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DOE OSTI2024

Three-dimensional continuum point cloud method for large deformation and its verification

This study presents a strong form based meshfree collocation method, which is named Continuum Point Cloud Method, to solve nonlinear field equations derived from classical mechanics for deformed bodies in three-dimensional Euclidean space. The method and its implementation are benchmarked against a nonlinear vector field using manufactured solutions. The analysis of mechanical fields firstly focuses on the study of St. Venant Kirchhoff and compressible neo-Hookean materials. Results for various initial boundary value problems are presented, including benchmark cases involving unidirectional tension and simple shear. Subsequently, the study concludes with an analysis of a displacement-controlled simulation of a compressible neo-Hookean material, specifically a bar that is pulled to 50% of its original length and rotated 90°. The pure tension case yields a 1.5% error in displacement between computed and expected values and a combined tension and torsion loading case provides further insight into material behavior under complex loading conditions. The resulting normal axial and transverse stress-strain curves are also presented. Lastly, the consistency and robustness of the proposed nonlinear numerical schemes are successfully demonstrated through various numerical experiments.

Compressible neo-Hookean materials↗

DOE OSTI2026

High-Fidelity, Low-Dissipation/Symmetry-Preserving Numerical Scheme for Solving the Euler Equations with Unstructured, Metric-Based Mesh Adaptation

This work presents an overview of a high-fidelity compressible Euler solver that utilizes the continuous Galerkin (CG) method with added artificial numerical diffusion for stabilization to solve a variety of unsteady and steady benchmark inviscid flow problems. This work shows that discretizing the Euler equations with this CG approach and first order basis functions produces a cost-effective stencil as well as simple well-posed boundary conditions. We show through convergence testing with manufactured solutions that the reduced stencil of CG, combined with the low amount of artificial diffusion required when using the stabilization method outlined in this work, leads to stable and highly accurate results for a variety of unsteady and steady applications. When combined with the adaptive mesh refinement approach used for many of the cases in this work, our results show that the flow solver achieves even more accurate results. A variety of inviscid flow cases are presented in this work, including transient 2D cases with complex shock structures and several steady 3D airfoils sections with a constant span.

Doetsch, Kevin [ORNL] (ORCID:0000000267051705)↗

DOE OSTI2020

CI-MBPT and Intensity-Based Lifetime Calculations for Th II

Lifetime calculations of Th II J = 1.5 and 2.5 odd states are performed with configuration–interaction many-body perturbation theory (CI-MBPT). For many J = 2.5 states, lifetimes are quite accurate, but two pairs of J = 2.5 odd states and many groups of J = 1.5 states are strongly mixed, making theoretical predictions unreliable. To solve this problem, a method based on intensities is used. To relate experimental intensities to lifetimes, two parameters, one an overall coefficient of proportionality for transition rates and one temperature of the Boltzmann distribution of populations, are introduced and fitted to minimize the deviation between theoretical and intensity-derived lifetimes. For strongly mixed groups of states, the averaged lifetimes obtained from averaged transition rates were used instead of individual lifetimes in the fit. Close agreement is obtained. Then intensity branching ratios are used to extract individual lifetimes for the strongly mixed states. The resulting lifetimes are compared to available directly measured lifetimes and reasonable agreement is found, considering limited accuracy of intensity measurements. The method of intensity-based lifetime calculations with fit to theoretical lifetimes is quite general and can be applied to many complex atoms where strong mixing between multiple states exists.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2024

Green's function methods for multiphysics simulations (Final Report)

Green's functions are important tools for analyzing mathematical properties of partial differential equations (PDEs), and for numerically solving PDEs, especially when equations for the same operator but with multiple right hand sides need to be solved simultaneously. This proposal aims at developing efficient and accurate numerical methods for computing Green's functions, which can be used to tackle a challenging question in multiphysics simulation of DOE-mission science problems: how to couple quantum physics with classical physics. The key mathematical difficulty is properly formulate a "boundary condition" for the region described by quantum physics, and conventional approaches often model such boundary conditions in an empirical way. The proposed Green's function methods use the Dirichlet-to-Neumann map to formulate a boundary condition that is non-empirical and can couple the quantum and classical regions in an in principle exact way. The key ingredient of the new methods is to construct the Dirichlet-to-Neumann map in an efficient, accurate and versatile manner. The new methods have provably low complexity and are ideally suited for massively parallel and emerging many-core computational systems.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

PyOECP: A flexible open-source software library for estimating and modeling the complex permittivity based on the open-ended coaxial probe (OECP) technique

Here, we present PyOECP, a Python-based flexible open-source software for estimating and modeling the complex permittivity obtained from the open-ended coaxial probe (OECP) technique. The transformation of the measured reflection coefficient to complex permittivity is performed based on three different methods. The software library contains the dielectric spectra of common reference liquids, which can be used to transform the reflection coefficient into the dielectric spectra. Several Python routines that are commonly employed (e.g., SciPy and NumPy) in the field of science and engineering are required only so that the users can alter the software structure depending on their needs. The modeling algorithm exploits the Markov Chain Monte Carlo method for the data regression. The discrete relaxation models can be built by a proper combination of well-known relaxation models. In addition to these models, electrode polarization, a typical measurement artifact for interpreting dielectric spectra, can be incorporated into the modeling algorithm. A continuous relaxation model, which solves the Fredholm integral equation of the first kind (a mathematically ill-posed problem), is also included. This open-source software enables users to freely adjust the physical parameters to obtain physical insight into their materials under test and will be consistently updated for more accurate measurement and interpretation of dielectric spectra in an automated manner. This work describes the theoretical and mathematical background of the software, lays out the workflow, and validates the software functionality based on both synthetic and empirical data included in the software.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

A second-order distributed memory parallel fast sweeping method for the Eikonal equation

The Eikonal equation is used to calculate wave propagation and distance fields, and due to its complexity requires numerical treatment for its solution. In this work, we present a second-order distributed memory parallel fast sweeping method. The second-order solution switches on a two-point stencil when two upwind points are available, and reverts to first-order otherwise. In all examples, the second-order method improves the solution over the first-order, allowing for significant savings in memory while achieving the same accuracy. Parallelization over distributed memory saw good weak scaling with optimal convergence. The computational time for second-order was approximately 2.5 times slower than first-order, where the largest amount of mesh points ran on 144 cores (512 GB) was ≈20 billion. The savings in memory from the second-order method combined with the distributed memory algorithm result in the ability to solve problems much larger than are possible with the serial first-order method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

Implementation of Perturbation Theory and Sensitivity Capabilities in Griffin

Griffin is a Multiphysics Object-Oriented Simulation Environment (MOOSE) based reactor Multiphysics analysis application, jointly developed by Argonne and Idaho National Laboratories under the DOE-NE NEAMS program. This fiscal year, capabilities for reactivity and sensitivity evaluation using perturbation methods were implemented and verified. The First Order Perturbation Method (FOPT) was employed to compute reactivity worth resulting from small perturbations in input parameters, while the Generalized Perturbation Theory (GPT) was used to evaluate sensitivities of a range of response types, including reaction rate ratio, k-eigenvalue, neutron generation time, and effective delayed neutron fraction. These perturbation methods enable users to quantify how response quantities change due to a perturbation in a input parameter without explicitly performing an additional transport simulation for each perturbed state. In particular, the GPT formulation accounts for indirect effects arising from flux changes by solving generalized inhomogeneous equations, for which a Neumann series-based iterative solution method was developed and implemented in Griffin. The implemented reactivity and sensitivity evaluation capabilities were verified using two test problems: an infinite homogeneous system and a two-dimensional hexagonal core. The results showed excellent agreement with reference solutions obtained by a direct method based on finite difference approximation as well as GPT-based results from the PERSENT code, confirming the accuracy of both reactivity and sensitivity evaluations. Additionally, preliminary uncertainty quantification (UQ) results were obtained by combining the sensitivity values computed using GPT and external covariance data, demonstrating that the implemented sensitivity results can be reliably used for uncertainty calculations. To further demonstrate the generality and practical strength of the implementation, the sensitivity evaluation capability was successfully applied to the Empire microreactor with a geometrically complex design that poses significant modeling challenges. The results confirm that Griffin enables sensitivity evaluations even for irregular and highly heterogeneous reactor configurations, thereby establishing a foundation for UQ applications in advanced reactor designs and analyses.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2025

Additional considerations in analytical solution for time-dependent heat conduction in a three-dimensional multilayer sphere

This work presents an analytical method to solve the heat conduction equation in three dimensions for problems consisting of multilayer concentric spheres. The method can be used to treat time-varying heat conduction problems where the heat source that drives the transient is time-invariant. Equally applicable to all Poisson-type problems with concentric spherical geometry, the method consists of representing the solution as a summation of weighted eigenfunctions. The weights for each eigenfunction are computed algebraically. Previous work has already established the core constituents of the methodology. The current work augments the existing methods by including consideration of nonzero interface resistance between layers and explicit discussion on the boundary condition homogenization required to treat inhomogeneous problems. Also, two demonstration problems are presented. One demonstration problem is based on the method of manufactured solutions and therefore allows for comparison with exact expressions for the solution temperature distribution. The second, more complex, demonstration problem relies on the finite element method for comparisons. The expected convergence behavior is observed for both demonstration problems.

97 - MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Overset-Grid Method with Smooth Orbital Partitioning for Molecular Scattering Calculations

To solve molecular photoionization and electron scattering problems, we use an overset-grid representation of electronic continuum functions, which has an extended central spherical grid that overlaps small spherical grids (subgrids) centered on each atom of a polyatomic molecule. Here, in this work, we present an improved algorithm that smoothly partitions the total wave function between the central grid and the atomic subgrids. The smooth partitioning allows one to use approximately one-fourth the number of partial waves on the central grid compared to our previous implementation with switching functions. The resulting numerical method for treating electron scattering and photoionization of polyatomic molecules combines the accuracy and flexibility of pure numerical grid representations with the rapid convergence of hybrid combinations of atom-centered basis-set expansions and grid methods. The overset-grid representation is implemented using the complex Kohn variational principle for scattering and photoionization amplitudes. The faster convergence with respect to the number of central grid partial waves is demonstrated and accuracy is verified by comparisons with the previous implementation and with far more computationally demanding single-center numerical expansions in electron-molecule scattering and photoionization calculations on the neon dimer (Ne 2 ) system, carbon tetrafluoride (CF 4 ) molecule, and the pyridine (C 5 H 5 N) molecule in the static-exchange approximation.

Molecules↗

DOE OSTI2024

LossLens: Diagnostics for Machine Learning Through Loss Landscape Visual Analytics

Modern machine learning often relies on optimizing a neural network's parameters using a loss function to learn complex features. Beyond training, examining the loss function with respect to a network's parameters (i.e., as a loss landscape) can reveal insights into the architecture and learning process. While the local structure of the loss landscape surrounding an individual solution can be characterized using a variety of approaches, the global structure of a loss landscape, which includes potentially many local minima corresponding to different solutions, remains far more difficult to conceptualize and visualize. To address this difficulty, we introduce LossLens, a visual analytics framework that explores loss landscapes at multiple scales. LossLens integrates metrics from global and local scales into a comprehensive visual representation, enhancing model diagnostics. Here we demonstrate LossLens through two case studies: visualizing how residual connections influence a ResNet-20, and visualizing how physical parameters influence a physics-informed neural network (PINN) solving a simple convection problem.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Promise of Graph Sparsification and Decomposition for Noise Reduction in QAOA: Analysis for Trapped-Ion Compilations

We develop new approximate compilation schemes that significantly reduce the expense of compiling the Quantum Approximate Optimization Algorithm (QAOA) for solving the Max-Cut problem. Our main focus is on compilation with trapped-ion simulators using Pauli-X operations and all-to-all Ising Hamiltonian HIsing evolution generated by Molmer-Sorensen or optical dipole force interactions, though some of our results also apply to standard gate-based compilations. Our results are based on principles of graph sparsification and decomposition; the former reduces the number of edges in a graph while maintaining its cut structure, while the latter breaks a weighted graph into a small number of unweighted graphs. Though these techniques have been used as heuristics in various hybrid quantum algorithms, there have been no guarantees on their performance, to the best of our knowledge. This work provides the first provable guarantees using sparsification and decomposition to improve quantum noise resilience and reduce quantum circuit complexity. For quantum hardware that uses edge-by-edge QAOA compilations, sparsification leads to a direct reduction in circuit complexity. For trapped-ion quantum simulators implementing all-to-all HIsing pulses, we show that for a (1−ϵ) factor loss in the Max-Cut approximation (ϵ>0), our compilations improve the (worst-case) number of HIsing pulses from O(n2) to O(nlog(n/ϵ)) and the (worst-case) number of Pauli-X bit flips from O(n2) to O(nlog(n/ϵ)ϵ2) for n-node graphs. This is an asymptotic improvement for any constant ϵ>0. We demonstrate that significant improvements to the approximation ratio are obtained using decomposition in simulated trapped-ion experiments with dephasing noise. We further present a generic argument showing that sparsification results in an exponentially improved circuit fidelity lower bound in digital computing schemes based on one- and two-qubit gates, which are relevant to a wide variety of hardwares such as superconducting qubits and certain neutral atom or trapped ion setups, and more sophisticated noise models. We anticipate these approximate compilation techniques will be useful tools in a variety of future quantum computing experiments.

Moondra, Jai [Georgia Institute of Technology]↗

DOE OSTI2024

Computing with a Chemical Reservoir

Contemporary computation is expensive, with large language models and artificial intelligence becoming more common in daily life. However, high-performance computing is reaching the limits in speed and energy expenditure, and domain science requires ever-increasing computational capacity, with simulations and data analysis pipelines ever-growing in complexity. As we progress towards post-exascale computation, with the associated high energy costs, new methods of energy-conscious computation are required. Novel analog and hybrid digital-analog systems can overcome these challenges, and chemical reactions offer a promising avenue. Computers based on chemistry can provide compact desktop devices with immense computational power. These devices are readily scalable by considering greater reaction systems or vessels, meeting the high-performance requirements for scientific workflows. In this article, we present ChemComp, a compilation pipeline for the conversion of ordinary differential equations into implementable chemical reactions. We then demonstrate the solving capabilities of ChemComp by emulating a potential chemical reservoir device. We leverage the multi-layer intermediate representation (MLIR) compiler framework to implement an expressive chemical reaction abstraction and propose a path for chemical reaction networks (CRNs) to represent mathematical problems effectively. Combined, we demonstrate a potential workflow that can harness chemistry’s computing power to create energy-efficient, high-performance computation systems for contemporary computing needs.

artificial intelligence↗

DOE OSTI2021

PyOECP: A flexible open-source software for the measurement and modeling of the dielectric spectrum from the reflection coefficient

We present PyOECP, a Python-based flexible open-source software for estimating and modeling the complex permittivity obtained from the open-ended coaxial probe (OECP) technique. The transformation of the measured reflection coefficient to complex permittivity is performed based on two different models, including the capacitance model and the antenna model. The software library contains dielectric spectra of common reference liquids, which can be used to transform the reflection coefficient into the dielectric spectra. Several Python routines that are commonly employed (e.g., SciPy and NumPy) are only required so that the users can alter the software structure depending on their needs. The modeling algorithm exploits the Markov chain Monte Carlo method for the data regression. The discrete relaxation models can be built by a proper combination of well-known relaxation models. In addition to these models, the electrode polarization, which is a common measurement artifact for interpreting the dielectric spectra, can be incorporated in the modeling algorithm. A continuous relaxation model, which solves the Fredholm integral equation of the first kind (a mathematically ill-posed problem) is also included.

Yoon, Tae-Jun↗

DOE OSTI2022

Newton trust-region methods with primary variable switching for simulating high temperature multiphase porous media flow

Coupling multiphase flow with energy transport due to high temperature heat sources introduces significant new challenges since boiling and condensation processes can lead to dry-out conditions with subsequent re-wetting. The transition between two-phase and single-phase behavior can require changes to the primary dependent variables adding discontinuities as well as extending constitutive nonlinear relations to extreme physical conditions. Practical simulations of large-scale engineered domains lead to Jacobian systems with a very large number of unknowns that must be solved efficiently using iterative methods in parallel on high-performance computers. Performance assessment of potential nuclear repositories, carbon sequestration sites and geothermal reservoirs can require numerous Monte-Carlo simulations to explore uncertainty in material properties, boundary conditions, and failure scenarios. Due to the numerical challenges, standard NR iteration may not converge over the range of required simulations and require more sophisticated optimization method like trust-region. In this study, we use the open-source simulator PFLOTRAN for the important practical problem of the safety assessment of future nuclear waste repositories in the U.S. DOE geologic disposal safety assessment Framework. The simulator applies the PETSc parallel framework and a backward Euler, finite volume discretization. We demonstrate failure of the conventional NR method and the success of trust-region modifications to Newton’s method for a series of test problems of increasing complexity. Trust-region methods essentially modify the Newton step size and direction under some circumstances where the standard NR iteration can cause the solution to diverge or oscillate. Furthermore, we show how the Newton Trust-Region method can be adapted for Primary Variable Switching (PVS) when the multiphase state changes due to boiling or condensation. The simulations with high-temperature heat sources which led to extreme nonlinear processes with many state changes in the domain did not converge with NR, but they do complete successfully with the trust-region methods modified for PVS. This implementation effectively decreased weeks of simulation time needing manual adjustments to complete a simulation down to a day. Finally, we show the strong scalability of the methods on a single node and multiple nodes in an HPC cluster.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

Barcoded reciprocal hemizygosity analysis via sequencing illuminates the complex genetic basis of yeast thermotolerance

Decades of successes in statistical genetics have revealed the molecular underpinnings of traits as they vary across individuals of a given species. But standard methods in the field cannot be applied to divergences between reproductively isolated taxa. Genome-wide reciprocal hemizygosity mapping (RH-seq), a mutagenesis screen in an interspecies hybrid background, holds promise as a method to accelerate the progress of interspecies genetics research. Here, we describe an improvement to RH-seq in which mutants harbor barcodes for cheap and straightforward sequencing after selection in a condition of interest. As a proof of concept for the new tool, we carried out genetic dissection of the difference in thermotolerance between two reproductively isolated budding yeast species. Experimental screening identified dozens of candidate loci at which variation between the species contributed to the thermotolerance trait. Hits were enriched for mitosis genes and other housekeeping factors, and among them were multiple loci with robust sequence signatures of positive selection. Together, these results shed new light on the mechanisms by which evolution solved the problems of cell survival and division at high temperature in the yeast clade, and they illustrate the power of the barcoded RH-seq approach.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2019

A space-time adaptive finite element method with exponential time integrator for the phase field model of pitting corrosion

In this paper we propose a space-time adaptive finite element method for the phase field model of pitting corrosion, which is a parabolic partial differential equation system consisting of a phase variable and a concentration variable. A major challenge in solving this phase field model is that the problem is very stiff, which makes the time step size extremely small for standard temporal discretizations. Another difficulty is that a high spatial resolution is required to capture the steep gradients within the diffused interface, which results in very large number of degrees of freedom for uniform meshes. To overcome the stiffness of this model, we combine the Rosenbrock–Euler exponential integrator with Crank–Nicolson scheme for the temporal discretization. Moreover, by exploiting the fact that the speed of the corroding interface decreases with time, we derive an adaptive time stepping formula. For the spatial approximation, we propose a simple and efficient strategy to generate adaptive meshes that reduces the computational cost significantly. Thus, the proposed method utilizes local adaptivity and mesh refinement for efficient simulation of the corrosive dissolution over long times in heterogeneous media with complex microstructures. We also present an extensive set of numerical experiments in both two and three dimensional spaces to demonstrate efficiency and robustness of the proposed method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Investigation of CAD-based Geometry Workflows for Multiphysics Fusion Problems Using OpenMC and MOOSE

Fusion system designs are complex and require intricate and accurate meshes to be properly modeled. In this study, we investigate the use of CAD-based geometry workflows in fusion systems multiphysics problems. A simplified tokamak was introduced and modeled in CAD using a multiphysics coupling of OpenMC Monte Carlo transport and MOOSE heat conduction. The meshed geometry was prepared using direct accelerated geometry Monte Carlo (DAGMC) for particle transport, and a volumetric mesh was also prepared to be used in MOOSE and to tally OpenMC results. Cardinal was used to run OpenMC Monte Carlo particle transport within MOOSE framework. The heat source distribution and tritium production were calculated in OpenMC. The data transfer system was used to transfer heat source and temperature distribution between OpenMC and MOOSE. Two computational studies related to mesh refinement were performed: (1) refining the DAGMC and volumetric meshes used for tallying results and solving heat conduction and (2) only refining the DAGMC particle transport mesh. The refinement of the tally mesh has a much larger effect on the runtime compared to the refinement of the DAGMC particle transport surface mesh.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Improving Cyber Situational Understanding

Effective cybersecurity operations require the ability to analyze large amounts of information to assess security risks and formulate defensive strategies against adversaries. This has become more complex in recent years as the sprawl and interconnectivity of devices grows through implementation of virtualization, cloud computing, and Internet of Things (IoT). The amount of data and analysis required for effective cybersecurity command and control decisions far exceeds humans’ capacity to perform manually. We characterize the analysis problem as cyber situational understanding. The research presented to improve cyber situational understanding focuses on vulnerability analysis and threat intelligence. Regarding vulnerabilities, entities must analyze and plan work for between thousands and tens of thousands of software vulnerabilities annually. Entities heavily use network firewalls to limit vulnerability exposure. As a result, some of these vulnerabilities permit exposure to adversarial exploitation, whereas others are inaccessible and therefore present negligible risk of exploitation. Distinguishing between high and low risk software vulnerabilities requires a deep understanding of the vulnerability, network firewall protection, and characteristics of the targeted device. This problem is solved by extracting network service features from vulnerability data features using both machine-learning and natural language processing. Then, the network firewall topology is parsed to determine which vulnerabilities are reachable by adversaries. Ultimately, a state-based safety analysis ascertains which vulnerabilities are unsafe. A related vulnerability analysis problem occurs in cybersecurity operations when associating an entity’s hardware and software assets to public vulnerability databases. Assets often reveal hardware and software through installation artifacts and network service identification, and entities store these artifacts in inventory databases. However, software and hardware vendors apply a standard Common Platform Enumeration (CPE) naming convention when publicly reporting vulnerabilities. Associating these two datasets often requires many hours to days of manual inspection. The proposed solution automates the mapping approach of human analysts using fuzzy matching techniques, natural language processing, and, ultimately, machine learning to present a small set of recommendations for mapping the two datasets. The result significantly reduces human analysis time and reduces the occurrence of false positives in vulnerability notifications. Finally, cyber threat intelligence (CTI) requires associating cyber observable artifacts, such as IP addresses, URIs, and file hashes, with cyber threat tactics, techniques, and procedures. Unfortunately, most CTI data is compartmentalized across multiple organizations and cannot be shared due to the legal and reputational risk with cyber threat being associated with the entity. The approach to solving this problem inovlves using a distributed ledger with anonymous token spending and authentication. This allows a consortium of semi-trusted entities to share the workload of curating CTI for a threat sharing community’s cooperative benefit.

Huff, Philip↗