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DOE OSTI2023

Neural Network-Based Variational Methods for Solving Quadratic Porous Medium Equations in High Dimensions

Here, in this paper, we propose and study neural network-based methods for solutions of high-dimensional quadratic porous medium equation (QPME). Three variational formulations of this nonlinear PDE are presented: a strong formulation and two weak formulations. For the strong formulation, the solution is directly parameterized with a neural network and optimized by minimizing the PDE residual. It can be proved that the convergence of the optimization problem guarantees the convergence of the approximate solution in the $L^1$ sense. The weak formulations are derived following (Brenier in Examples of hidden convexity in nonlinear PDEs, 2020) which characterizes the very weak solutions of QPME. Specifically speaking, the solutions are represented with intermediate functions who are parameterized with neural networks and are trained to optimize the weak formulations. Extensive numerical tests are further carried out to investigate the pros and cons of each formulation in low and high dimensions. This is an initial exploration made along the line of solving high-dimensional nonlinear PDEs with neural network-based methods, which we hope can provide some useful experience for future investigations.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Time-stepping DPG formulations for the heat equation

For a wide range of PDEs, the discontinuous Petrov–Galerkin (DPG) methodology of Demkowicz and Gopalakrishnan provides discrete stability starting from a coarse mesh and minimization of the residual in a user-controlled norm, among other appealing features. Research on DPG for transient problems has mainly focused on spacetime discretizations, which has theoretical advantages, but practical costs for computations and software implementations. The sole examination of time-stepping DPG formulations was performed by Führer, Heuer, and Gupta, who applied Rothe’s method to an ultraweak formulation of the heat equation to develop an implicit time-stepping scheme; their work emphasized theoretical results, including error estimates in time and space. Here, we follow Führer, Heuer, and Gupta in examining the heat equation; our focus is on numerical experiments, examining the stability and accuracy of several formulations, including primal as well as ultraweak, and explicit as well as implicit and Crank–Nicolson time-stepping schemes. We are additionally interested in communication-avoiding algorithms, and we therefore include a highly experimental formulation that places all the trace terms on the right-hand side of the equation.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

A constitutive model for glass–ceramic materials

Glass–ceramics have received recent attention for use in glass–ceramic to metal hermetic seals. Due to their heterogeneous microstructure, these materials exhibit a number of advantageous responses over conventional glass based seals. Key amongst them is the possibility of a controllable thermal strain response and apparent coefficient of thermal expansion which may be used to minimize thermally induced residual stresses for aforementioned seals. Furthermore, these behaviors result from an inorganic glass matrix and variety of crystalline ceramic phases including silica polymorph(s) that may undergo reversible solid-to-solid transformations with associated inelastic strain. Correspondingly, these materials exhibit complex thermomechanical responses associated with multiple inelastic mechanisms (viscoelasticity and phase transformation). While modeling these behaviors is essential for developing and analyzing the corresponding applications, no such model exists. Therefore, in this work a three-dimensional continuum constitutive model for glass–ceramic materials combining these various inelastic mechanisms is developed via an internal state variable approach. A corresponding fully implicit three dimensional numerical formulation is also proposed and implemented. The model is used to simulate existing experiments and validate the proposed formalism. As an example, the simple seal problem of a glass–ceramic seal inside a concentric metal shell is explored. Finally, the impact of the cooling rates, viscoelastic shift factors, and inelastic strain on final residual stress state are all investigated and the differing contributions highlighted.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Variational actor-critic algorithms,

We introduce a class of variational actor-critic algorithms based on a variational formulation over both the value function and the policy. The objective function of the variational formulation consists of two parts: one for maximizing the value function and the other for minimizing the Bellman residual. Besides the vanilla gradient descent with both the value function and the policy updates, we propose two variants, the clipping method and the flipping method, in order to speed up the convergence. We also prove that, when the prefactor of the Bellman residual is sufficiently large, the fixed point of the algorithm is close to the optimal policy.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

A data-driven peridynamic continuum model for upscaling molecular dynamics

Nonlocal models, including peridynamics, often use integral operators that embed lengthscales in their definition. However, the integrands in these operators are difficult to define from the data that are typically available for a given physical system, such as laboratory mechanical property tests. In contrast, molecular dynamics (MD) does not require these integrands, but it suffers from computational limitations in the length and time scales it can address. To combine the strengths of both methods and to obtain a coarse-grained, homogenized continuum model that efficiently and accurately captures materials’ behavior, we propose a learning framework to extract, from MD data, an optimal Linear Peridynamic Solid (LPS) model as a surrogate for MD displacements. To maximize the accuracy of the learnt model we allow the peridynamic influence function to be partially negative, while preserving the well-posedness of the resulting model. To achieve this, we provide sufficient well-posedness conditions for discretized LPS models with sign-changing influence functions and develop a constrained optimization algorithm that minimizes the equation residual while enforcing such solvability conditions. This framework guarantees that the resulting model is mathematically well-posed, physically consistent, and that it generalizes well to settings that are different from the ones used during training. We illustrate the efficacy of the proposed approach with several numerical tests for single layer graphene. Our two-dimensional tests show the robustness of the proposed algorithm on validation data sets that include thermal noise, different domain shapes and external loadings, and discretizations substantially different from the ones used for training.

homogenization↗

DOE OSTI2024

Spot pattern welding scanning strategy for sensor embedding and residual stress reduction in laser-foil-printing additive manufacturing

Here, this paper aims to present spot pattern welding (SPW) as a scanning strategy for laser-foil-printing (LFP) additive manufacturing (AM) in place of the previously used continuous pattern welding (CPW) (line-raster scanning). The SPW strategy involves generating a sequence of overlapping spot welds on the metal foil, allowing the laser to form dense and uniform weld beads. This in turn reduces thermal gradients, promotes material consolidation and helps mitigate process-related risks such as thermal cracking, porosity, keyholing and Marangoni effects. 304L stainless steel (SS) feedstock is used to fabricate test specimens using the LFP system. Imaging techniques are used to examine the melt pool dimensions and layer bonding. In addition, the parts are evaluated for residual stresses, mechanical strength and grain size. Compared to CPW, SPW provides a more reliable heating/cooling relationship that is less dependent on part geometry. The overlapping spot welds distribute heat more evenly, minimizing the risk of elevated temperatures during the AM process. In addition, the resulting dense and uniform weld beads contribute to lower residual stresses in the printed part. To the best of the authors’ knowledge, this is the first study to thoroughly investigate SPW as a scanning strategy using the LFP process. In general, SPW presents a promising strategy for securing embedded sensors into LFP parts while minimizing residual stresses.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Ruthenium/Carbon Nanocomposites for Efficient Hydrogen Electrocatalysis: Impacts of Halide Residues

Ruthenium has emerged as a promising substitute for platinum toward the hydrogen evolution/oxidation reaction (HER/HOR). Herein, ruthenium/carbon composites are prepared by magnetic induction heating (300 A, 10 s) of RuCl3, RuBr3 or RuI3 loaded on hollow N-doped carbon cages (HNC). The HNC-RuCl3-300A sample consists of Ru nanoparticles (dia. 1.96 nm) and abundant Cl residues. HNC-RuBr3-300A possesses a larger nanoparticle size (≈19.36 nm) and lower content of Br residues. HNC-RuI3-300A contains only bulk-like Ru agglomerates with a minimal amount of I residues, due to reduced Ru-halide bonding interactions. Among these, HNC-RuCl3-300A exhibits the best HER activity in alkaline media, with a low overpotential of only -26 mV to reach 10 mA cm-2, even outperforming Pt/C, and can be used as the cathode catalyst for anion exchange membrane water electrolyzer (along with commercial RuO2 as the anode catalyst), producing 0.5 A cm- 2 at 1.88 V for up to 100 h, a performance markedly better than that with Pt/C. HNC-RuCl3-300A also exhibits the best HOR activity, with a half-wave potential (+18 mV) even lower than that of Pt/C (+35 mV). These activities are ascribed to the combined contributions of small Ru nanoparticles and Ru-to-halide charge transfer that weaken H adsorption.

Yu, Bingzhe↗

DOE OSTI2021

Residual stresses and microstructure within Allvac 718Plus laser powder bed fusion bars

The residual stresses within Allvac 718Plus bars built using LBPF with different laser powers, speeds and table displacements were measured using diffraction and mechanical methods and modelled with the baseplate attached and then removed. The residual stress profiles within the bars from the top surface down through the bulk were all quite similar, becoming less tensile due to a strain hardening mechanism. Table displacement has the greatest impact on residual stress, decreasing with increasing displacement/powder layer thickness. There was good agreement amongst the modeling and measurements. The microstructures were examined and varied slightly with energy density with higher densities having larger grains and enhanced post solidification diffusion. We found energy density had minimal impact on the residuals stresses within the parameters to produce dense material.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Laboratory Evaluation to Increase Effectiveness of Field-Scale Soil Flushing in the Hanford 100 Areas

This laboratory study was initiated to develop an improved technical understanding of the key controlling geochemical and physical processes of mobilizing residual Cr(VI) in Hanford sediments to provide increased effectiveness in soil flushing activities planned for Hanford 100 Areas. This was accomplished by (1) quantifying Cr mass, release rate, and surface phase changes as Cr is leached from different Hanford sediments; (2) maximizing Cr leaching during soil flushing by evaluating different leach solutions and leach strategies; and (3) minimizing leaching of remaining residual Cr after soil flushing ends. To quantify geochemical controls on Cr leaching from sediments, sequential liquid extractions were used to identify aqueous, adsorbed, and solid Cr surface phases (precipitates or Cr incorporated into other phases) before and after water-saturated and unsaturated leach experiments with pH 8 artificial groundwater and with other amendment solutions. Changes in the Cr release rate from sediments were also correlated to changes in Cr surface phases. During unsaturated infiltration, water advection occurs primarily through larger pores, with less movement through smaller grain layers leading to a slower release of Cr trapped in smaller pores next to smaller grains. To quantify these physical controls on Cr leaching from sediments, 10 ft high 1-D infiltration experiments were conducted at differing leach solution application rates, and Cr leaching during application and subsequent residual water flow was quantified. Qualitative 2-D experiments were also conducted to evaluate surfactant addition to increase flow in low-permeability zones. Cr-contaminated Hanford sediments from the 100-H, 100-K, 100-D, and 200 East Areas exhibited a wide variety of leach behavior from rapid release of a small amount of Cr to fast (i.e., minutes) and slow (i.e., hours or more) release of high Cr. Sediments with low labile Cr (< 0.2 µg/g) exhibited fast Cr release but less overall release, and most (>95%) leached from the sediments within a few pore volumes in water-saturated columns. With nearly no sorption of chromate, aqueous and sorbed Cr (as chromate) were released quickly from sediment within the first few pore volumes, resulting in high leach concentrations, fast initial Cr release rates, and changes in pre- and post-leach extractions. In contrast, sediments with high labile Cr (0.2 to 20 µg/g) exhibited a combination of fast and slow Cr release due to multiple Cr surface phases contributing to Cr release from the sediment at different rates with greater overall release. This resulted in elevated Cr effluent concentrations even after dozens of pore volumes were leached. In addition, the Cr release rate decreased with increasing time during leaching. A decrease in labile Cr (aqueous Cr, adsorbed Cr, pH 5 acetate dissolved precipitates) in post-leach extractions compared to pre-leach extractions showed initial aqueous and adsorbed Cr release, followed by dissolution of high-solubility precipitates such as CaCrO 4 (if present), then slow dissolution of calcite that may contain some chromate and possibly BaCrO 4 . The labile Cr in all sediments correlated well with the Cr release rate (r 2 = 0.81). Labile Cr also correlated well with the leached mass in water-saturated columns (r 2 = 0.98), and therefore can be used for prediction of potential removal with flushing applications.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2024

Biocompatible organosolv fractionation via a novel alkaline lignin-first strategy towards lignocellulose valorization

Simultaneous valorization of both carbohydrate and lignin fractions in lignocellulose remains a great challenge. Herein, a novel lignin-first strategy using triethylene glycol (TEG) under alkaline conditions for effective biomass fractionation producing highly digestible carbohydrates and reactive lignin was developed. Delignification was over 80% and fermentable sugar yields were close to 90% after pretreatment at 90°C. The biocompatibility of TEG allowed direct enzymatic hydrolysis of the solid residue without washing, thus minimizing wastewater generation. Furthermore, the obtained lignin (TEGL) had an uncondensed structure with well-preserved β-O-4 linkage, leading to near-equal aromatic monomer yields compared to cellulolytic enzyme lignin after catalytic-free pyrolysis, demonstrating high valorization potential. Finally, the proposed TEG solvent system is promising for a green and sustainable biorefinery process to achieve the complete utilization of lignocellulose.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

An optical-input Maximum Likelihood Estimation feedback system demonstrated on tokamak horizontal equilibrium control

A readily parallelized Maximum Likelihood Estimation (MLE) algorithm with linear computational complexity is demonstrated in real time using only measurements from an extreme ultraviolet (EUV) diagnostic to control the horizontal position of a tokamak plasma. A set of trial emissivity profiles are parameterized by the control quantity of interest (R m ), and the MLE is identified from the profile which minimizes the signal reconstruction residual. The algorithm depends on an empirically determined likelihood function with exponential form. EUV emission (λ ≈ 15eV-1keV) is captured in a poloidal plane by four 16-channel AXUV diodes mounted at different poloidal angles with radial and angular resolution sufficient to discern plasma equilibrium evolution in HBT-EP. Calculations of the plasma major radius by the system are consistent within diagnostic uncertainty for the majority of the discharge with those of: a weighted average of vertical soft X-ray or EUV chords, magnetic sensors, and an equilibrium reconstruction. The feedback system corrects for a horizontal displacement of the major radius equal to 20% of the plasma minor radius by adjusting the vertical field produced from 40 in-vessel control coils in real time. The MLE calculation is performed on a GPU in a 15 μs cycle, with similar performance in this application to a simple weighted average of vertical chords. Finally, results demonstrate horizontal position control using magnetic actuators and an optical observer.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Spatial and temporal variability of tritium in precipitation within South Africa and it's bearing on hydrological studies

Tritium, the radioactive isotope of hydrogen, has been used to understand groundwater recharge processes for decades. The current variation of tritium in the atmosphere is largely attributed to stratospheric production and fall out rates as well as global circulation phenomena controlling the hydrological cycle. Global controls on the variability in atmospheric tritium activity are poorly suited to explain local variation and tritium activities in precipitation are often assumed to be uniform over both local and regional catchments and watersheds. This assumption can result in both over and under estimation of modern recharge within an aquifer when using tritium as the recharge proxy. In order to minimize the inherent prediction residuals associated with tritium based recharge investigations, the variability of tritium in precipitation was modelled from 127 spatial precipitation samples taken over a two year period, combined with a 76 precipitation sample group-set taken over a one year period in a single location. Precipitation events were traced backward in time, from the point of collection, using HYSPLIT modelling to ascertain the origins of moisture content as well as the altitudes of moisture origin reached along the particle track. Tritium activities, collected over a one year period in Paarl, range from 0.45 to 4.16 TU and have a mean of 1.59 TU. Spatial storm events in the Western Cape in 2017 and 2018 had a range from 0 to 2.2 and 0.37 to 3.27 TU, respectively, with mean activities of 1.18 (n = 34) and 1.25 TU (n = 32). Both storm events had similar tritium variability (σ = 0.5 n = 35 and 0.48 n = 32). Regional precipitation events had the largest range of tritium activities (0.55–12.2 TU). Although not all tritium activities can be explained by interrogating the water mass origin, this study suggests that approximately 90% of events can be completely or partially attributed to the origin of the water mass. The variability of tritium, both spatially and temporally, was higher than expected, confirming that when uniform tritium inputs are used, the groundwater system would provide inaccurate modern recharge estimates. Higher spatial resolution of tritium variation in precipitation for a particular region will improve our ability to relate tritium activities in groundwater to local precipitation.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

Accelerating Multivariate Functional Approximation Computation with Domain Decomposition Techniques⋆

Modeling large datasets through Multivariate Functional Approximations (MFA) provide an elegant way to handle many visualization and scientific analysis workflows. The process necessitates scalable data partitioning methods to compute MFA representations efficiently without compromising the accuracy or continuity of the reconstructed solution. We propose a domain -decomposed method for computing the MFA with B -spline bases, which reduces the total work per task and uses a restricted Additive Schwarz (RAS) method to converge the control point data degrees -of -freedom along subdomain boundaries. We provide an in-depth analysis of the parallel approach with domain decomposition solvers, aiming to minimize local subdomain error residuals and recover high -order continuity at subdomain interfaces with appropriate choices of knot overlaps. The communication cost, determined by the overlap regions in the RAS implementation, is optimized to recover the numerical error profile of the single subdomain case. Our proposed method stands in contrast to previous methods, which typically only recover either C 0 or at best C 1 continuity for arbitrary B -spline degree expansions, or those that require post -processing to blend discontinuities in the reconstructed data. We demonstrate the effectiveness of our approach using analytical and real -world datasets in 1D, 2D, and 3D through both strong and weak scaling studies. The performance results indicate that the overall cost of computing the approximation is directly proportional to the underlying nearest -neighbor communication implementation, and is only weakly dependent on the overlap region size that determines the size of the messages. This finding underscores the efficiency and scalability of our proposed method, making it a promising solution for handling large datasets in scientific workflows.

additive Schwarz solvers↗

DOE OSTI2023

Vadose Zone Soil Flushing for Chromium Remediation: A Laboratory Investigation to Support Field‐scale Application

Cr(VI) flushing from the vadose zone to the groundwater (with subsequent Cr(VI) removal in groundwater by pump-and-treat system) is a promising remedial technique that has recently been used at field scale. This laboratory study was conducted to provide the technical basis to design a field soil flushing strategy. The objectives were to (1) quantify the relationship between sediment Cr(VI) and Cr(III) mass and release rates and subsequent Cr(VI) leaching; (2) investigate different methodologies to maximize Cr(VI) leaching, and (3) investigate methods to minimize leaching of remaining residual Cr. Characterization of Cr-contaminated sediments (Hanford Site, WA) exhibited Cr(VI) showed that leach rates that were correlated to different Cr surface phases. Sediments with low leachable Cr(VI) (<2 μg/g) leached Cr rapidly, so slow infiltration of water in a single pulse was sufficient to leach most Cr. In contrast, sediments with high Cr (2 to 200 μg/g) released some Cr(VI) quickly but 10 to 50% Cr(VI) slowly (tens to hundreds of hours). Efficient unsaturated leaching of these sediments required a different infiltration strategy that includes: multiple slow leach pulses with time between flushing cycles; the use of a surfactant to increase Cr leaching from low-permeability zones, and the use of a reductant (Na-dithionite or Ca-polysulfide) in the final leach water was highly effective at decreasing residual Cr leaching. This study clearly demonstrated that the methodology of basing laboratory Cr flushing on parameters such as Cr release mass and rates could be used to improve the efficiency of soil flushing at field scale.

Accelerated Cr Flushing↗

DOE OSTI2021

Optimization-based algorithms for nonlinear mechanics and frictional contact

An optimization-based strategy for solving nonlinear mechanics problems is proposed. In contrast to typical nonlinear equation solver algorithms that aim to find zeros in the residual force function, we minimize an energy (or energy-like) function to encourage solutions which are locally stable equilibria. These smooth and potentially non-convex objective functions are minimized using a preconditioned conjugate-gradient trust-region algorithm. Contact is formulated as an inequality constrained minimization problem, and is solved with an augmented Lagrangian algorithm. Friction is included in the approach via a regularized quasi-potential energy, and other dissipative behavior is included through the use of variational constitutive updates. Finally, to accelerate convergence rates for the Lagrange multipliers, we propose a novel multiplier update algorithm utilizing the Fischer-Burmeister function, and demonstrate super-linear solver convergence for some applications.

42 ENGINEERING↗

DOE OSTI2023

The Mitigation Hierarchy

The mitigation hierarchy is a widely used framework to inform conservation decisions. The hierarchy offers a structured set of steps for how projects can lessen negative impacts or lead to an increase in biodiversity. In its simplest form, the mitigation hierarchy includes three stages: (1) avoid creating impacts from the outset, (2) minimize the impacts that cannot be avoided, and (3) compensate for or offset the impacts that cannot be minimized. Proper application of the hierarchy should decrease impacts of the project over time, such that most of the impact is alleviated through avoidance, leaving a modest amount remaining to minimize, and only a residual to compensate. In practice, avoidance should be prioritized and can be a cost-effective means of mitigation. Whereas compensation should be considered the lowest priority and should only be applied in situations in which the previous mitigation steps were unable to fully alleviate undesirable impacts.

biodiversity↗

DOE OSTI2023

La Jerarquia de Mitigacion (Spanish)

biodiversity↗

DOE OSTI2021

Resolving Discrepancies in Spin-Torque Ferromagnetic Resonance Measurements: Lineshape versus Linewidth Analyses

When spin-orbit torques are measured using spin-torque ferromagnetic resonance, two alternative ways of analyzing the results to extract the torque efficiencies—lineshape analysis and analysis of the change in linewidth versus direct current—often give inconsistent results. We identify a source for these inconsistencies. We show that fits of spin-torque ferromagnetic resonance data to the standard analysis framework leave significant residuals that we identify as due to (i) current-induced excitations of a small volume of magnetic material with magnetic damping much larger than that of the bulk of the magnetic layer, which we speculate is associated with the heavy-metal–magnet interface and (ii) oscillations of the sample magnetization at the modulation frequency due to heating. Here, the dependence of the residual signals on direct current can interfere with an accurate extraction of spin-torque efficiencies by the linewidth method. We show that the discrepancies between the two types of analysis can be largely eliminated by extrapolation of the window of magnetic fields used in the linewidth fits to small values so as to minimize the influence of the residual signals.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗