paper is by no means a complete survey of the relevant sources of uncertainty. For example, we have yet to begin to address alternate transport models in a detailed manner (e.g., Tan-Ahrens), or the many models that use additional layers to approximate melting, turbulence, or epitaxial phenomena). Likewise, we have not explored the impact upon uncertainty of thermal models that use temperature-dependent thermal transport coefficients, or the wide range of material models that can be applied. Instead, this paper focuses on using one simple model, the Urtiew-Grover model, to understand the sources of error in T measurement so that we may identify how best to focus future research efforts to return the best improvements and avoid working on over-optimizing a single type of measurement. To this end, we work through some of the best and worst case scenarios for T measurement.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Noise-canceling quantum feedback: Non-Hermitian dynamics with applications to state preparation and magic state distillation

Time-continuous quantum measurement allows for the tracking of a quantum system in real time via sequences of short, and individually weak, measurement intervals. Such measurements are necessarily invasive, imparting backaction to the system, and allowing the observer to update their state estimate based on stochastic measurement outcomes. Feedback control then involves real-time interventions by an observer, conditioned on the time-continuous measurement signal that they receive. Here, we consider here diffusive quantum trajectories and focus on the “noise-canceling” subset of feedback protocols that aim to minimize the degree of stochasticity in the dynamics. We derive such a class of feedback operations, showing that under the idealized assumptions of pure states, unit measurement efficiency, and zero time delay in implementing feedback operations, perfectly noise-canceling feedback always exists. We consider the resulting noise-canceled dynamics generated by an effective non-Hermitian Hamiltonian; while non-Hermitian Hamiltonians from continuous monitoring generally describe rare dynamics (accessible by costly postselection), the use of noise-canceling feedback here leads to non-Hermitian dynamics that occur deterministically. We demonstrate this via examples of entangled state preparation and stabilization. We then illustrate the potential for the application of noise cancellation to boost success rates in magic state distillation protocols. We show that adding feedback based on noise cancellation into a time-continuous five-to-one distillation protocol leads to higher probabilities of successful distillation across a range of input errors and increases the threshold on input errors for which the protocol is effective. Our results highlight the efficacy of noise-canceling feedback-aided protocols for quantum state preparation and stabilization tasks.

Karmakar, Tathagata [University of California, Ber↗

Integration of the NCRC Database and Other INL Databases

The Nuclear Computational Resource Center provides a portal by which industry professionals, educational staff, students, national laboratory employees, and others may request access to certain engineering software tools. As the tools provided through the Nuclear Computational Resource Center portal are not open-source and freely available, a set of approvals are necessary before access is granted. All code recipients must be associated with an institution that has a license with Idaho National Laboratory for the code requested. Information about these licenses is controlled by Idaho National Laboratory’s Technology Deployment organization and housed in a Technology Deployment database. Those requesting code access who are not citizens of the United States must also have a security plan, mandated by Idaho National Laboratory policy. Security plans are managed by the International Access Program and are stored in an International Access Program database known as IFacts. Granting access to software thus depends on information stored in the Technology Deployment database and IFacts. In the past, no connection between the Nuclear Computational Resource Center portal and these databases existed, making checking the status of license agreements and security plans time consuming and error prone. This report demonstrates that the Nuclear Computational Resource Center portal now connects to both the Technology Deployment database and IFacts, greatly improving the ease of use of the Nuclear Computational Resource Center system for administrators, which leads to a better overall experience for those requesting code access.

99 GENERAL AND MISCELLANEOUS↗

Code Coverage Status of the ARC Code DIF3D

The Argonne Reactor Code (ARC) software system supports users in their fast reactor design goals by providing neutronic, thermal-hydraulic, and structural analysis capabilities. DIF3D plays a pivotal role in the ARC system as the primary homogenized assembly neutronic calculation methodology for fast reactor problems. Over its 40 years history, ARC software usage with DIF3D has been applied to numerous fast and thermal spectrum reactor analysis projects with good to excellent comparison against experiments. With continued improvement of computation resources, many of the geometry modeling capabilities in DIF3D that were primarily used in low order schemes are not really needed anymore. Today, the diffusion and transport capabilities of DIF3D-VARIANT are primarily used in the reactor design process with some scattered usage of DIF3D-FD and DIF3D-Nodal. In recent work, the DIF3D software verification was completed for DIF3D-FD and DIF3D-VARIANT on the geometry options used in the Versatile Test Reactor project. While we can be confident that these capabilities of DIF3D are well used and thus trusted, it does not demonstrate that all possible input options of DIF3D are actually working, but just those that were tested as part of VTR are and that they are correct. Thus, the purpose of the present work is to identify a set of test problems for DIF3D and assess the code coverage of DIF3D for those test problems. The goal is to document what parts of the existing DIF3D code are touched by the set of test problems and which are not. Because the verification work done on DIF3D-VARIANT and DIF3D-FD was focused on the most common uses of DIF3D for fast reactor analysis, the code coverage assessment of those capabilities is the highest priority. This will ensure that nothing is being missed by the existing verification test problems that DIF3D relies upon. The DIF3D-Nodal capability will also be inspected for code coverage as part of this work to further ensure that regular regression testing of DIF3D will trap any likely errors the end user might experience with the DIF3D software. The code coverage analysis of DIF3D was performed with the Code Coverage Tool of the Intel Fortran compiler which requires modifications to the compilation of DIF3D. The detailed coverage tables are given for each submodule of DIF3D separately, and for the submodules which are primarily developed for DIF3D, most of the source files could be at least partially touched. Most of the uncovered parts/files could be easily ignored, because they are either for error message and debugging output or obviously not needed by DIF3D. Out of the entire source codes of DIF3D, only a few uncovered modules deserve further investigation.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Assessing correlated truncation errors in modern nucleon-nucleon potentials

We test the BUQEYE model of correlated effective field theory (EFT) truncation errors on Reinert, Krebs, and Epelbaum's semilocal momentum-space implementation of the chiral EFT (𝜒⁢EFT ) expansion of the nucleon-nucleon (NN) potential. This Bayesian model hypothesizes that dimensionless coefficient functions extracted from the order-by-order corrections to NN observables can be treated as draws from a Gaussian process (GP). We combine a variety of graphical and statistical diagnostics to assess when predicted observables have a 𝜒⁢EFT convergence pattern consistent with the hypothesized GP statistical model. Our conclusions are that, first, the BUQEYE model is generally applicable to the potential investigated here, which enables statistically principled estimates of the impact of higher EFT orders on observables. Second, parameters defining the extracted coefficients such as the expansion parameter 𝑄 must be well chosen for the coefficients to exhibit a regular convergence pattern—a property we exploit to obtain posterior distributions for such quantities. Third, the assumption of GP stationarity across lab energy and scattering angle is not generally met; this necessitates adjustments in future work. We provide a workflow and interpretive guide for our analysis framework, and show what can be inferred about probability distributions for 𝑄, the EFT breakdown scale Λ 𝑏 , the scale associated with soft physics in the 𝜒⁢EFT potential 𝑚 eff , and the GP hyperparameters. All our results can be reproduced using a publicly available Jupyter notebook, which can be straightforwardly modified to analyze other 𝜒⁢EFT NN potentials.

Bayesian methods↗

Elliptically-Contoured Tensor-variate Distributions with Application to Image Learning

Statistical analysis of tensor-valued data has largely used the tensor-variate normal (TVN) distribution that may be inadequate for data arising from distributions with heavier or lighter tails. We study a general family of elliptically contoured (EC) TV distributions and derive its characterizations, moments, marginal, and conditional distributions. We describe procedures for maximum likelihood estimation from data that are (1) uncorrelated draws from an EC distribution, (2) from a scale mixture of the TVN distribution, and (3) from an underlying but unknown EC distribution, for which we extend Tyler’s robust estimator. A detailed simulation study highlights the benefits of choosing an EC distribution over the TVN for heavier-tailed data. We develop TV classification rules using discriminant analysis and EC errors and show that they better predict cats and dogs from images in the Animal Faces-HQ dataset than the TVN-based rules. A novel tensor-on-tensor regression and TV analysis of variance (TANOVA) framework under EC errors is also demonstrated to better characterize gender, age, and ethnic origin than the usual TVN-based TANOVA in the celebrated labeled faces of the wild dataset.

97 MATHEMATICS AND COMPUTING↗

Annotation of DOM metabolomes with an ultrahigh resolution mass spectrometry molecular formula library

Current approaches to analyzing metabolomic data often rely on matching MS/MS fragmentation data to sparse libraries or databases. This approach results in limited identification of features, often with less than 10% of the dataset being annotated. A complementary approach is to assign molecular formula to features based on accurate mass measurements, but the platforms commonly used for metabolomics do not have the needed accuracy or resolving power to do this robustly, particularly for larger molecules. Using our newly modified analysis tool, CoreMS, we generated a library of molecular formula from pooled samples analyzed with LC-21T FT-ICR MS. This library successfully annotated approximately 53.2% of features identified from the exometabolome of marine diatom Phaeodactylum tricornutum – a nearly ten-fold increase over the 5.9% annotation rate achieved using a conventional MS/MS library matching approach. Using this FT-ICR MS library approach, we were able to differentiate differences in the exometabolome of P. tricornutum in iron replete and iron limited conditions, with 668 metabolites being differentially expressed (p < 0.05, 2 x intensity difference) under these conditions. The traditional MS/MS fragmentation-based annotation approach only annotated 61 of these metabolites, while our novel pipeline annotated 450 metabolites and revealed 12 metabolites that were significantly more abundant under low iron conditions. Our results demonstrate the utility of ultrahigh resolution mass spectrometry for generating more comprehensive and confident molecular annotations.

21T-FTICR-MS, CoreMS↗

Toward a Generalizable Prediction Model of Molten Salt Mixture Density with Chemistry‐Informed Transfer Learning

Optimally designing applications of molten salts requires knowledge of their thermophysical properties over a wide range of temperatures and compositions. There exist significant gaps in existing databases and this data can be challenging to experimentally measure due to high temperatures, salt corrosivity, and salt hygroscopicity. Existing databases have been used to create Redlich–Kister (RK) models for mixture density showing improved accuracy with respect to ideal mixing assumptions, but these models require subcomponent data measurements for each new system, therefore lacking generality. In order to address generalizability and data sparsity, a transfer learning procedure is proposed to train deep neural networks (DNNs) using a combination of semi‐empirical relationships (RK), data from the thermophysical arm of the molten salt thermal properties database and universal ab initio properties of component mixtures taken from the joint automated repository for various integrated simulations (JARVIS) classical force‐field inspired descriptors database to predict density in molten salts. Herein, it is shown that DNNs predict molten salt density with an r 2 over 0.99 and a mean absolute percentage error under 1%, outperforming alternative methods.

inorganic materials↗

Stable Simulation of the Community Atmosphere Model Using Machine‐Learning Physical Parameterization Trained With Experience Replay

In recent years, machine learning (ML) models have been used to improve physical parameterizations of general circulation models (GCMs). A significant challenge of integrating ML models into GCMs is the online instability when they are coupled for long‐term simulation. We present a new strategy that demonstrates robust online stability when the physical parameterization package of an atmospheric GCM is replaced by a deep ML model. The method uses experience replay with a multistep training scheme of the ML model in which the model's own output at the previous time step is used in the training. Predicted physics tendencies in the replay buffer with the most recent errors in the training iterations are reused, making the ML model learn from its own errors. The training method reduces the gap between the offline and online environments of the ML model. The method is used to train the ML model as the physical parameterization of the Community Atmosphere Model (CAM5) with training data from the Multi‐scale Modeling Framework high resolution simulations. Three 6‐year online simulations of the CAM5 are carried out by using the ML physics package. The simulated spatial distributions of precipitation, surface temperature and zonally averaged atmospheric fields demonstrate overall better accuracy than that of the standard CAM5 and benchmark model even without the use of additional physical constraints or tuning. This work is the first to demonstrate a solution to address the online instability problem in climate modeling with ML physics by using experience replay.

54 ENVIRONMENTAL SCIENCES↗

Adaptive Control for Load-Following of Boiling Water Reactors Part I: Linear Systems and Fully-Observable Dynamics

Automation control is a key strategy to improve the economic competitiveness of nuclear power plants. Not only does it help reduce operational costs, but it also extends the value proposition of these plants to nontraditional markets, including unattended operations in remote villages and space. However, the dynamics of the operating environments of nuclear reactors are subject to changes over time, and there are no widely adopted methods to ensure that the automation strategy will remain effective over the extended durations required for these applications. Adaptive control is a discipline that offers the possibility to accommodate such changes online. However, it relies on mathematical assumptions that must be respected to ensure robustness and reliability. In this work, we derive an adaptive control formulation for linear systems in which all states are observable and apply it to an instance of load-follow operation for Boiling Water Reactors. We assumed uncertainty in two factors: the temperature coefficient and the control rod worth, both of which are affected over time by the evolution of the nuclear reactor core environment. With an arbitrary penalty factor of 5, we found that the mean absolute and integral time absolute errors can be reduced by more than 90%, underscoring the strength of adaptive control. To extend the application to more challenges, different uncertainties and load-follow trajectories, as well as new formulations that include non-linearity and partial observability, are currently being developed.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗

Optimizing lossy state preparation for quantum sensing using Hamiltonian engineering

One of the most prominent platforms for demonstrating quantum sensing below the standard quantum limit is the spinor Bose–Einstein condensate. While a quantum advantage using several tens of thousands of atoms has been demonstrated in this platform, it faces an important challenge: atom loss. Atom loss is a Markovian error process modeled by Lindblad jump operators, and a no-go theorem, which we also show here, states that the loss of atoms in all spin components reduces the quantum advantage to a constant factor. Here, we show that this no-go theorem can be circumvented if we constrain atom losses to a single spin component. Moreover, we show that in this case, the maximum quantum Fisher information with N atoms scales as N 3/2 , establishing that a scalable quantum advantage can be achieved despite atom loss. Although Lindblad jump operators are generally non-Hermitian and non-invertible, we use their Moore–Penrose inverse to develop a framework for constructing several states with this scaling of Fisher information in the presence of losses. We use Hamiltonian engineering with realistic Hamiltonians to develop experimental protocols for preparing these states. Finally, we discuss possible experimental techniques to constrain the losses to a single spin mode.

74 ATOMIC AND MOLECULAR PHYSICS↗

Single-qubit multi-party transmission using universal symmetric quantum cloning

This study considers the hypothetical quantum network case where Alice wishes to transmit one qubit of information (specifically a pure quantum state) to M parties, where M is some large number. The remote receivers locally perform single-qubit quantum state tomography on the transmitted qubits in order to compute the quantum state within some error rate (dependent on the tomography technique and the number of transmitted qubits). We show that with the use of an intermediate optimal symmetric universal quantum cloning machine (between Alice and the remote receivers) as a repeater-type node in a hypothetical quantum network, Alice can send significantly fewer qubits compared to direct transmission of the message qubits to each of the M remote receivers. This is possible due to two properties of quantum cloning. The first is that single qubit quantum clones retain the same Bloch angle as the initial quantum state. This means that if the mixed state of the quantum clone can be computed to high enough accuracy, the original pure quantum state can be inferred by extrapolating that vector to the surface of the Bloch sphere. The second property is that the state overlap of approximate quantum clones, with respect to the original pure quantum state, quickly converges (specifically for 1 → M , the limit of the fidelity as M goes to infinity is $\frac{2}{3}$). This means that Alice can prepare a constant number of qubits (which are then passed through the quantum cloning machine) in order to achieve a desired error rate if M is large enough. Combined, these two properties mean that for a large M , Alice can prepare many orders of magnitude fewer qubits in order to achieve the same single qubit transmission accuracy compared to the naive direct qubit transmission approach.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Commercial integration of advanced nuclear energy with Artificial Intelligence (AI): Possible implications

The integration of advanced nuclear technologies (both fission and fusion) with artificial intelligence (AI) presents unprecedented national security challenges and opportunities. As fusion energy approaches commercial viability alongside advanced Small Modular Reactors (SMRs), their integration with AI and Artificial General Intelligence (AGI) systems could fundamentally transform the global energy and AI landscapes — two pillars of national security. This document briefly examines how AI could accelerate nuclear energy development and deployment while altering existing power structures, a lot could be done to deepen the discussions. Simultaneously, it observes how nuclear-powered AI may expedite advances toward AGI and beyond. These issues are deeply interconnected and thus need to be examined as a whole and more comprehensively than what’s being summarized here. For instance, AI-powered autonomous operation of nuclear facilities could reduce human error but introduce new cybersecurity vulnerabilities and uncertainties. Further investigation would also address how AI-enhanced nuclear technologies might complicate proliferation concerns through advanced fuel cycle management, nuclear materials production and safeguard. The strategic advantage gained by first entities achieving successful AI-nuclear integration could reshape global and national security framework. Timely analysis of these implications may be crucial for policymakers seeking to harness these technologies' benefits while effectively mitigating their potential risks.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Enhancing Fluid Flow Pressure and Saturation Prediction Accuracy and Reducing Uncertainty with Committee Machine – Illinois Basin Decatur Project (IBDP) as a Case Study

Presentation at the 17th International Conference on Greenhouse Gas Control Technologies GHGT-17 held in Calgary, Canada, October 20-24, 2024. Carbon capture and storage (CCS) is a way to play a critical role in the global transition to a low-emission economy. Current progress is hampered by a number of factors, among which the lack of risk-informed design tools and decision support frameworks is seen as a major roadblock. Significant interest exists in using artificial intelligence to accelerate CCS site feasibility studies, as well as to facilitate the permit application process. Existing works commonly train a single deep learning model. This work investigates the feasibility of using a conventional ensemble learning (committee machine) technique to further improve prediction accuracy. Ensemble-based algorithms generally improve over individual base learners in terms of robustness and accuracy. Deep ensembles, however, are time-consuming to create and train. A pragmatic question is whether small-sized ensembles may lead to prediction improvement. Here we evaluated the efficacy of an ensemble learning technique using the latent spectral model (LSM), an efficient deep neural operator algorithm, as base learners. Preliminary results, obtained using the Illinois Basin-Decatur Project (IBDP) carbon sequestration data/model, show that small-sized ensembles can improve prediction over the base learners, achieving prediction accuracy of ~1.6 psi root mean square error (RMSE) on pressure (relative the average reservoir pressure of 3150 psi), and less than 1.3% for saturation.

Sun, Alexander↗

Enhancing Fluid Flow Pressure and Saturation Prediction Accuracy and Reducing Uncertainty with Committee Machine – Illinois Basin Decatur Project (IBDP) as a Case Study

This is the conference paper accompanying an oral presentation at the 17th International Conference on Greenhouse Gas Control Technologies GHGT-17 held in Calgary, Canada, October 20-24, 2024. Carbon capture and storage (CCS) is a way to play a critical role in the global transition to a low-emission economy. Current progress is hampered by a number of factors, among which the lack of risk-informed design tools and decision support frameworks is seen as a major roadblock. Significant interest exists in using artificial intelligence to accelerate CCS site feasibility studies, as well as to facilitate the permit application process. Existing works commonly train a single deep learning model. This work investigates the feasibility of using a conventional ensemble learning (committee machine) technique to further improve prediction accuracy. Ensemble-based algorithms generally improve over individual base learners in terms of robustness and accuracy. Deep ensembles, however, are time-consuming to create and train. A pragmatic question is whether small-sized ensembles may lead to prediction improvement. Here we evaluated the efficacy of an ensemble learning technique using the latent spectral model (LSM), an efficient deep neural operator algorithm, as base learners. Preliminary results, obtained using the Illinois Basin-Decatur Project (IBDP) carbon sequestration data/model, show that small-sized ensembles can improve prediction over the base learners, achieving prediction accuracy of ~1.6 psi root mean square error (RMSE) on pressure (relative the average reservoir pressure of 3150 psi), and less than 1.3% for saturation.

Sun, Alexander↗

Comparing Classical and Machine Learning Force Fields for Modeling Deformation of Metal–Organic Frameworks Relevant for Direct Air Capture

Deformation of metal–organic frameworks (MOFs) induced by adsorbate molecules can affect adsorption properties such as capacity and selectivity, but most computational studies of MOFs assume framework rigidity to simplify calculations. Although flexible force fields (FFs) for MOFs have been parametrized for specific materials, the generality of FFs for reliably modeling adsorbate-induced deformation to accuracy nearing that of density functional theory (DFT) has not been established. This work confirms using DFT calculations that adsorbate-induced deformation can affect CO 2 and H 2 O adsorption energies in a considerable fraction of MOFs promising for direct air capture (DAC). We then benchmark the efficacy of several general-purpose FFs in describing adsorbate-induced deformation for DAC against DFT. Our results show that current classical FFs are insufficient for describing MOF deformation, especially in cases of interest for DAC where strong interactions exist between adsorbed molecules and MOF frameworks. Some emerging machine learning force fields (MLFFs) we tested, particularly CHGNet, MACE-MP-0, and Equiformer V2, appear to be more promising than the classical FF for emulating the deformation behavior described by DFT. The best performing FF (CHGNet), however, fails to achieve the accuracy required for practical predictions with a mean absolute adsorption energy error of 0.124 eV.

adsorption↗

Spatially Accelerated Winding Numbers for Curved Geometry

The generalized winding number (GWN) is a scalar field that supports robust containment queries on curved geometry, including non-watertight, overlapping, and nested boundary representations. While queries can be easily parallelized over samples, direct evaluation on parametric curves and surfaces remains costly for large and complex models. Fast, state-of-the-art GWN approaches leverage a spatial index to approximate the GWN, typically coupled with a Taylor expansion which approximates the GWN contribution for far clusters of geometric primitives. However, such methods operate only on discrete inputs such as triangle meshes and point clouds, and would introduce containment errors near boundaries if applied to curved input. We extend support for fast GWN evaluation over arbitrary collections of NURBS curves in 2D and trimmed NURBS patches in 3D via a Bounding Volume Hierarchy that stores efficiently precomputed moment data in the hierarchy nodes. When querying the hierarchy, approximations for far clusters are used alongside direct evaluation for nearby NURBS primitives, achieving sub-linear complexity while preserving the geometric features in the vicinity of the query point. Central to our performance improvements is an adaptive subdivision strategy for NURBS primitives during a preprocessing phase, creating better spatial partitions while retaining the same accuracy for containment decisions as a direct evaluation. We demonstrate the performance and accuracy of our approach across a large collection of 2D and 3D datasets.

Computer science↗