Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “inversion methods”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 307 records · Page 17
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Fast inversion, preconditioned quantum linear system solvers, fast Green's-function computation, and fast evaluation of matrix functions

Preconditioning is the most widely used and effective way for treating ill-conditioned linear systems in the context of classical iterative linear system solvers. We introduce a quantum primitive called fast inversion, which can be used as a preconditioner for solving quantum linear systems. The key idea of fast inversion is to directly block encode a matrix inverse through a quantum circuit implementing the inversion of eigenvalues via classical arithmetics. We demonstrate the application of preconditioned linear system solvers for computing single-particle Green's functions of quantum many-body systems, which are widely used in quantum physics, chemistry, and materials science. We analyze the complexities in three scenarios: the Hubbard model, the quantum many-body Hamiltonian in the plane-wave-dual basis, and the Schwinger model. We also provide a method for performing Green's function calculation in second quantization within a fixed-particle manifold and note that this approach may be valuable for simulation more broadly. Aside from solving linear systems, fast inversion also allows us to develop fast algorithms for computing matrix functions, such as the efficient preparation of Gibbs states. Furthermore, we introduce two efficient approaches for such a task, based on the contour-integral formulation and the inverse transform, respectively.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Chapter 4 - Recent Advances in Identification of Differential Equations from Noisy Data: IDENT Review

Differential equations and numerical methods are extensively used to model various real-world phenomena in science and engineering. With modern developments, we aim to find the underlying differential equation from a single observation of time-dependent data. If we assume that the differential equation is a linear combination of various linear and nonlinear differential terms, then the identification problem can be formulated as solving a linear system. The goal then reduces to finding the optimal coefficient vector that best represents the time derivative of the given data. We review some recent works on the identification of differential equations. We find some common themes for the improved accuracy: (i) The formulation of linear system with proper denoising is important, (ii) how to utilize sparsity and model selection to find the correct coefficient support needs careful attention, and (iii) there are ways to improve the coefficient recovery. We present an overview and analysis of recent developments on the topic.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

High-throughput spin-bath characterization of spin defects in semiconductors

Detailed knowledge of the local environments of spin defects in semiconductors, such as nitrogenvacancy (NV) centers in diamond or divacancies in silicon carbide, is crucial for optimizing control and entanglement protocols in quantum sensing and information applications. However, at present a direct experimental characterization of individual defect environments is not scalable, as conventional spin-bath measurements are time consuming and difficult to automate. Achieving high-throughput characterization requires short experiments to probe the spin bath. However, with fewer and noisier measurements, the inverse problem of recovering spin-bath properties from measured data becomes ill posed, with multiple spin baths having a high likelihood of yielding the same data. In this work, we present a set of computational tools to resolve the ill-posed inverse problem of recovering the atomic positions and hyperfine couplings of random nuclei surrounding spin defects from sparse, noisy experimental coherence data, which can be obtained in hours. Here, we use a trans-dimensional Bayesian approach that incorporates ab initio data to yield full posterior distributions over nuclear spin environments, enabling robust recovery from limited data. We also provide practical tools and guidelines to determine the limits of detectability for hyperfine couplings under specific dynamical decoupling sequences and sampling conditions. In addition, we demonstrate how the tools developed here, in combination with ab initio simulations of spin baths, can guide the design of efficient experimental protocols for application-specific high-throughput screening. To showcase the utility of our approach, we apply it to design fast dynamical decoupling experiments to characterize the spin baths often individual NV centers in diamond. While the primary focus is on accelerating spin-bath characterization of spin defects, this Bayesian approach also lays the foundation for digital-twin studies of spin defects, where a virtual model of the spin-defect system evolves in real time with ongoing experimental measurements. Together, the set of tools we designed and applied paves the way for scalable deployment of spin defects in semiconductors for quantum sensing and information applications.

Bayesian methods↗
DOE OSTI2021

A general approach to seismic inversion with automatic differentiation

Imaging Earth structure or seismic sources from seismic data involves minimizing a target misfit function, and is commonly solved through gradient-based optimization. The adjoint-state method has been developed to compute the gradient efficiently; however, its implementation can be time-consuming and difficult. We develop a general seismic inversion framework to calculate gradients using reverse-mode automatic differentiation. The central idea is that adjoint-state methods and reverse-mode automatic differentiation are mathematically equivalent. Here, the mapping between numerical PDE simulation and deep learning allows us to build a seismic inverse modeling library, ADSeismic, based on deep learning frameworks, which supports high performance reverse-mode automatic differentiation on CPUs and GPUs. We demonstrate the performance of ADSeismic on inverse problems related to velocity model estimation, rupture imaging, earthquake location, and source time function retrieval. ADSeismic has the potential to solve a wide variety of inverse modeling applications within a unified framework.

58 GEOSCIENCES↗
DOE OSTI2022

Multimodal parameter spaces of a complex multi-channel neuron model

One of the most common types of models that helps us to understand neuron behavior is based on the Hodgkin–Huxley ion channel formulation (HH model). A major challenge with inferring parameters in HH models is non-uniqueness: many different sets of ion channel parameter values produce similar outputs for the same input stimulus. Such phenomena result in an objective function that exhibits multiple modes (i.e., multiple local minima). This non-uniqueness of local optimality poses challenges for parameter estimation with many algorithmic optimization techniques. HH models additionally have severe non-linearities resulting in further challenges for inferring parameters in an algorithmic fashion. To address these challenges with a tractable method in high-dimensional parameter spaces, we propose using a particular Markov chain Monte Carlo (MCMC) algorithm, which has the advantage of inferring parameters in a Bayesian framework. The Bayesian approach is designed to be suitable for multimodal solutions to inverse problems. We introduce and demonstrate the method using a three-channel HH model. We then focus on the inference of nine parameters in an eight-channel HH model, which we analyze in detail. We explore how the MCMC algorithm can uncover complex relationships between inferred parameters using five injected current levels. The MCMC method provides as a result a nine-dimensional posterior distribution, which we analyze visually with solution maps or landscapes of the possible parameter sets. The visualized solution maps show new complex structures of the multimodal posteriors, and they allow for selection of locally and globally optimal value sets, and they visually expose parameter sensitivities and regions of higher model robustness. We envision these solution maps as enabling experimentalists to improve the design of future experiments, increase scientific productivity and improve on model structure and ideation when the MCMC algorithm is applied to experimental data.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Comparison of Shape Optimization Methods for Heat Exchanger Fins Using Computational Fluid Dynamics

Inverse design techniques are one way to leverage advances in 3D printing, artificial intelligence, and computational resources to achieve increased performance of heat exchangers. Two optimization techniques (genetic algorithm and particle swarm) and three geometry representations (binary level set, composite Bézier, and free form deformation) are used to increase the heat transfer and reduce the pressure drop of a heat exchanger fin. After running 210,810 OpenFOAM simulations, results indicate that a significant performance increase of the fin can be realized in less than 48 hrs, allowing for such a process to be integrated in traditional design processes. The best design increased the performance of the objective function, compared to the baseline rectangular geometry by 75%. A custom distributed infrastructure was built, allowing for all methods to reach 95% of the final objective values in a little over 4 hrs, handling 1674 OpenFoam simulations per hour.

42 ENGINEERING↗
DOE OSTI2024

Digital Multiphase Composites via Additive Manufacturing

Abstract Mechanical properties of traditional engineering materials are typically coupled to each other, presenting a challenge to practitioners with multi‐dimensional material property requirements. In this work, continuous, independent control over multiple mechanical properties is demonstrated in composite materials realized using additive manufacturing. For the first time, composites additively manufactured from rigid plastic, soft elastomer, and liquid constituents are experimentally characterized, demonstrating materials which span four orders of magnitude in modulus and two orders of magnitude in toughness. By forming analytical mappings between relative concentrations of constituents at the microscale and resulting macroscale material properties, inverse material design is enabled; the method is showcased by printing artifacts with prescribed toughness and elasticity distributions. The properties of these composites are placed in the context of biological tissues, showing they have promise as mechanically plausible tissue mimics.

Smith, Lawrence T.↗
DOE OSTI2020

An error-in-constitutive equations strategy for topology optimization for frequency-domain dynamics

This paper presents a topology optimization formulation for frequency-domain dynamics to reduce solution dependence upon initial guess and considered loading conditions. Due to resonance phenomena in undamped steady-state dynamics, objectives measuring dynamic response possess many local minima that may represent poor solutions to a design problem, an issue exacerbated for design with respect to multiple frequencies. In this work, we propose an extension of the modified error-in-constitutive-equations (MECE) method, used previously in material identification inverse problems, as a new approach for frequency-domain dynamics topology optimization to mitigate these issues. The main idea of the proposed framework is to incorporate an additional penalty-like term in the objective function that measures the discrepancy in the constitutive relations between stresses and strains and between inertial forces and displacements. Then, the design problem is cast within a PDE-constrained optimization formulation in which we seek displacements, stresses, inertial forces, and a density-field solution that minimize our new objective subject to conservation of linear momentum plus some additional constraints. We show that this approach yields superior designs to conventional gradient-based optimization approaches that solely use a functional of displacements as the objective, while strictly enforcing the constitutive equations. The MECE strategy integrates into a density-based topology optimization scheme for void–solid or two-phase material structural design. We highlight the merits of our approach in a variety of scenarios for direct frequency response design, considering multiple frequency load cases and structural objectives.

42 ENGINEERING↗
DOE OSTI2022

PICSAR-QED: a Monte Carlo module to simulate strong-field quantum electrodynamics in particle-in-cell codes for exascale architectures

Abstract Physical scenarios where the electromagnetic fields are so strong that quantum electrodynamics (QED) plays a substantial role are one of the frontiers of contemporary plasma physics research. Investigating those scenarios requires state-of-the-art particle-in-cell (PIC) codes able to run on top high-performance computing (HPC) machines and, at the same time, able to simulate strong-field QED processes. This work presents the PICSAR-QED library, an open-source, portable implementation of a Monte Carlo module designed to provide modern PIC codes with the capability to simulate such processes, and optimized for HPC. Detailed tests and benchmarks are carried out to validate the physical models in PICSAR-QED, to study how numerical parameters affect such models, and to demonstrate its capability to run on different architectures (CPUs and GPUs). Its integration with WarpX, a state-of-the-art PIC code designed to deliver scalable performance on upcoming exascale supercomputers, is also discussed and validated against results from the existing literature.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Measuring the cross section of the N 15 ( α , γ ) 19 F reaction using a single-fluid bubble chamber

15 N(α, γ) 19 F is believed to be the primary means of stellar nucleosynthesis of fluorine. Here we present the use of a single-fluid bubble chamber to measure the cross section of the time-inverse photo-dissociation reaction. The method benefits from a luminosity increase of several orders of magnitude due to the use of a thicker liquid target - compared to thin films or gas targets - and from the reciprocity theorem. We discuss the results of experiments at the Thomas Jefferson National Accelerator Facility, where the cross section of the photodisintegration process 19 F(γ, α) 15 N was measured by bombarding a superheated fluid of C 3 F 8 with bremsstrahlung γ rays produced by impinging a 4 - 5.5 MeV electron beam on a Cu radiator. From the photodissociation yield the cross section was extracted by performing a convolution with a Monte Carlo–generated γ-ray beam spectrum. The measurement produced a cross section that was then time inverted using the reciprocity theorem. The cross section for the 15 N(α, γ) 19 F reaction was determined down to a value in the range of hundreds of picobarns. We report that with further improvements of the experimental setup the technique could potentially push cross section measurements down to the single picobarn range.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Nuclear Data Adjustment for Nonlinear Applications in the OECD/NEA WPNCS SG14 Benchmark -- A Bayesian Inverse UQ-based Approach for Data Assimilation

The Organization for Economic Cooperation and Development (OECD) Working Party on Nuclear Criticality Safety (WPNCS) proposed a benchmark exercise to assess the performance of current nuclear data adjustment techniques applied to nonlinear applications and experiments with low correlation to applications. This work introduces Bayesian Inverse Uncertainty Quantification (IUQ) as a method for nuclear data adjustments in this benchmark, and compares IUQ to the more traditional methods of Generalized Linear Least Squares (GLLS) and Monte Carlo Bayes (MOCABA). Posterior predictions from IUQ showed agreement with GLLS and MOCABA for linear applications. When comparing GLLS, MOCABA, and IUQ posterior predictions to computed model responses using adjusted parameters, we observe that GLLS predictions fail to replicate computed response distributions for nonlinear applications, while MOCABA shows near agreement, and IUQ uses computed model responses directly. We also discuss observations on why experiments with low correlation to applications can be informative to nuclear data adjustments and identify some properties useful in selecting experiments for inclusion in nuclear data adjustment. Performance in this benchmark indicates potential for Bayesian IUQ in nuclear data adjustments.

FOS: Computer and information sciences↗
DOE OSTI2024

Methods of fabricating porous ceramic electrodes for solid state battery applications

Compositions and methods for the fabrication of electrode and porous lithium-garnet electrolyte scaffolds for use in solid state batteries and other devices are provided. The methods produce porous structures using phase inversion or high shear compaction processes to fabricate a solid-state battery electrode material from LLZO electrolytes. Engineered electrode structures with a porous scaffold of solid electrolyte material provide lower interfacial resistances and a mechanical support for a thin solid electrode layer improving performance.

Tucker, Michael↗
DOE OSTI2021

Removal of spurious data in Bragg coherent diffraction imaging: an algorithm for automated data preprocessing

Bragg coherent diffraction imaging (BCDI) provides a powerful tool for obtaining high-resolution structural information from nanocrystalline materials. Here a BCDI sample consisting of a large number of randomly oriented nanoscale crystals is considered. Ideally, only one crystal is oriented to produce a Bragg peak on the detector. However, diffraction from other crystals often produces additional signals on the detector. Before the measured diffraction patterns can be processed into structural images, scientists routinely need to manually identify and remove the `alien' intensities from sources other than the intended crystal. With the development of modern high-coherence storage rings, such as the upgraded Advanced Photon Source (APS), the already slow process of manual preprocessing will be untenable for the large volumes of data that will be produced. An automated method of identifying and deleting alien intensities is proposed. This method exploits the fact that BCDI of a perfect crystal produces diffraction data with inversion symmetry around the Bragg peak. This approach uses the machine learning clustering method DBSCAN to distinguish between diffraction from multiple sources, and then calculates cluster size and inversion symmetry to assess whether clusters of intensity belong to desired data or alien signals. This approach can dramatically reduce the amount of time spent manually processing data, allowing BCDI data processing capabilities to keep pace with the technological advances of fourth-generation synchrotron light sources.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Sequential ensemble transform for Bayesian inverse problems

In this work, we present the Sequential Ensemble Transform (SET) method, an approach for generating approximate samples from a Bayesian posterior distribution. The method explores the posterior distribution by solving a sequence of discrete optimal transport problems to produce a series of transport plans which map prior samples to posterior samples. We prove that the sequence of Dirac mixture distributions produced by the SET method converges weakly to the true posterior as the sample size approaches infinity. Furthermore, our numerical results indicate that, when compared to standard Sequential Monte Carlo (SMC) methods, the SET approach is more robust to the choice of Markov mutation kernels and requires less computational efforts to reach a similar accuracy when used to explore complex posterior distributions. Finally, we describe adaptive schemes that allow to completely automate the use of the SET method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Simultaneous determination of electrical conductivity and thickness of nonmagnetic metallic foils using two-sided multifrequency eddy current techniques

Here, in this paper, we describe a simple method for performing multifrequency eddy current characterization of free-standing uniform-thickness metallic foils using a forked inductive coil arrangement. The method involves measuring the mutual inductance between two coils when a foil is present between the coils, and when it is not present; the ratio of these mutual inductances is compared with an analytical solution, and foil conductivity, thickness, and sheet resistance are simultaneously estimated using numerical inversion and least-squares fitting. This method was used to characterize 34 non-ferrous metallic samples with thicknesses between 50 and 640 μm and with conductivities between 0.8 × 10 7 and 5.8 × 10 7 S/m. The estimated thicknesses from eddy current characterization agreed well with those measured using confocal optical techniques; the two approaches agreed to within 1 μm for samples that were thinner than 200 μm, and to within 0.5% for samples that had a thickness of 200 μm or greater. The estimated conductivities from eddy current characterization were in close agreement with expected values, given knowledge of the materials used. A particular strength of this approach is that the instrumentation needed is broadly available in research and development laboratories and the associated fixturing is easy to manufacture and assemble. A calibration procedure is described that can be used to reduce errors from geometric uncertainties. This calibration requires a sample that has only a known conductivity or thickness; both do not need to be known. The method described herein is likely extensible to conductivities and thickness well outside the ranges measured as part of this work.

47 OTHER INSTRUMENTATION↗
DOE OSTI2020

Stochastic gradient descent algorithm for stochastic optimization in solving analytic continuation problems

We propose a stochastic gradient descent based optimization algorithm to solve the analytic continuation problem in which we extract real frequency spectra from imaginary time Quantum Monte Carlo data. The procedure of analytic continuation is an ill-posed inverse problem which is usually solved by regularized optimization methods, such like the Maximum Entropy method, or stochastic optimization methods. The main contribution of this work is to improve the performance of stochastic optimization approaches by introducing a supervised stochastic gradient descent algorithm to solve a flipped inverse system which processes the random solutions obtained by a type of Fast and Efficient Stochastic Optimization Method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Approximate inverse-based block preconditioners in poroelasticity

We focus on the fully implicit solution of the linear systems arising from a three-field mixed finite element approximation of Biot’s poroleasticity equations. The objective is to develop algebraic block preconditioners for the efficient solution of such systems by Krylov subspace methods. In this work, we investigate the use of approximate inverse-based techniques to decouple the native system of equations and obtain explicit sparse approximations of the Schur complements related to the physics-based partitioning of the unknowns by field type. Here, the proposed methods are tested in various numerical experiments including real-world applications dealing with petroleum and geotechnical engineering.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Lossy checkpoint compression in full waveform inversion: a case study with ZFPv0.5.5 and the overthrust model

This paper proposes a new method that combines checkpointing methods with error-controlled lossy compression for large-scale high-performance full-waveform inversion (FWI), an inverse problem commonly used in geophysical exploration. This combination can significantly reduce data movement, allowing a reduction in run time as well as peak memory. In the exascale computing era, frequent data transfer (e.g., memory bandwidth, PCIe bandwidth for GPUs, or network) is the performance bottleneck rather than the peak FLOPS of the processing unit. Like many other adjoint-based optimization problems, FWI is costly in terms of the number of floating-point operations, large memory footprint during backpropagation, and data transfer overheads. Past work for adjoint methods has developed checkpointing methods that reduce the peak memory requirements during backpropagation at the cost of additional floating-point computations. Combining this traditional checkpointing with error-controlled lossy compression, we explore the three-way tradeoff between memory, precision, and time to solution. We investigate how approximation errors introduced by lossy compression of the forward solution impact the objective function gradient and final inverted solution. Empirical results from these numerical experiments indicate that high lossy-compression rates (compression factors ranging up to 100) have a relatively minor impact on convergence rates and the quality of the final solution.

58 GEOSCIENCES↗