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Nuclear Safety [Vol. 37, No. 2, April-June 1996]

Nuclear Safety is a journal that covers significant issues in the field of nuclear safety. Its primary scope is safety in the design, construction, operation, and decommissioning of nuclear power reactors worldwide and the research and analysis activities that promote this goal, but it also encompasses the safety aspects of the entire nuclear fuel cycle, including fuel fabrication, spent-fuel processing and handling, and nuclear waste disposal, the handling of fissionable materials and radioisotopes, and the environmental effects of all these activities. Table of Contents for this issue follows. GENERAL SAFETY CONSIDERATIONS: 97 The Nuclear Community and the Public: Cognitive and Cultural Influences on Thinking About Nuclear Risk, M. A. Meyer; 109 Twenty-Third Water Reactor Safety Information Meeting, D. A. Copinger; ACCIDENT ANALYSIS: 126 Analysis of a PWR LBLOCA Without SCRAM, Trevor N. Tyler, Rafael Macian-Juan and John H. Mahaffy; DESIGN FEATURES: 139 Vulnerability of Multiple-Barrier Systems, N. C. Lind; ENVIRONMENTAL EFFECTS: 149 A Study of Wet Catalytic Oxidation of Radioactive Spent Ion Exchange Resin by Hydrogen Peroxide, Xingchao Jian, Tianbao Wu, and Guichun Yun; 157 A Comparison Study and Resolution of Differences Between Emergency Response and Safety Analysis Codes Used at the Savannah River Site, A. A. Simpkins; OPERATING EXPERIENCES: 164 Reactor Shutdown Experience, Compiled by J. W. Cletcher; RECENT DEVELOPMENTS: 167 Reports, Standards, and Safety Guides, D. S. Queener; 172 Proposed Rule Changes as of Dec. 31,1995; ANNOUNCEMENTS: 178 American Nuclear Society 1997 Annual Meeting; 178 American Nuclear Society Nuclear Criticality and Safety Division Topical Meeting; 176 The Authors.

05 NUCLEAR FUELS↗

The Study of TRR Radial Thermal Shielding Dismantling Process - 20063

The decommissioning of nuclear facilities has become an important worldwide topic because many nuclear power facilities will permanently cease operation in the foreseeable future. Taiwan Research Reactor (TRR) has stepped into the decommissioning phase in 2004, and the dismantling processes will start in 2022. TRR is a heavy water reactor designed by Canatom Company with output thermal power 40 MW. On January 3, 1973, it reaches criticality. TRR had been operated for 15 years and was permanently shut down in early 1988. The decommissioning plan of TRR was approved in 2004. According to the Nuclear Reactor Facilities Regulation Act in Taiwan, a nuclear facility must be dismantled in 25 years after stepping into the decommissioning phase. Therefore, TRR decommissioning must be completed before 2029. One of the most important tasks of TRR decommissioning is to dismantle reactor body. In the task of TRR decommissioning, mechanical cutting with remote handling is used to dismantle radial thermal shielding, which are the internal components of the TRR. This study outlines the internal components of the TRR and explains the difficulties encountered during the dismantling processes. Considering the structure and radiation dose rate of TRR and its internal components, the dismantling method and packaging method are properly arranged to complete the TRR dismantling task. This study describes the process of dismantling the radial thermal shielding during the dismantling processes and considers the impact of the radiation dose on the staff during the operation. The calculation of the radiation dose rate for the personnel during the segmentation process is based on the evaluation result by using VRdose. If the calculation of personnel working dose rate is too high, we will increase the shielding or use remote handling to reduce the operator's exposure dose in the dismantling processes to comply with the As Low As Reasonably Achievable (ALARA) principle. In this study, the latest developments in the TRR decommissioning program are described. It also provides usable experience and information regarding the future decommissioning of other nuclear facilities or nuclear power plants in Taiwan. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Development of an implicit electromagnetic capability for a hybrid gyrokinetic ion-fluid electron model

Here we report on the development and implementation of a hybrid kinetic ion–fluid electron model for electromagnetic COGENT simulations of edge plasmas. COGENT is a finite-volume gyrokinetic code that employs a locally field-aligned coordinate system combined with a mapped multi-block grid technology to handle strongly anisotropic edge plasma turbulence. The simulation model involves the long-wavelength limit of the ion gyrokinetic equation coupled to the vorticity and Ohm's law equations for the electromagnetic field perturbations. In order to handle the fast Alfvén wave time scales, an implicit-explicit time integration approach with a physics-based preconditioner is used. The model is successfully applied to the simulations of ion-scale resistive-drift ballooning turbulence in a toroidal annulus geometry. Substantial speed-up over a fully explicit time integration approach is observed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Optimal Strategies for Hybrid Battery‐Storage Systems Design

As stationary hybrid energy‐storage systems (HESS) for power systems applications have recently drawn interest due to their enhanced performance and decreasing cost, developing systematic approaches for HESS design while considering controls is gaining traction. Herein, a method is presented to optimally design hybrid battery storage by proposing a mathematical modeling framework, formulated as a mixed integer linear programming model. The optimization is capable of handling multiple subsystems of batteries, considering their economic and technological performance. Decisions involve sizing of the batteries, optimal temporal and strategic dispatch to end uses, and energy sources for charging each battery. The applicability of the model is tested on four case studies for three battery chemistries representing distinct objectives: high‐power, high‐energy, and second life. Compared to traditionally designed battery storage with a homogeneous battery, optimally designed hybrid systems can save 12%–26% of system costs, depending on the nature of the dispatch profile. Findings point to design preference toward the second life battery supplemented with some high‐power or high‐energy battery capacity, or both. With the utilized electricity price structure, customers can experience approximately 10%–35% reduction in their bills.

Koleva, Mariya↗

Carbon capture, utilization, and storage hub development on the Gulf Coast

Abstract The Gulf Coast of the United States hosts diverse power generation, refining, and petrochemical processing facilities, resulting in the nation's largest volumetric concentration of industrial CO 2 emissions, rivaled only by the Ohio River Valley. These emissions sources are concentrated in specific industrial clusters that allow combining emissions streams to achieve economies of scale. The region is currently undergoing globally significant industrial expansion and investment as a result of abundant and inexpensive regional unconventional natural gas availability, and is a growing exporter of liquefied natural gas (LNG). Opportunities to integrate CO 2 emission management within the diverse energy chains in the region are volumetrically significant and include both concentrated and dilute sources. Significant examples of capture, transport, and storage exist. Offshore storage is particularly attractive, as it provides simplified land leasing models (single governmental land owner), proven reservoir quality, and presents fewer risks to both protected groundwater and populated areas. Projects can now take advantage of recently expanded opportunities under section 45Q of the Internal Revenue Service tax code. The region continues to evolve as an active carbon‐handling hub, and is uniquely suited to justify additional investment in carbon capture, utilization, and storage (CCUS) technologies via a large‐scale integrated project development. Continued development of integrated projects will allow the region to continue to grow economically within its strong fossil‐fuel handling competence focus while advancing low‐carbon energy technologies that maintain globally competitiveness. © 2021 The Authors. Greenhouse Gases: Science and Technology published by Society of Chemical Industry and John Wiley & Sons Ltd.

45Q↗

Dynamic Material Flow Analysis of Silicon Photovoltaic Modules to Support a Circular Economy Transition

Solar photovoltaics (PV) are the fastest growing renewable energy technologies for clean, cheap, and sustainable electricity generation. To prepare for rapid scale-up, the PV industry needs to project material requirements to build out all aspects of the supply chain appropriately and plan to handle large volumes of module waste. Impacts of deploying different material circularity strategies to reduce waste and conserve primary resources need to be quantified to inform sustainable material management. Here, we introduce the photovoltaic dynamic material flow analysis (PV DMFA) model based on PV electricity generation. The model quantifies material flows and stocks in the cradle-to-cradle life cycles of utility-scale c-Si PV systems in the United States through 2100. We present case studies for solar flat glass and aluminum frame materials under various scenarios to project the impacts of PV performance, reliability, and processing parameters, material circularity strategies, and module design shifts. In the absence of circularity measures, ~100 million MT of flat glass and ~12 million MT of aluminum would be needed for PV installations by 2100 to meet projected growth in domestic utility PV demand to nearly 1000 TWh in 2100. With optimistic but feasible improvements in efficiency, reliability, and circularity, material intensity and waste could be reduced by nearly 50%. Efficient module collection, minimally intrusive recycling, and careful scrap handling and cleaning could improve material circularity in the PV value chain. This model serves as a sustainability data support tool that may aid in the circular economy transition for PV systems.

circular economy↗

Predicting Low Toxicity and Scalable Solvent Systems for High–Speed Roll–to–Roll Perovskite Manufacturing

Printed lead-based perovskite photovoltaics (PV) have gained interest due to their potential to be manufactured with scalable roll-to-roll techniques. In industrial scale-up, toxicity of inks can constrain roll-to-roll manufacturing due to the added cost of managing toxic effluents. Due to solvent toxicity, few perovskite solution chemistries in published works are scalable to gigawatt production capacity at low cost. Herein, it is shown that for scalable PV production, the use of aprotic polar solvents should be avoided due to their overall toxicity. Compliance with worldwide worker safety regulations for solvent exposure limits could require additional air handling requirements for some solvents, which in turn would affect cost-effectiveness. It is shown that costs associated with handling of hazardous substances can be significant and estimate an added cost of ¢3.7/W for dimethylformamide (DMF)-based inks. To solve this problem, a new perovskite ink solvent system is developed that is composed entirely of ether and alcohol, which has an effective exposure limit 14× higher than DMF, making it suitable for industrial coating processes. Here, it is shown that the new ink solvent system is capable of fabricating high-efficiency perovskite solar cells processed in 1 min on a standard roll-to-roll system.

36 MATERIALS SCIENCE↗

Scalable Data-Intensive Geocomputation: A Design for Real-Time Continental Flood Inundation Mapping

The convergence of data-intensive and extreme-scale computing enables an integrated software and data ecosystem for scientific discovery. Developments in this realm will fuel transformative research in data-driven interdisciplinary domains. Geocomputation provides computing paradigms in Geographic Information Systems (GIS) for interactive computing of geographic data, processes, models, and maps. Because GIS is data-driven, the computational scalability of a geocomputation workflow is directly related to the scale of the GIS data layers, their resolution and extent, as well as the velocity of the geo-located data streams to be processed. Unique in high user interactivity and low end-to-end latency requirements, geocomputation applications will dramatically benefit from the convergence of high-end data analytics (HDA) and high-performance computing (HPC). The application level challenge, however, is to identify and eliminate computational bottlenecks that arise along a geocomputation workflow. Indeed, poor scalability at any of the workflow components is detrimental to the entire end-to-end pipeline. Here, we study a large geocomputation use case in flood inundation mapping that handles multiple national-scale geospatial datasets and targets low end-to-end latency. We discuss benefits and challenges for harnessing both HDA and HPC for data-intensive geospatial data processing and intensive numerical modeling of geographic processes. We propose an HDA+HPC geocomputation architecture design that couples HDA (e.g., Spark)-based spatial data handling and HPC-based parallel data modeling. Key techniques for coupling HDA and HPC to bridge the two different software stacks are reviewed and discussed.

Liu, Yan↗

A Vision for Coupling Operation of US Fusion Facilities with HPC Systems and the Implications for Workflows and Data Management

The operation of large US Department of Energy (DOE) research facilities, like the DIII-D National Fusion Facility, results in the collection of complex multi-dimensional scientific datasets, both experimental and model-generated. In the future, it is envisioned that integrated data analysis coupled with large-scale high performance computing (HPC) simulations will be used to improve experimental planning and operation. Practically, massive data sets from these simulations provide the physics basis for generation of both reduced semi-analytic and machine-learning-based models. Storage of both HPC simulation datasets (generated from US DOE leadership computing facilities) and experimental datasets presents significant challenges. In this paper, we present a vision for a DOE-wide data management workflow that integrates US DOE fusion facilities with leadership computing facilities. Data persistence and long-term availability beyond the length of allocated projects is essential, particularly for verification and recalibration of artificial intelligence and machine learning (AI/ML) models. Because these data sets are often generated and shared among hundreds of users across multiple leadership computing facility centers, they would benefit from cross-platform accessibility, persistent identifiers (e.g. DOI, or digital object identifier), and provenance tracking. Here, the ability to handle different data access patterns suggests that a combination of low cost, high latency (e.g. for storing ML training sets) and high cost, low latency systems (e.g. for real-time, integrated machine control feedback) may be needed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Stochastic projective splitting

Here, we present a new, stochastic variant of the projective splitting (PS) family of algorithms for inclusion problems involving the sum of any finite number of maximal monotone operators. This new variant uses a stochastic oracle to evaluate one of the operators, which is assumed to be Lipschitz continuous, and (deterministic) resolvents to process the remaining operators. Our proposal is the first version of PS with such stochastic capabilities. We envision the primary application being machine learning (ML) problems, with the method’s stochastic features facilitating “mini-batch” sampling of datasets. Since it uses a monotone operator formulation, the method can handle not only Lipschitz-smooth loss minimization, but also min–max and noncooperative game formulations, with better convergence properties than the gradient descent-ascent methods commonly applied in such settings. The proposed method can handle any number of constraints and nonsmooth regularizers via projection and proximal operators. We prove almost-sure convergence of the iterates to a solution and a convergence rate result for the expected residual, and close with numerical experiments on a distributionally robust sparse logistic regression problem.

97 MATHEMATICS AND COMPUTING↗

Machine-Learning-based Algorithms for Automated Image Segmentation Techniques of Transmission X-ray Microscopy (TXM)

Four state-of-the-art Deep Learning-based Convolutional Neural Networks (DCNN) were applied to automate the semantic segmentation of a 3D Transmission x-ray Microscopy (TXM) nanotomography image data. The standard U-Net architecture as baseline along with UNet++, PSPNet, and DeepLab v3+ networks were trained to segment the microstructural features of an AA7075 micropillar. A workflow was established to evaluate and compare the DCNN prediction dataset with the manually segmented features using the Intersection of Union (IoU) scores, time of training, confusion matrix, and visual assessment. Comparing all model segmentation accuracy metrics, it was found that using pre-trained models as a backbone along with appropriate training encoder-decoder architecture of the Unet++ can robustly handle large volumes of x-ray radiographic images in a reasonable amount of time. This opens a new window for handling accurate and efficient image segmentation of in situ time-dependent 4D x-ray microscopy experimental datasets.

36 MATERIALS SCIENCE↗

Ni/SiO 2 catalysts for polyolefin deconstruction via the divergent hydrogenolysis mechanism

Noble metal-based hydrogenolysis is emerging as a key chemical deconstruction technology of polyolefins into valuable products. Still, the catalyst cost and availability are significant barriers to handling the large volume of plastics. Cheap earth-abundant metals have been deemed inactive for polyolefin hydrogenolysis. Herein, we report that Ni/SiO 2 is active in deconstructing low-density polyethylene to n-alkanes (C 6 -C 35 ) at mild conditions (300 °C, 30barH 2 ) with maximum liquid yields of 65 wt%. In this study, we expose a new mechanism of long-alkane hydrogenolysis that encompasses chain location-dependent single and multiple C-C bond cracking events and rationalizes product selectivity and molecular weight dependence. Ni/SiO 2 catalysts are reusable and can handle multiple plastics producing feedstock-dependent products (i.e., n-alkanes, iso-alkanes, cyclics, aromatics, etc.). The findings broaden the scope of viable catalysts polyolefin hydrogenolysis and unleash the potential to manage the volume of plastic waste.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

The nth-plant scenario for blended feedstock conversion and preprocessing nationwide: biorefineries and depots

The sustainability of the biofuel industry depends on the development of a mature conversion technology on a national level that can take advantage of the economies of scale: the nth-plant. Defining the future location and supply logistics of conversion plants is imperative to ultimately transform the nation’s renewable biomass resources into cost-competitive, high-performance feedstock for production of biofuels and bioproducts. Since the US has put restrictions on production levels of conventional biofuels from edible resources, the nation needs to plan for the widespread accessibility and development of the cellulosic biofuel scenario. Conventional feedstock supply systems will be unable to handle cellulosic biomass nationwide, making it essential to expand the industry with an advanced feedstock supply system incorporating a distributed network of preprocessing depots and conversion plants, or biorefineries. Current studies are mostly limited to designing supply systems for specific regions of the country. We developed a national database with potential locations for depots and biorefineries to meet the nation’s target demand of cellulosic biofuel. Blended feedstock with switchgrass and corn stover (harvested by either a two- or three-pass method) are considered in a Mixed Integer Linear Programming model to deliver on-spec biomass that considers both, a desired quantity and quality at the biorefinery. A total delivered feedstock cost that is less than $79.07/dt (2016$) is evaluated for years 2022, 2030, and 2040. In 2022, 124 depots and 59 biorefineries could be supplied with 42.8 million dt of corn stover and switchgrass. In 2030 and 2040, the total accessible biomass could increase to 215% and 393% respectively when compared to 2022. However, an $8/dry tons reduction in targeted delivery cost could reduce total accessible biomass by 67%. Kansas, Nebraska, South Dakota and Texas were identified as potential states with a strong biofuel economy given that they had six or more biorefineries located in all scenarios. In some scenarios, Colorado, Alabama, Georgia, Minnesota, Mississippi and South Carolina would greatly benefit from a depot network as these could only deliver to a biorefinery in a nearby state. To elaborate the impact of a nationwide consideration, the findings were compared with existing literature for different US regions. We also present results for biorefinery capacities that are double, triple, and quadruple in size.

09 BIOMASS FUELS↗

Air quality impacts from the development of unconventional oil and gas well pads: Air toxics and other volatile organic compounds

Unconventional oil and natural gas development (UOGD) has expanded rapidly across the United States in recent decades and raised concerns about associated air quality impacts. While significant effort has been made to quantify methane emissions, relatively few observations have been made of Volatile Organic Compounds (VOCs), especially during drilling and completion of new wells. Extensive air monitoring during development of several large, multi-well pads in Broomfield, Colorado, in the Denver-Julesburg Basin, provides a novel opportunity to examine changes in local air toxics and other VOC concentrations during well drilling and completions and production. These operations offer an especially useful case to study as several management practices were implemented to reduce emissions (e.g., electrified, grid-powered drill rigs and closed loop fluid handling systems to reduce truck traffic and limit fluid handling on the pad). With simultaneous measurements of methane and 50 VOCs from October 2018 to December 2022 at as many as 19 sites near well pads, in adjacent neighborhoods, and at a more distant reference location, we identify impacts from each phase of well development and production. Use of weekly, time-integrated canisters, a Proton Transfer Reaction Mass Spectrometer (PTR-MS), continuous photoionization detectors (PID) to trigger canister collection upon detection of VOC-rich plumes, and an instrumented vehicle, provided a powerful suite of measurements to characterize both transient plumes and longer-term changes in air quality. Prior to the start of well development, VOC gradients were small across Broomfield. Once drilling commenced, concentrations of oil and gas (O&G) related VOCs, including alkanes and aromatics, increased around active well pads. Concentration increases were clearly apparent during certain operations, including drilling, coil tubing/millout operations, and production tubing installation. Emissions of C 8 –C 10 n-alkanes during drilling operations highlighted the importance of VOC emissions from synthetic drilling mud chosen to reduce odor impacts. More than 90 samples were collected of transient plumes. Using composition measurements, meteorological data, and information about well pad activities, these plumes were connected with specific UOGD operations including drilling, flowback, and production equipment maintenance. The chemical signatures of these plumes differed by operation type (e.g., C 8 –C 10 n-alkanes constituted a larger fraction of measured VOCs in drilling-related plumes). Concentrations of individual, oil and gas-related VOCs in these plumes were often several orders of magnitude higher than in background air, with maximum ethane and benzene concentrations of 79,600 and 819 ppbv, respectively. Because these plumes typically impact a monitoring site for just several minutes, they are easily missed by slower-responding instruments. Study measurements highlight future emission mitigation opportunities during UOGD operations, including better control of emissions from shakers that separate drill cuttings from drilling mud, production separator maintenance operations, and periodic emptying of sand cans during flowback operations.

54 ENVIRONMENTAL SCIENCES↗

Removable coatings: Thermal stability and decontamination of steel surfaces from 241 Am

This study presents a comparative analysis of several strippable materials for decontamination of steel surfaces from 241 Am. The strippable coatings were chosen to have a history of application, to be commercially available, easily handled and have different composition and formulation. Carbon steel and stainless steel surfaces (coupons) were utilized as the most representative industrial materials, and the experimental series were expanded to include the rusting treatment of these surfaces as it is common for decommissioned old nuclear facilities. The experiments followed the path of pre-screening of the strippable materials (easiness of application, peeling etc.), their characterization with Fourier-transform infrared (FTIR) spectroscopy and thermogravimetric analysis (TGA), decontamination factors (DF) or removal efficiencies for different types of steel surfaces, and enhancement of the removal efficiencies of the select strippable coatings via amendment with EDTA. As a result, DF and removal efficiencies for stainless steel (both pristine and with rusting treatment) are higher than for pristine carbon steel, and decontamination factors and removal efficiencies are higher for pristine than for rusted carbon steel across all the coatings. It is also shown that EDTA amendment can improve DF and removal efficiency for a strippable coating (i.e., CC Strip), however other factors should also be considered. Thus, the coating CC Strip exhibited easiness in handling and high DF (up to 97% when EDTA-amended), but its drying period was the longest among the rest of the materials and its thermal decomposition indicates on a risk of intense release of heat in case of a fire event.

36 MATERIALS SCIENCE↗

Latent map Gaussian processes for mixed variable metamodeling

Gaussian processes (GPs) are ubiquitously used in sciences and engineering as metamodels. Standard GPs, however, can only handle numerical or quantitative variables. Here we introduce latent map Gaussian processes (LMGPs) that inherit the attractive properties of GPs and are also applicable to mixed data which have both quantitative and qualitative inputs. The core idea behind LMGPs is to learn a continuous, low-dimensional latent space or manifold which encodes all qualitative inputs. To learn this manifold, we first assign a unique prior vector representation to each combination of qualitative inputs. We then use a low-rank linear map to project these priors on a manifold that characterizes the posterior representations. As the posteriors are quantitative, they can be directly used in any standard correlation function such as the Gaussian or Matern. Hence, the optimal map and the corresponding manifold, along with other hyperparameters of the correlation function, can be systematically learned via maximum likelihood estimation. Through a wide range of analytic and real-world examples, we demonstrate the advantages of LMGPs over state-of-the-art methods in terms of accuracy and versatility. In particular, we show that LMGPs can handle variable-length inputs, have an explainable neural network interpretation, and provide insights into how qualitative inputs affect the response or interact with each other. We also employ LMGPs in Bayesian optimization and illustrate that they can discover optimal compound compositions more efficiently than conventional methods that convert compositions to qualitative variables via manual featurization.

42 ENGINEERING↗

NeuroSEM: A hybrid framework for simulating multiphysics problems by coupling PINNs and spectral elements

Multiphysics problems that are characterized by complex interactions among fluid dynamics, heat transfer, structural mechanics, and electromagnetics, are inherently challenging due to their coupled nature. While experimental data on certain state variables may be available, integrating these data with numerical solvers remains a significant challenge. Physics-informed neural networks (PINNs) have shown promising results in various engineering disciplines, particularly in handling noisy data and solving inverse problems in partial differential equations (PDEs). However, their effectiveness in forecasting nonlinear phenomena in multiphysics regimes, particularly involving turbulence, is yet to be fully established. Here, this study introduces NeuroSEM, a hybrid framework integrating PINNs with the highfidelity Spectral Element Method (SEM) solver, Nektar++. NeuroSEM leverages the strengths of both PINNs and SEM, providing robust solutions for multiphysics problems. PINNs are trained to assimilate data and model physical phenomena in specific subdomains, which are then integrated into the Nektar++ solver. We demonstrate the efficiency and accuracy of NeuroSEM for thermal convection in cavity flow and flow past a cylinder. The framework effectively handles data assimilation by addressing those subdomains and state variables where the data is available. We applied NeuroSEM to the Rayleigh-B´enard convection system, including cases with missing thermal boundary conditions and noisy datasets. Finally, we applied the proposed NeuroSEM framework to real particle image velocimetry (PIV) data to capture flow patterns characterized by horseshoe vortical structures. Our results indicate that NeuroSEM accurately models the physical phenomena and assimilates the data within the specified subdomains. The framework’s plug-and-play nature facilitates its extension to other multiphysics or multiscale problems. Furthermore, NeuroSEM is optimized for efficient execution on emerging integrated GPU-CPU architectures. This hybrid approach enhances the accuracy and efficiency of simulations, making it a powerful tool for tackling complex engineering challenges in various scientific domains.

42 ENGINEERING↗

A resolution independent neural operator

The Deep operator network (DeepONet) is a powerful yet simple neural operator architecture that utilizes two deep neural networks to learn mappings between infinite-dimensional function spaces. This architecture is highly flexible, allowing the evaluation of the solution field at any location within the desired domain. However, it imposes a strict constraint on the input space, requiring all input functions to be discretized at the same locations; this limits its practical applications. Here, in this work, we introduce a general framework for operator learning from input–output data with arbitrary number and locations of sensors. This begins by introducing a resolution-independent DeepONet (RI-DeepONet), enabling it to handle input functions that are arbitrarily, but sufficiently finely, discretized. To this end, we propose two dictionary learning algorithms to adaptively learn a set of appropriate continuous basis functions, parameterized as implicit neural representations (INRs), from correlated signals defined on arbitrary point cloud data. These basis functions are then used to project arbitrary input function data as a point cloud onto an embedding space (i.e., a vector space of finite dimensions) with dimensionality equal to the dictionary size, which can be directly used by DeepONet without any architectural changes. In particular, we utilize sinusoidal representation networks (SIRENs) as trainable INR basis functions. The introduced dictionary learning algorithms are then used in a similar way to learn an appropriate dictionary of basis functions for the output function data, which defines a new neural operator architecture referred to as the R esolution I ndependent N eural O perator (RINO). In the RINO, the operator learning task simplifies to learning a mapping from the coefficients of input basis functions to the coefficients of output basis functions. We demonstrate the robustness and applicability of RINO in handling arbitrarily (but sufficiently richly) sampled input and output functions during both training and inference through several numerical examples.

Deep operator network (DeepONet)↗