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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 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Simulation of the Fast Reactor Fuel Assembly Duct-Bowing Reactivity Effect Using Monte Carlo Neutron Transport and Finite Element Analysis

This paper discusses a new method of simulating the fuel assembly duct-bowing reactivity coefficient for EBR-II run 138B. Quantification of the fuel assembly duct-bowing reactivity effect in liquid metal–cooled fast reactors has been a persistent problem since they were first designed and operated. Simulation of the duct-bowing reactivity effect is difficult because the level of detail required to simulate the effect has exceeded most modeling capabilities. The new method outlined in this paper utilizes the finite element analysis code ANSYS to analyze the thermal and structural components. Here, the displacement of the fuel assembly duct due to thermal expansion and mechanical interaction was calculated by ANSYS using recorded EBR-II run 138B temperature and power boundary value data. The displacement values were incorporated into to a Monte Carlo model of EBR-II run 138B and keff was calculated. Multiple Monte Carlo calculations were performed with duct displacement values corresponding to different reactor temperatures. Using the calculated keff values associated with the different duct displacement results allowed calculation of the duct-bowing reactivity coefficient. The duct-bowing reactivity coefficient was calculated to be –14.5 × 10 –4 $/°C/ ± 4.4%.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2023

Local Decomposition of Hexahedral Singular Nodes into Singular Curves

Hexahedral (hex) meshing is a long studied topic in geometry processing with many challenging associated problems. Hex meshes vary from structured to unstructured depending on application or domain of interest. Fully structured meshes require that all interior mesh edges be adjacent to four hexes each. Edges failing this criteria are singular and indicate an unstructured hex mesh. Singular edges join together into singular curves that either form closed cycles, end on the mesh boundary, or end at a singular node, a complex junction of more than two singular curves. Hex meshes with more complex singular nodes tend to have more distorted elements and smaller scaled Jacobian values. In this work, we study the topology of singular nodes. We show that all eight of the most common singular nodes are decomposable into just singular curves. We further show that all singular nodes, regardless of edge valence, are locally decomposable. Finally we demonstrate these decompositions on hex meshes, thereby decreasing their distortion and converting all singular nodes into singular curves. In conclusion, with this decomposition, the enigmatic complexity of 3D singular nodes becomes effectively 2D.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Elucidating the Onset of Plasticity in Sliding Contacts Using Differential Computational Orientation Tomography

Abstract Depending on the mechanical and thermal energy introduced to a dry sliding interface, the near-surface regions of the mated bodies may undergo plastic deformation. In this work, we use large-scale molecular dynamics simulations to generate “differential computational orientation tomographs” (dCOT) and thus highlight changes to the microstructure near tribological FCC alloy surfaces, allowing us to detect subtle differences in lattice orientation and small distances in grain boundary migration. The analysis approach compares computationally generated orientation tomographs with their undeformed counterparts via a simple image analysis filter. We use our visualization method to discuss the acting microstructural mechanisms in a load- and time-resolved fashion, focusing on sliding conditions that lead to twinning, partial lattice rotation, and grain boundary-dominated processes. Extracting and laterally averaging the color saturation value of the generated tomographs allows us to produce quantitative time- and depth-resolved maps that give a good overview of the progress and severity of near-surface deformation. Corresponding maps of the lateral standard deviation in the color saturation show evidence of homogenization processes occurring in the tribologically loaded microstructure, frequently leading to the formation of a well-defined separation between deformed and undeformed regions. When integrated into a computational materials engineering framework, our approach could help optimize material design for tribological and other deformation problems. Graphic Abstract .

36 MATERIALS SCIENCE↗
DOE OSTI2020

Systematic over-estimation of lattice thermal conductivity in materials with electrically-resistive grain boundaries

Reducing the thermal conductivity κ of a material via nano-structuring to create small grain sizes is one of the most common strategies to improve thermoelectric materials. In such polycrystalline materials heat carrying phonons are scattered at the grain boundaries, which directly improves the thermoelectric quality factor and ultimately the figure-of-merit zT. In some cases, however, such as in Mg 3 Sb 2 , SnSe, and Mg 2 Si an opposite trend is found where higher lattice thermal conductivity reported in small grain polycrystalline material than in large grain or single crystal materials. This unphysical result indicates a problem with the conventional use of the Wiedemann–Franz law. Here, we trace this problematic finding to the electrical resistance at the grain boundaries, which leads to an overestimation of the phonon or lattice contribution of the thermal conductivity κ L . In materials with significant grain boundary electrical resistance, the estimated electronic contribution to the thermal conductivity LσT is low because the measured electrical conductivity σ is low. However within the grain electrons may still be transporting more heat than the total conductivity suggests, leading to an overestimation of κ L if the conventional κ L = κ – LσT is used with the measured values of κ and σ. Here, the overestimation of κL in small-grain samples is shown to be pervasive across a broad range of thermoelectric materials, including Mg 3 Sb 2 , Mg 2 Si, PbTe, PbSe, SnSe, (Hf,Zr)CoSb, CoSb 3 , and Bi 2 Te 3 alloys, and a correction is necessary to properly understand and predict their charge and heat transport.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Information theory optimization of signals from small-angle scattering measurements

Small-angle X-ray scattering (SAXS) of particles in solution informs on the conformational states and assemblies of biological macromolecules (bioSAXS) outside of cryo- and solid-state conditions. In bioSAXS, the SAXS measurement under dilute conditions is resolution limited, and through an inverse Fourier transform, the measured SAXS intensities directly relate to the physical space occupied by the particles via the P (r)-distribution. Yet, this inverse transform of SAXS data has been historically cast as an ill-posed, ill-conditioned problem requiring an indirect approach. Here, we show that through the applications of matrix and information theories, the inverse transform of SAXS intensity data is a well-conditioned problem. The so-called ill-conditioning of the inverse problem is directly related to the Shannon number. By exploiting the oversampling enabled by modern detectors, a direct inverse Fourier transform of the SAXS data is possible, provided the recovered information does not exceed the Shannon number. The Shannon limit corresponds to the maximum number of significant singular values that can be recovered in a SAXS experiment, suggesting this relationship is a fundamental property of band-limited inverse integral transform problems. This correspondence reduces the complexity of the inverse problem to the Shannon limit and maximum dimension. We propose a hybrid scoring function using an information theory framework that assesses both the quality of the model-data fit as well as the quality of the recovered P (r)-distribution. The hybrid score utilizes the Akaike information criteria and Durbin-Watson statistic that considers parameter-model complexity, i.e., degrees of freedom, and the randomness of the model-data residuals. The described tests and findings extend the boundaries for bioSAXS by completing the information theory formalism initiated by Peter B. Moore to enable a quantitative measure of resolution in SAXS, robustly determine maximum dimension, and more precisely define the best parameter model appropriately representing the observed scattering data.

Rambo, Robert P. [Science and Technology Facilitie↗
DOE OSTI2021

Lattice determination of 𝐼=0 and 2 𝜋⁢𝜋 scattering phase shifts with a physical pion mass

Phase shifts for 𝑠-wave 𝜋⁢𝜋 scattering in both the 𝐼 =0 and 𝐼 =2 channels are determined from a lattice QCD calculation performed on 741 gauge configurations obeying G-parity boundary conditions with a physical pion mass and lattice size of 32 3 ×64. These results support our recent 2021 study of direct 𝐶⁢𝑃 violation in 𝐾 → 𝜋⁢𝜋 decay, improving our earlier 2015 calculation. The phase shifts are determined for both stationary and moving 𝜋⁢𝜋 systems, at three (𝐼 = 0) and four (𝐼 = 2) different total momenta. We implement several 𝜋⁢𝜋 interpolating operators including a scalar bilinear “𝜎” operator and paired single-pion bilinear operators with the constituent pions carrying various relative momenta. Several techniques, including correlated fitting and a bootstrap determination of p-values have been used to refine the results and a comparison with the generalized eigenvalue problem method is given. A detailed systematic error analysis is performed which allows phase shift results to be presented at a fixed energy.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Hydro-Code Implementation and Testing of a Kinetic Phase Transition Framework

In this report we describe the Kinetic Phase Transition (KPT) framework that has been worked out over the last 10 years (from around 2014) and the implementation of it into three different codes, the one-dimensional hydro- LASLO and the three-dimensional magneto-hydro- ALEGRA, Sandia codes, via subroutines in the LAMBDA Equations of State and constitutive models package, and Flag, an arbitrary Lagrangian-Eulerian multiphysics code developed within the Lagrangian Applications project (LAP) at LANL. We discuss the introduction of phase mass (and/or volume) fractions that are needed in a code for it to be ‘phase aware’, that is, not only the thermodynamic state is known in each point but also the mixture of the materials’ phases in that point. Further we point to the need of a full Equations of State for each phase in a material to achieve phase awareness and we review the equilibrium phase model, where a phase mixture is at its lowest Gibbs free energy state, to make this point clear. Contrasting the kinetic phase transition to this equilibrium model seamlessly introduce us to the KPT framework that is subsequently thoroughly discussed. While the determination of the total state and the states and mass fractions of phases in each point is a problem that can borrow many of its numerical details from Eulerian codes and mixture of materials (not phases), the update of mass fractions with time in a KPT framework needs a new set of considerations. General for any update model is that we need to prevent mass fractions from becoming unphysical (negative or their sum to be larger than one). We have solved this problem by implementing a subdivision of the hydro time step that prevents the phase from being fully present to not present at all in one subdivided time step by limiting the size of the subdivided time step. This scheme also corrects numerical problems from abrupt changes in parameter values, the so called Gibbs phenomena, that gives rise to slushing between phases in the KPT framework. Interspersed throughout the report are discussions on different thermodynamics considerations. EOS validity windows, limitations on the EOS phase space, are needed for the KPT framework and are discussed separately and exemplified. The KPT framework described in this report has been verified by code comparison, but validation is still an active area of research. There is room for improvement in the update model, both in the model for determination of rates and in how to prevent the mass fractions from becoming unphysical. In addition, the parameters in the KPT update model and the placement of the phase boundary in the EOS phase space, and interactions with other constitutive models, are closely related and interfering with each other. One possible way forward is to simultaneously develop KPT parameters, EOS, and constitutive models for each material.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Physics‐Informed Machine Learning Method for Large‐Scale Data Assimilation Problems

Abstract We develop a physics‐informed machine learning approach for large‐scale data assimilation and parameter estimation and apply it for estimating transmissivity and hydraulic head in the two‐dimensional steady‐state subsurface flow model of the Hanford Site given synthetic measurements of said variables. In our approach, we extend the physics‐informed conditional Karhunen‐Loéve expansion (PICKLE) method to modeling subsurface flow with unknown flux (Neumann) and varying head (time‐dependent Dirichlet) boundary conditions. We demonstrate that the PICKLE method is comparable in accuracy with the standard maximum a posteriori (MAP) method, but is significantly faster than MAP for large‐scale problems. Both methods use a mesh to discretize the computational domain. In MAP, the parameters and states are discretized on the mesh; therefore, the size of the MAP parameter estimation problem directly depends on the mesh size. In PICKLE, the mesh is used to evaluate the residuals of the governing equation, while the parameters and states are approximated by the truncated conditional Karhunen‐Loéve expansions with the number of parameters controlled by the smoothness of the parameter and state fields, and not by the mesh size. For a considered example, we demonstrate that the computational cost of PICKLE increases near linearly (as N 1.15 ) with the number of grid nodes N , while that of MAP increases much faster (as N 3.28 ). We also show that once trained for one set of Dirichlet boundary conditions (i.e., one river stage), the PICKLE method provides accurate estimates of the hydraulic head for any value of the Dirichlet boundary conditions (i.e., for any river stage).

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

The transition from resistance to acceptance: Managing a marine invasive species in a changing world

Abstract Marine invasive species can transform coastal ecosystems, yet mitigating their effects can be difficult, and even impractical. Often, marine invasive species are managed at poorly matched spatial scales, and at the same time, rates of spread and establishment are increasing under climate change and can outpace resources available for population suppression. These circumstances challenge traditional conservation goals of maintaining a historic environmental state, especially for a species like the European green crab ( Carcinus maenas ), a formidable invader with few examples of successful long‐term removal programs. A management paradigm where decision alternatives include resisting or accepting a new ecological trajectory may be needed. We apply mathematical concepts from decision theory to develop a quantitative framework for navigating management decisions in this new resist‐accept paradigm. We develop a model of European green crab growth, removal and colonization, and we find optimal levels of removal effort that minimize both ecological change and removal cost. We establish a benchmark of colonization pressure at which green crab density becomes decoupled from a decision maker's actions, such that population control can no longer shape the invasion trajectory. For informing the decision boundary between resistance and acceptance, our results highlight that a decision maker's understanding of how removal cost scales with removal effort is more important than understanding the density‐impact relationship. We show that assuming stationary system dynamics can result in sub‐optimal levels of species removal effort, highlighting the importance of developing anticipatory management strategies by accounting for non‐stationary dynamics. Policy implications . For marine invasive species that can disperse across long distances and recolonize rapidly after removal, the focus of conservation policy should shift away from understanding how to resist change to understanding when to stop resisting change. Navigating this decision problem involves trade‐offs among competing objectives, highlighting the need for structured approaches to elicit objective weights that reflect the values of the decision maker. For natural resource managers facing possible ecosystem transformation, this decision framework can enable proactive and strategic decisions made under uncertainty in a changing world.

Keller, Abigail G. [Department of Environment Scie↗
DOE OSTI2021

Inverse Design of Two-Dimensional Airfoils Using Conditional Generative Models and Surrogate Log-Likelihoods

Abstract This paper shows how to use conditional generative models in two-dimensional (2D) airfoil optimization to probabilistically predict good initialization points within the vicinity of the optima given the input boundary conditions, thus warm starting and accelerating further optimization. We accommodate the possibility of multiple optimal designs corresponding to the same input boundary condition and take this inversion ambiguity into account when designing our prediction framework. To this end, we first employ the conditional formulation of our previous work BézierGAN–Conditional BézierGAN (CBGAN)—as a baseline, then introduce its sibling conditional entropic BézierGAN (CEBGAN), which is based on optimal transport regularized with entropy. Compared with CBGAN, CEBGAN overcomes mode collapse plaguing conventional GANs, improves the average lift-drag (Cl/Cd) efficiency of airfoil predictions from 80.8% of the optimal value to 95.8%, and meanwhile accelerates the training process by 30.7%. Furthermore, we investigate the unique ability of CEBGAN to produce a log-likelihood lower bound that may help select generated samples of higher performance (e.g., aerodynamic performance). In addition, we provide insights into the performance differences between these two models with low-dimensional toy problems and visualizations. These results and the probabilistic formulation of this inverse problem justify the extension of our GAN-based inverse design paradigm to other inverse design problems or broader inverse problems.

Engineering↗
DOE OSTI2021

MOOSE Framework Meshing Enhancements to Support Reactor Analysis

MOOSE-based physics codes require an input finite element mesh on which the physics solution is calculated, reported, and transferred to other physics codes. The use of difficult-touse, external licensed software is often required to generate high quality meshes for reactor geometries. High-fidelity geometry modeling also requires elaborate tracking of groups of elements for material property assignment and output reporting which can be considerably complex for the user to identify and maintain. Under the U.S. Department of Energy Office of Nuclear Energy Advanced Modeling and Simulation (NEAMS) program, several meshingrelated enhancements have been developed for the MOOSE framework to address user challenges in creating finite element meshes for advanced reactor geometries. MOOSE mesh generators have been developed to mesh hexagonal geometries (pins, ducted assemblies, and cores) commonly found in liquid-metal cooled fast reactor concepts. The mesh generator used for hexagonal pin cells is generic for regular polygons and therefore may also be used for Cartesian pin cells. Hexagonal pin cells can be stitched into ducted assemblies, and assemblies can be stitched together into a core. The user may specify region ids, region names, and other preferences on the mesh. This control is useful for later material mapping in the MOOSE-based physics codes input. A capability was also developed for meshing rotating control drums including determination of material volume fractions in each mesh element as a function of time. Control drum meshes may be stitched to other hexagonal assemblies to create a core configuration. Additional mesh generators were developed that wrap around the hexagonal meshing capabilities and utilize “extra element integer” ID values on each element. In regular Cartesian or hexagonal assemblies or cores, the bookkeeping of element groups for both material assignment and output reporting can now be automated through assignment of pin, assembly, core, axial and depletion id values stored as extra element integers. The extra element tags on the mesh greatly speed the reactor analyst’s efforts to map materials to meshes, track depletion zones, and parse output such as axial pin power distributions. At the highest level, pin, assembly, and core mesh generators (with this reactor terminology) have also been developed to easily generate regular Cartesian and hexagonal cores, including axial extrusion. These reactor geometry builders call upon the previously mentioned capabilities to produce analysis-ready 3D meshes including material assignments. Open source mesh triangulation capabilities were also investigated for integration into the MOOSE framework to address the need for meshing the core periphery region which extends from the irregular outer assembly border to a cylindrical boundary. Options are limited due to licensing constraints, and the recommendation is pursue building a native MOOSE Delaunay triangulator routine with full functionality. Finally, a series of verification problems were performed with NEAMS physics tools. All developed capabilities will be available in the new open-source “Reactor” module of the MOOSE framework, which is accessible to any MOOSE-based NEAMS physics tool.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2024

Evanescent and inertial-like waves in rigidly rotating odd viscous liquids

Three-dimensional non-rotating odd viscous liquids give rise to Taylor columns and support axisymmetric inertial-like waves ( J. Fluid Mech ., vol. 973, 2023, A30). When an odd viscous liquid is subjected to rigid-body rotation however, there arise in addition a plethora of other phenomena that need to be clarified. In this paper, we show that three-dimensional incompressible or two-dimensional compressible odd viscous liquids, rotating rigidly with angular velocity 𝛺, give rise to both oscillatory and evanescent inertial-like waves or a combination thereof (which we call of mixed type) that can be non-axisymmetric. By evanescent, we mean that along the radial direction, typically when moving away from a solid boundary, the velocity field decreases exponentially. These waves precess in a prograde or retrograde manner with respect to the rotating frame. The oscillatory and evanescent waves resemble respectively the body and wall-modes observed in (non-odd) rotating Rayleigh–Bénard convection ( J. Fluid Mech ., vol. 248, 1993, pp. 583–604). We show that the three types of waves (wall, body or mixed) can be classified with respect to pairs of planar wavenumbers 𝜅 which are complex, real or a combination, respectively. Experimentally, by observing the precession rate of the patterns, it would be possible to determine the largely unknown values of the odd viscosity coefficients. This formulation recovers as special cases recent studies of equatorial or topological waves in two-dimensional odd viscous liquids which provided examples of the bulk–interface correspondence at frequencies 𝜔 < 2⁢𝛺. We finally point out that the two- and three-dimensional problems are formally equivalent. Their difference then lies in the way data propagate along characteristic rays in three dimensions, which we demonstrate by classifying the resulting Poincaré–Cartan equations.

Mechanics↗
DOE OSTI2021

FROSch Preconditioners for Land Ice Simulations of Greenland and Antarctica

Numerical simulations of Greenland and Antarctic ice sheets involve the solution of large-scale highly nonlinear systems of equations on complex shallow geometries. This work is concerned with the construction of Schwarz preconditioners for the solution of the associated tangent problems, which are challenging for solvers mainly because of the strong anisotropy of the meshes and wildly changing boundary conditions that can lead to poorly constrained problems on large portions of the domain. Here, two-level GDSW (Generalized Dryja–Smith–Widlund) type Schwarz preconditioners are applied to different land ice problems, i.e., a velocity problem, a temperature problem, as well as the coupling of the former two problems. We employ the MPI-parallel implementation of multi-level Schwarz preconditioners provided by the package FROSch (Fast and Robust Schwarz)from the Trilinos library. The strength of the proposed preconditioner is that it yields out-of-the-box scalable and robust preconditioners for the single physics problems. To our knowledge, this is the first time two-level Schwarz preconditioners are applied to the ice sheet problem and a scalable preconditioner has been used for the coupled problem. The pre-conditioner for the coupled problem differs from previous monolithic GDSW preconditioners in the sense that decoupled extension operators are used to compute the values in the interior of the sub-domains. Several approaches for improving the performance, such as reuse strategies and shared memory OpenMP parallelization, are explored as well. In our numerical study we target both uniform meshes of varying resolution for the Antarctic ice sheet as well as non uniform meshes for the Greenland ice sheet are considered. We present several weak and strong scaling studies confirming the robustness of the approach and the parallel scalability of the FROSch implementation. Among the highlights of the numerical results are a weak scaling study for up to 32 K processor cores (8 K MPI-ranks and 4 OpenMP threads) and 566 M degrees of freedom for the velocity problem as well as a strong scaling study for up to 4 K processor cores (and MPI-ranks) and 68 M degrees of freedom for the coupled problem.

58 GEOSCIENCES↗
DOE OSTI2022

FROSch Preconditioners for Land Ice Simulations of Greenland and Antarctica

Numerical simulations of Greenland and Antarctic ice sheets involve the solution of large-scale highly nonlinear systems of equations on complex shallow geometries. This work is concerned with the construction of Schwarz preconditioners for the solution of the associated tangent problems, which are challenging for solvers mainly because of the strong anisotropy of the meshes and wildly changing boundary conditions that can lead to poorly constrained problems on large portions of the domain. In this study, two-level generalized Dryja--Smith--Widlund (GDSW)--type Schwarz preconditioners are applied to different land ice problems, i.e., a velocity problem, a temperature problem, as well as the coupling of the former two problems. We employ the message passing interface (MPI)--parallel implementation of multilevel Schwarz preconditioners provided by the package FROSch (fast and robust Schwarz) from the Trilinos library. The strength of the proposed preconditioner is that it yields out-of-the-box scalable and robust preconditioners for the single physics problems. To the best of our knowledge, this is the first time two-level Schwarz preconditioners have been applied to the ice sheet problem and a scalable preconditioner has been used for the coupled problem. The preconditioner for the coupled problem differs from previous monolithic GDSW preconditioners in the sense that decoupled extension operators are used to compute the values in the interior of the subdomains. Additionally, several approaches for improving the performance, such as reuse strategies and shared memory OpenMP parallelization, are explored. In our numerical study we target both uniform meshes of varying resolution for the Antarctic ice sheet as well as nonuniform meshes for the Greenland ice sheet. We present several weak and strong scaling studies confirming the robustness of the approach and the parallel scalability of the FROSch implementation. Among the highlights of the numerical results are a weak scaling study for up to 32,K processor cores (8,K MPI ranks and 4 OpenMP threads) and 566,M degrees of freedom for the velocity problem as well as a strong scaling study for up to 4,K processor cores (and MPI ranks) and 68,M degrees of freedom for the coupled problem.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Sensitivity analysis of a layered piezoelectric system using ZFEM

The complex variable finite element method (ZFEM) is a numerical technique which aims to find the partial derivatives of the independent variables with respect to variation in dependent parameters declared in the physics. This is done by combining the complex Taylor series expansion within the weak formulation of the governing equation in a coupled system of linear equations forming a complex valued block matrix given by the Cauchy–Riemann matrix representation. In this work, two-dimensional linear first-order elements have been implemented in ZFEM to predict the design derivatives of the mechanical displacement field and the voltage potential field for a layered piezoelectric system in a steady-state study with Dirichlet boundary condition applied at the top and bottom edges of the geometry. This approach allows the standard FEM solution to quantify the sensitivity of the mechanical displacement and voltage potential fields with respect to small variations in the material properties through the information obtained from the computation of the derivatives. The domain is formed by a layered body with PZT-4 and PZT-5 stacked together. For result verification, the numerical solution obtained with ZFEM was compared to results from a commercial FEM package and the solution from the imaginary part was compared to the exact solution of a well-known benchmark problem. In conclusion, comparison of the results showed good agreement for both the real and imaginary parts of the solution and the largest sensitivities were found in PZT-5 specifically in C 13 , C 33 , and ε 33 .

42 ENGINEERING↗
DOE OSTI2021

Deep Learning Approaches to Surrogates for Solving the Diffusion Equation for Mechanistic Real-World Simulations

In many mechanistic medical, biological, physical, and engineered spatiotemporal dynamic models the numerical solution of partial differential equations (PDEs), especially for diffusion, fluid flow and mechanical relaxation, can make simulations impractically slow. Biological models of tissues and organs often require the simultaneous calculation of the spatial variation of concentration of dozens of diffusing chemical species. One clinical example where rapid calculation of a diffusing field is of use is the estimation of oxygen gradients in the retina, based on imaging of the retinal vasculature, to guide surgical interventions in diabetic retinopathy. Furthermore, the ability to predict blood perfusion and oxygenation may one day guide clinical interventions in diverse settings, i.e., from stent placement in treating heart disease to BOLD fMRI interpretation in evaluating cognitive function (Xie et al., 2019; Lee et al., 2020). Since the quasi-steady-state solutions required for fast-diffusing chemical species like oxygen are particularly computationally costly, we consider the use of a neural network to provide an approximate solution to the steady-state diffusion equation. Machine learning surrogates, neural networks trained to provide approximate solutions to such complicated numerical problems, can often provide speed-ups of several orders of magnitude compared to direct calculation. Surrogates of PDEs could enable use of larger and more detailed models than are possible with direct calculation and can make including such simulations in real-time or near-real time workflows practical. Creating a surrogate requires running the direct calculation tens of thousands of times to generate training data and then training the neural network, both of which are computationally expensive. Often the practical applications of such models require thousands to millions of replica simulations, for example for parameter identification and uncertainty quantification, each of which gains speed from surrogate use and rapidly recovers the up-front costs of surrogate generation. We use a Convolutional Neural Network to approximate the stationary solution to the diffusion equation in the case of two equal-diameter, circular, constant-value sources located at random positions in a two-dimensional square domain with absorbing boundary conditions. Such a configuration caricatures the chemical concentration field of a fast-diffusing species like oxygen in a tissue with two parallel blood vessels in a cross section perpendicular to the two blood vessels. To improve convergence during training, we apply a training approach that uses roll-back to reject stochastic changes to the network that increase the loss function. The trained neural network approximation is about 1000 times faster than the direct calculation for individual replicas. Because different applications will have different criteria for acceptable approximation accuracy, we discuss a variety of loss functions and accuracy estimators that can help select the best network for a particular application. We briefly discuss some of the issues we encountered with overfitting, mismapping of the field values and the geometrical conditions that lead to large absolute and relative errors in the approximate solution.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2020

Risk to Ecological Resources on Burial Waste Sites on the Hanford Site, Washington - 20248

The US and other nations have a large nuclear and chemical waste remediation task remaining from World War II, the Cold War, and industrial activities. The US Department of Energy (DOE) has the largest task in the U.S., with Hanford (Washington State) being the most contaminated site, with the longest and most costly cleanup program projected to extend to the end of the century. One of the greatest remediation problems at Hanford are the burial waste facilities, some of which are inside the 200 Areas on the Central Plateau, while others are outside the 200 Areas. These areas are associated with waste sites, pipes, and contaminated trenches, posing technical cleanup challenges to meet DoE's remediation goals, including protection of human health and the environment commensurate with Tri- Party Agreement and current regulatory requirements. In this paper we select one of the legacy waste sites (the BC Cribs and Trenches) as a case study to explore how risk to ecological resources varies during and as a consequence of remediation on sites primarily considered legacy waste sites. We used the risk methodology developed by the Consortium for Risk Evaluation with Stakeholder Participation (CRESP) during the Hanford Site-wide Risk Review. The CRESP methodology included evaluating the risk to receptors, including human health, the Columbia River, groundwater, and ecological and cultural resources. The risk evaluation process for ecological receptors included defining the boundaries of each evaluation unit (EU) to be remediated, definition of a suitable buffer area that might be affected, and consideration of the known resource value based on field work. This information, coupled with known remediation options or strategies, allowed us to develop a risk rating for ecological resources. Site risks were evaluated on a scale of 'not discernible' to 'very high' risk. Consideration of the risks at the buried waste sites was complicated by uncertainties in remediation methods and the degree of restoration that would occur as part of the remediation process. We use the BC Cribs and Trenches as a case study to explore why the risks are low currently but increase during remediation. The current 'not discernible to low' risk rating is due to the lack of high quality ecological resources on the BC Cribs and Trenches EU, except for edge areas (with some state-listed species). During remediation the risks increase to 'medium', mainly due to high quality resources on adjacent buffer lands, which could be disrupted during active remediation. Medium and high quality resources on the edge of the site are continuous with higher quality native shrub-steppe habitat on the buffer. Ecological resources on some of the areas surrounding the 200 East and West Areas are some of the highest quality shrub-steppe areas on the Hanford Site, and risk to these resources could be prevented by planning before and during remediation to minimize disruption. For example, lay down areas for the BC Cribs and Trenches can be minimized by careful planning. Heavy truck and other vehicular traffic can be minimized. Spread of the noxious weeds now on some of the site can be prevented, and the spread of invasive species into the site (particularly near undisturbed shrub-steppe habitat) can be reduced. Further, the areas around and between the 200 East and West Areas have been largely undisturbed and can serve as a source of seeds and propagules for any revegetation that occurs as part of the remediation process. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2025

Propagating information content: an example with advection

The mathematical algorithm to derive geophysical information from remote sensing observations is called a retrieval. The mathematics of many retrieval problems are ill-posed, and thus a priori information is used to help constrain the derived geophysical variable to realistic values. One quantity of interest, therefore, is the information content of the observation. Perfect information content in the observation would be achieved if the retrieval were able to capture any perturbation in the desired geophysical variable with the proper magnitude. Many new data products can be derived by combining geophysical variables retrieved from multiple different remote sensors. This paper explores, for the first time, how to derive the information content of these derived products. The approach uses traditional error propagation techniques to derive the uncertainty of the derived field twice, both when the observations are used in the retrieval and also when only the a priori information from each remote sensor is propagated. These two uncertainties are then used to provide an estimate of the information content of the derived geophysical variable. This study demonstrates how to propagate the uncertainties from six different instruments to provide the information content for water vapor and temperature advection. A multi-month analysis demonstrates that, in a mean sense, the information content for temperature advection is nearly unity for all heights below 700 m while, the information content for water vapor advection is somewhat more variable but still larger than 0.6 in the convective boundary layer.

Turner, David D. [National Oceanic and Atmospheric↗