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DOE OSTI2024

A Stochastic Calculus Approach to Boltzmann Transport

Traditional Monte Carlo methods for particle transport utilize source iteration to express the solution, the flux density, of the transport equation as a Neumann series. Our contribution is to show that the particle paths simulated within source iteration are associated with the adjoint flux density and the adjoint particle paths are associated with the flux density. Here, we make our assertion rigorous through the use of stochastic calculus by representing the particle path used in source iteration as a solution to a stochastic differential equation (SDE). The solution to the adjoint Boltzmann equation is then expressed in terms of the same SDE, and the solution to the Boltzmann equation is expressed in terms of the SDE associated with the adjoint particle process. An important consequence is that the particle paths used within source iteration simultaneously provide Monte Carlo samples of the flux density and adjoint flux density in the detector and source regions, respectively. The significant practical implication is that particle trajectories can be reused to obtain both forward and adjoint quantities of interest. To the best our knowledge, the reuse of entire particles paths has not appeared in the literature. Monte Carlo simulations are presented to support the reuse of the particle paths.

Boltzmann transport↗

DOE OSTI2025

A physics-constrained deep learning treatment of runaway electron dynamics

An adjoint formulation leveraging a physics-informed neural network (PINN) is employed to advance the density moment of a runaway electron (RE) distribution forward in time. A distinguishing feature of this approach is that once the adjoint problem is solved, its solution can be used to project the RE density forward in time for an arbitrary initial momentum space distribution of REs. Furthermore, by employing a PINN, a parametric solution to the adjoint problem can be learned. Thus, once trained, this adjoint-deep learning framework is able to efficiently project the RE density forward in time across various plasma conditions while still including a fully kinetic description of RE dynamics. As an example application, the temporal evolution of the density of primary electrons is studied, with particular emphasis on evaluating the decay of a RE population when below threshold. Predictions from the adjoint-deep learning framework are found to be in good agreement with a traditional relativistic electron Fokker–Planck solver, for several distinct initial conditions, and across an array of physics parameters. Once trained, the PINN thus provides a means of generating RE density time histories with exceptionally low online execution time.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Lattice study of correlators of chromoelectric fields for heavy quarkonium dynamics in the quark-gluon plasma

We perform a lattice calculation of the correlators of two chromoelectric fields in the adjoint representation connected by adjoint Wilson lines at nonzero temperature. These correlators arise in the study of quarkonium dynamics and of adjoint heavy quark diffusion in deconfined matter. We work in SU(3) gauge theory using either gradient flow or multilevel algorithms for noise reduction, and discuss the renormalization of the correlators on the lattice. We find that a Casimir factor rescaling relates the adjoint correlators corresponding to the diffusion of an adjoint heavy quark and the octet-octet quarkonium transitions to the chromoelectric correlator in the fundamental representation describing the diffusion of a heavy quark.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

Development of a Method for Shape Optimization for a Gas Turbine Fuel Injector Design Using Metal-Additive Manufacturing

Adjoint shape optimization has enabled physics-based optimal designs for aerodynamic surfaces. Additive manufacturing (AM) makes it possible to manufacture complex shapes. However, there has been a gap between optimal and manufacturable surfaces due to the inherent limitations of commercial computational fluid dynamics (CFD) codes to implement geometric constraints during adjoint computation. In such cases, the design sensitivities are exported and used to perform constrained shape modifications using parametric information stored in computer aided design (CAD) files to satisfy manufacturability constraints. However, modifying the design using adjoint methods in CFD solvers and performing constrained shape modification in CAD can lead to inconsistencies due to different shape parameterization schemes. This paper describes a method to enable the simultaneous optimization of the fluid domain and impose AM manufacturability constraints, resolving one of the key issues of geometry definition for isogeometric analysis. Similar to a grid convergence study, the proposed method verifies the consistencies between shape parameterization techniques present within commercial CAD and CFD software during mesh movement as a part of the adjoint shape optimization routine. By identifying the appropriate parameters essential to a shape optimization study, the error metric between the different parameterization techniques converges to demonstrate sufficient consistencies for justifiable exchange of data between CAD and CFD. For the identified shape optimization parameters, the error metric to measure the deviation between the two parameterization schemes lies within the AM laser-powder bed fusion (L-PBF) process tolerance. Additionally, comparison for subsequent objective function calculations between iterations of the optimization loop showed acceptable differences within 1% variation between the modified geometries obtained using the two parameterization schemes. This method provides justification for the use of multiphysics guided adjoint design sensitivities computed in CFD software to perform shape modifications in CAD to incorporate AM manufacturability constraints during the shape optimization loop such that optimal designs are also additively manufacturable.

33 ADVANCED PROPULSION SYSTEMS↗

DOE OSTI2025

Technical Report on Subsurface Monitoring of the Brady Hot Spring Geothermal Site, Nevada, based upon Full Waveform Inversion

Abilities to accurately characterize the subsurface in a geothermal setting is key to assess and support production. An important element of geothermal reservoir monitoring is also the ability to investigate fluid transport within fracture network. This report focuses on improving subsurface imaging and monitoring in geothermal settings using full waveform inversion based on the adjoint method and time-lapse imaging. To assess our method, we rely on a dense seismic dataset collected in 2016 at the Brady Hot Springs geothermal site in Nevada for the DOE-funded project Poroelastic Tomography by Adjoint Inverse Modeling of Data from Seismology, Geodesy, and Hydrology. This dataset captures subsurface changes across four stages of geothermal power plant operations, which involve varying rates of fluid injection and extraction. Two velocity models were previously derived from this dataset using different methods: one based on travel times and another on sweep interferometry. Our first step is to refine these models using adjoint tomography, which has been applied successfully at global and regional-scales but is less common at the reservoir-scale. Two approaches are then explored for time-lapse analysis: directly comparing refined tomographic models from different stages or backpropagating waveform differences relative to a baseline tomographic model. The main take away is that both approaches highlight similar reservoir behaviors, but the latter approach is more computationally effective in capturing small-scale changes in subsurface properties. For this work, we leverage the use of Salvus (www.mondaic.com), an end-to-end seismic imaging solution, relying on the spectral element method to compute forward and adjoint simulations, and developed by Mondaic Ltd. It includes integrated workflow management that handles waveform and metadata, launches simulations, computes waveform misfits and adjoint sources, and iterates for model updates by nonlinear optimization.

15 GEOTHERMAL ENERGY↗

DOE OSTI2021

Composing effective prediction at five points

Color-kinematics duality in the adjoint has proven key to the relationship between gauge and gravity theory scattering amplitude predictions. In recent work, we demonstrated that at four-point tree-level, a small number of color-dual EFT building blocks could encode all higher-derivative single-trace massless corrections to gauge and gravity theories compatible with adjoint double-copy. One critical aspect was the trivialization of building higher-derivative color-weights — indeed, it is the mixing of kinematics with non-adjoint-type color-weights (like the permutation-invariant d 4 ) which permits description via adjoint double-copy. Here we find that such ideas clarify the predictions of local five-point higher-dimensional operators as well. We demonstrate how a single scalar building block can be combined with color structures to build higher-derivative color factors that generate, through double copy, the amplitudes associated with higher-derivative gauge-theory operators. These may then be suitably mapped, through another double-copy, to higher-derivative corrections in gravity.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

Exotic hidden-heavy hadrons and where to find them

The Born-Oppenheimer potentials for QCD with light quarks include adjoint-hadron potentials that are repulsive at short distances and heavy-hadron-pair potentials that approach thresholds at large distances. The adjoint-hadron potentials must connect smoothly to the heavy-hadron-pair potentials at intermediate distances. We identify exotic hidden-heavy hadrons as bound states and resonances in adjoint-hadron potentials that cross below a heavy-hadron-pair threshold before approaching it. This explains why many exotic hidden-charm and hidden-bottom hadrons have energies near heavy-hadron-pair thresholds. The remarkable properties of some exotic hidden-heavy mesons can be explained by fine tunings of adjoint-meson energies in QCD.

Born-Oppenheimer approximation↗

DOE OSTI2021

Decoupled Fréchet kernels based on a fractional viscoacoustic wave equation

We formulate the Fréchet kernel computation using the adjoint-state method based on a fractional viscoacoustic wave equation. We first numerically prove that both the 1/2- and the 3/2-order fractional Laplacian operators are self-adjoint. Using this property, we show that the adjoint wave propagator preserves the dispersion and compensates the amplitude, while the time-reversed adjoint wave propagator behaves identically as the forward propagator with the same dispersion and dissipation characters. Without introducing rheological mechanisms, this formulation adopts an explicit Q parameterization, which avoids the implicit Q in the conventional viscoacoustic/viscoelastic full waveform inversion (Q-FWI). In addition, because of the decoupling of operators in the wave equation, the viscoacoustic Fréchet kernel is separated into three distinct contributions with clear physical meanings: lossless propagation, dispersion, and dissipation. Here, we find that the lossless propagation kernel dominates the velocity kernel, while the dissipation kernel dominates the attenuation kernel over the dispersion kernel.

58 GEOSCIENCES↗

DOE OSTI2026

Directional dependence of equilibrated TLD-400 chips in multiple radiation fields

Fielding of thermoluminescent dosimeters (TLDs) for measurement of photon radiation dose in experiments is the standard practice for γ-irradiation facilities, pulsed power x-ray facilities, and reactor facilities at Sandia National Laboratories (SNL). Due to the high-dose experimental conditions and the mixed ( 1 n, γ) fields in these facilities, SNL radiation metrologists have historically used CaF 2 :Mn TLDs (also known as TLD-400). Recent inquiries to the radiation metrology staff have raised concerns that the aluminum-equilibrated TLD-400 chips may exhibit a directionally dependent response. The metrologists were asked whether the dose measured by the chip may be impacted by the angle of incidence on the equilibrated TLD. To provide a thorough answer to this query, a set of adjoint Monte Carlo radiation transport calculations was performed for three different equilibrated TLDs as well as bare TLD chips using the Integrated Tiger Series (ITS) code. The key feature of the adjoint calculations performed in this study is that each photon escaping the modeled geometry was tallied into angular bins to provide information on both the energy and angular dependence of the equilibrated chip. After the adjoint Monte Carlo calculations were completed, the resulting energy-dependent response function for each angular bin was convolved with multiple photon energy spectra representing various radiation facilities at SNL. The radiation facilities selected for analysis span a range of photon energies from approximately 1 keV up to approximately 20 MeV. Thus, the presented results are applicable to a wide variety of radiation facilities around the world. Although the bare TLD-400 chip was expected to display the largest variation due to the photon angle of impact on the dosimeter, the dosimeter with the thinnest aluminum equilibrator (SNL thin equilibrated TLD-400) was determined to have the biggest differential between the impact angle with the maximum dose ( D max ) and the impact angle with the minimum dose ( D min ). However, the SNL normal equilibrated TLD-400 chip demonstrated a dramatic reduction in that differential between maximum and minimum dose angles. The reduction in this differential is one of the dominant factors in experimenters’ choice to field these dosimeters at SNL radiation facilities. The results from the PNNL (Hanford) energy-flattening field capsule are consistent with the previous publications. The differential dose responses due to the photon impact angle indicate that experimenters should strive to field their TLD-400 dosimeters in a consistent manner to avoid additional uncertainty in the measurements based on dosimeter orientation.

Adjoint radiation transport↗

DOE OSTI2024

Anomalies of 4d SpinG theories

Abstract We consider ’t Hooft anomalies of four-dimensional gauge theories whose fermion matter content admits Spin G (4) generalized spin structure, withGeither gauged or a global symmetry. We discuss methods to directly computew 2 ∪w 3 ’t Hooft anomalies involving Stiefel-Whitney classes of gauge and flavor symmetry bundles that such theories can have on non-spin manifolds, e.g.M 4 = ℂℙ 2 . Such anomalies have been discussed for SU(2) gauge theory with adjoint fermions, where they were shown to give an effect that was originally found in the Donaldson-Witten topological twist of$$ \mathcal{N} $$ N = 2 SYM theory. We directly compute these anomalies for a variety of theories, including generalGgauge theories with adjoint fermions, SU(2) gauge theory with fermions in general representations, and Spin(N) gauge theories with fundamental matter. We discuss aspects of matching these and other ’t Hooft anomalies in the IR phase where global symmetries are spontaneously broken, in particular for generalG gauge theory withN f adjoint Weyl fermions. For example, in the case ofN f = 2 we discuss anomaly matching in the IR phase consisting of$$ {h}_{G_{\textrm{gauge}}}^{\vee } $$ h G gauge ∨ copies of a ℂℙ 1 non-linear sigma model, including for thew 2 w 3 anomalies when formulated with$$ {\textrm{Spin}}_{\textrm{SU}{(2)}_{\textrm{global}}}(4) $$ Spin SU 2 global 4 structure.

Physics↗

DOE OSTI2026

CADIS and FW-CADIS Variance Reduction in Gamma Transport for Predicting Prompt Forensics Signatures

The goal of prompt nuclear forensics is to determine the characteristics of a nuclear detonation based on the signatures available almost immediately after the explosion. An important characteristic is the reaction time history (RTH), a measure of the device’s rate of neutron multiplication. The RTH can be estimated by observation of the gamma radiation emitted from the detonation, which can be detected directly or observed indirectly as Teller light. Gamma transport simulations used to predict these radiation fields are often modeled stochastically using the Monte Carlo N-Particle (MCNP) code, which can be a computationally demanding task due to the number of particle histories needed to achieve statistical convergence. In an attempt to improve the efficiency of these calculations, we evaluate two variance reduction techniques: Consistent Adjoint-Driven Importance Sampling (CADIS) and Forward-Weighted Consistent Adjoint-Driven Importance Sampling (FW-CADIS). These methods use a deterministically calculated adjoint flux to create weight windows and source biasing that guide MCNP sampling. We study the utility of CADIS and FW-CADIS for their use in MCNP gamma transport for nuclear forensics prediction simulations. Furthermore, the results demonstrate that both CADIS and FW-CADIS improve the accuracy for forensics-focused simulations, with CADIS being most beneficial in direct detection and FW-CADIS being ideal for computing a global Teller light source.

CADIS↗

DOE OSTI2024

Adapting CLUTCH methodology to multigroup TSUNAMI-3D for eigenvalue sensitivity calculations

The sensitivity of the eigenvalue to uncertainties in nuclear data and its evaluation are important for nuclear criticality safety. TSUNAMI-3D sequences within the SCALE code system offer several options to the user community for calculating eigenvalue sensitivity coefficients with multigroup (MG) and continuous energy (CE) 3D transport capabilities. TSUNAMI-3D sequences implement the adjoint-based perturbation theory with MG KENO code, the Contributon Linked eigenvalue sensitivity/Uncertainty estimation via Track length importance CHaracterization (CLUTCH) method with CE KENO code, and the Iterated Fission Probability (IFP) method with CE KENO and Shift codes. Each method has benefits and limitations depending on the problem that is run. The work presented here aims to adapt the CLUTCH method, which enables the Contributon method's mesh-free, memory-efficient approach for calculating adjoint-weighted tallies for sensitivity calculations, to the MG TSUNAMI-3D sequence. This application would eliminate the explicit adjoint KENO calculation, as well as the memory-consuming mesh flux moment tallies required by the conventional MG TSUNAMI-3D. Smaller memory footprints in the CLUTCH methodology and relatively shorter runtimes in MG KENO transport can make MG TSUNAMI-3D a viable method for some complex problems. Moreover, this adaptation allows MG sensitivity calculations with Shift, ORNL's next-generation high-performance Monte Carlo transport code, which currently does not offer any sensitivity capabilities with MG particle transport simulations. Initial implementation of the new MG TSUNAMI-3D sequence and its preliminary results with a selected critical benchmark experiment in the Verified, Archived Library of Inputs and Data (VALID) are presented in this study.

KENO↗

DOE OSTI2024

Qualitative Conditions for Reasonable Estimates of Kerma Using Total and Kerma Cross Section Attenuation of Photons

Performing a full adjoint simulation in the Integrated Tiger Series (ITS) can be time consuming to obtain statistically significant results. The ray-trace capability in ITS allows for rapid scoping calculations of the uncollided kerma from photon sources without needing to run a full adjoint simulation. However, the uncollided estimate will always underestimate the full-physics kerma since it neglects scattered radiation, and under certain conditions, the result from the capability may not provide a sufficiently accurate estimate of the full-physics kerma. To exemplify the conditions in which the capability provides reasonable estimates, two problem geometries with different materials are simulated using the full adjoint capability as well as the ray-trace capability with a total cross section treatment and a new kerma-attenuation cross-section treatment. The results are then compared to show under which conditions the estimates are accurate. Reasonable estimates are provided from the ray-trace feature when there is minimal scattering into a region of interest occurring, such as with low-Z material and when the photons travel through small amounts of material.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

Performance Improvements of the Griffin Solvers in FY24

The Griffin code is a MOOSE-based reactor physics application jointly developed by Idaho National Laboratory and Argonne National Laboratory under the Department of Energy Office of Nuclear Energy Nuclear Energy Advanced Modeling and Simulation Program. This fiscal year, we have made significant efforts to improve the performance of transport solver options and cross-section generation for the efficient use of Griffin in advanced reactor applications. For the HFEM-PN solver, the residual evaluations of HFEM kernels were optimized by utilizing the pre- computed averaged cross sections for individual elements. Numerical integration involving the evaluation of basis functions at quadrature points was bypassed by facilitating precomputed element mass matrices for response matrices. Red-black iterations were improved by introducing a new generalized minimum residual based solver. The memory usage of response matrix storage was significantly reduced by applying basis function rotations on interfaces and calculating volumetric odd-parity moments on the fly. Additionally, the adjoint flux and transient calculation capabilities of the HFEM-PN solver were successfully implemented and verified using the TWIGL benchmark problem. For the DFEM-SN solver, memory footprint and computation time were significantly reduced by not treating angular flux vectors as the MOOSE nonlinear system vectors. Specifically for IQS, scalar adjoint weighting was introduced to further eliminate angular adjoint flux storage in the MOOSE auxiliary system. It was demonstrated through the three-dimensional Advanced Burner Test Reactor core problem that the memory usage for transient calculations with the IQS method was reduced by over 7.5× compared to before the optimizations. For the self-shielding application programming interface, a new double-heterogeneity treatment method, named the Bell Function-Based Analytic Two-Region Slowing Down Method, was developed to efficiently flux-volume homogenize TRISO particles with the matrix. Additionally, optimizations were made to hyper- fine group (HFG) slowing down calculations by pretabulating collision probability coefficients and grouping isotopes, significantly reducing the computational time for calculating scattering sources per HFG. Lastly, the pin power reconstruction module was extended to account for temporal behavior in a microreactor analysis problem, specifically for a control drum transient. Verification tests for each of these improvements demonstrated significant performance enhancements and memory reduction.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2020

Diagnosing the sensitivity of grounding-line flux to changes in sub-ice-shelf melting

Abstract. Using a numerical ice flow model, we study changes in ice shelf buttressing and grounding-line flux due to localized ice thickness perturbations, a proxy for localized changes in sub-ice-shelf melting. From our experiments, applied to idealized (MISMIP+) and realistic (Larsen C) ice shelf domains, we identify a correlation between a locally derived buttressing number on the ice shelf, based on the first principal stress, and changes in the integrated grounding-line flux. The origin of this correlation, however, remains elusive from the perspective of a theoretical or physically based understanding. This and the fact that the correlation is generally much poorer when applied to realistic ice shelf domains motivate us to seek an alternative approach for predicting changes in grounding-line flux. We therefore propose an adjoint-based method for calculating the sensitivity of the integrated grounding-line flux to local changes in ice shelf geometry. We show that the adjoint-based sensitivity is identical to that deduced from pointwise, diagnostic model perturbation experiments. Based on its much wider applicability and the significant computational savings, we propose that the adjoint-based method is ideally suited for assessing grounding-line flux sensitivity to changes in sub-ice-shelf melting.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Blade planform design optimization to enhance turbine wake control

Abstract This study considers optimizing the planform of wind turbine blades to ultimately enhance wind plant controls, namely, wake steering strategies. Adjoint‐enabled unsteady actuator line simulations are carried out to obtain gradients for optimization of several different performance objectives with respect to blade chord length at 10 locations along blade span. We demonstrate different blade design optimizations that can maximize time‐averaged lateral wake deflection, entrainment of kinetic energy, or total power of multiple turbines. Our optimized designs can produce a 4+% increase in wake deflection, a 4× increase in vertical kinetic energy entrainment, or a 3.6% increase in power when compared with the baseline case. While lateral wake deflection is only modestly sensitive to chord changes, we find that increasing the outboard chord length can dramatically increase kinetic energy entrainment, resulting in faster wake recovery and gains in net power. While this work develops only a few case studies emphasizing relative performance improvements and general trends, these results show the promise of a framework that combines mid‐fidelity computation with adjoint‐based optimization for control and design problems.

WIND ENERGY↗

DOE OSTI2023

Linearization errors in discrete goal-oriented error estimation

This paper is concerned with goal-oriented a posteriori error estimation for nonlinear functionals in the context of nonlinear variational problems solved with continuous Galerkin finite element discretizations. A two-level, or discrete, adjoint-based approach for error estimation is considered. The traditional method to derive an error estimate in this context requires linearizing both the nonlinear variational form and the nonlinear functional of interest which introduces linearization errors into the error estimate. In this paper, we investigate these linearization errors. In particular, we develop a novel discrete goal-oriented error estimate that accounts for traditionally neglected nonlinear terms at the expense of greater computational cost. We demonstrate how this error estimate can be used to drive mesh adaptivity. Here, we show that accounting for linearization errors in the error estimate can improve its effectivity for several nonlinear model problems and quantities of interest. We also demonstrate that an adaptive strategy based on the newly proposed estimate can lead to more accurate approximations of the nonlinear functional with fewer degrees of freedom when compared to uniform refinement and traditional adjoint-based approaches.

42 ENGINEERING↗

DOE OSTI2021

A Feynman-Kac based numerical method for the exit time probability of a class of transport problems

The exit time probability, which gives the likelihood that an initial condition leaves a prescribed region of the phase space of a dynamical system at, or before, a given time, is arguably one of the most natural and important transport problems. In this work, we present an accurate and efficient numerical method for computing this probability for systems described by non-autonomous (time-dependent) stochastic differential equations (SDEs) or their equivalent Fokker-Planck partial differential equations. The method is based on the direct approximation of the Feynman-Kac formula that establishes a link between the adjoint Fokker-Planck equation and the forward SDE. The Feynman-Kac formula is approximated using the Gauss-Hermite quadrature rules and piecewise cubic Hermite interpolating polynomials, and a GPU accelerated matrix representation is used to compute the entire time evolution of the exit time probability using a single pass of the algorithm. The method is unconditionally stable, exhibits second order convergence in space, first order convergence in time, and it is straightforward to parallelize. Applications are presented to the advection diffusion of a passive tracer in a fluid flow exhibiting chaotic advection, and to the runaway acceleration of electrons in a plasma in the presence of an electric field, collisions, and radiation damping. Benchmarks against analytical solutions as well as comparisons with explicit and implicit finite difference standard methods for the adjoint Fokker-Planck equation are presented.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗