A method of solving the direct and inverse problem of supersonic flow along arbitrary stream filaments of revolution in turbomachines
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Wu, Chung-Hua↗
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Results for “inverse methods”
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Tabulated Fluid Properties Research Report
The Multiphysics Object-Oriented Simulation Environment (MOOSE) enables a wide range of advanced nuclear reactor simulations.[6] Under the guidance of MOOSE’s Thermal Hydraulics Team,I worked to expand the capabilities of Tabulated Fluid Properties (TFP) in the fluid properties module. The fluid properties module allows the user to determine a variety of fluid properties by interpolating points between tabulated data. I implemented the ability to use bilinear interpolation instead of bicubic interpolation for interpolating tabulated data. I also changed the method of variable set inversions to use a 2-dimensional Newton’s Method utility that I created. Variable set inversions are often done from (v,e) to (p,T), where v is specific volume, e is specific internal energy, p is pressure and T is temperature. New routines have also been added into TFP such that it can be used with more applications, such as the Navier Stokes and Thermal Hydraulics modules in MOOSE for Pronghorn[5] and RELAP-7[1] respectively. This work was spurred by interest from NASA in testing a Nuclear Thermal Propulsion (NTP) engine system. NTP engines have drastically different fluid properties throughout the engine and Tabulated Fluid Properties provides the flexibility needed to properly simulate and test these engines.
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
Towards robust autonomous impedance spectroscopy analysis: A calibrated hierarchical Bayesian approach for electrochemical impedance spectroscopy (EIS) inversion
Distribution-based analyses, such as the distribution of relaxation times (DRT) and the distribution of diffusion times (DDT), present model-free alternatives to equivalent circuit modeling for analysis of electrochemical impedance spectroscopy (EIS) data. However, reconstructing such distributions from noisy impedance data is an ill-posed problem that must be solved with specialized inversion algorithms, requiring careful control and tuning. Furthermore, most inversion algorithms developed to date can only solve problems of limited complexity. Herein, we present a new hierarchical Bayesian method for EIS inversion, leveraging efficient algorithms for optimization and Hamiltonian Monte Carlo (HMC) sampling to solve models of arbitrary complexity. We overcome the challenge of ad-hoc parameter tuning by encoding intrinsic characteristics of the DRT and DDT into flexible prior distributions and “pre-calibrating” the model to simulated data. This approach is versatile, highly robust to noise, and provides quantitative estimates of both the error structure of the data and the uncertainty in the recovered distributions. The model is validated with simulated data to demonstrate accurate recovery of the DRT and the DDT. The method also shows promise for simultaneous recovery of multiple distributions, raising the intriguing possibility of semi-autonomous EIS analysis and ad-hoc model construction. Finally, the practical utility of the method is illustrated with experimental data. Throughout, we draw comparisons to several recently published EIS inversion methodologies.
36 MATERIALS SCIENCE↗
Multi-frequency progressive refinement for learned inverse scattering
Interpreting scattered acoustic and electromagnetic wave patterns is a computational task that enables remote imaging in a number of important applications, including medical imaging, geophysical exploration, sonar and radar detection, and nondestructive testing of materials. However, accurately and stably recovering an inhomogeneous medium from far-field scattered wave measurements is a computationally difficult problem, due to the nonlinear and non-local nature of the forward scattering process. We design a neural network, called Multi-Frequency Inverse Scattering Network (MFISNet), and a training method to approximate the inverse map from far-field scattered wave measurements at multiple frequencies. We consider three variants of MFISNet, with the strongest performing variant inspired by the recursive linearization method — a commonly used technique for stably inverting scattered wavefield data — that progressively refines the estimate with higher frequency content. MFISNet outperforms past methods in regimes with high-contrast, heterogeneous large objects, and inhomogeneous unknown backgrounds.
97 MATHEMATICS AND COMPUTING↗
Simultaneous Optimization of Nuclear–Electronic Orbitals
Accurate modeling of important nuclear quantum effects, such as nuclear delocalization, zero-point energy, and tunneling, as well as non-Born-Oppenheimer effects, requires treatment of both nuclei and electrons quantum mechanically. The nuclear–electronic orbital (NEO) method provides an elegant framework to treat specified nuclei, typically protons, on the same level as the electrons. In conventional electronic structure theory, finding a converged ground state can be a computationally demanding task; converging NEO wavefunctions, due to their coupled electronic and nuclear nature, is even more demanding. Herein, we present an efficient simultaneous optimization method that uses the direct inversion in the iterative subspace method to simultaneously converge wavefunctions for both the electrons and quantum nuclei. In conclusion, benchmark studies show that the simultaneous optimization method can significantly reduce the computational cost compared to the conventional stepwise method for optimizing NEO wavefunctions for multicomponent systems.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Georgia Tech Accelerated, Compressed, and Regularized Compute of Kinetic-based PDEs (Final Report)
This report summarizes the collaborative effort between Lawrence Livermore National Laboratory and Georgia Tech to enhance the BoBa library for tensor train computation in PDE solvers, with a target on kinetic equations and their continuum limits. We aimed to reduce computational cost and memory usage by replacing traditional array-based computations with tensor trains. We examined the compressibility of time-evolving solutions to the Euler equations with discontinuities. We also explored using the first invsicid and linear regularization of the compressible flow equations via the information geometric regularization (IGR). We explored this in a tensor train formulation. To identify that inverse terms in the IGR equations pose problems for tensor train formulations and investigate efficient methods for batched inversion of tensor trains.
97 MATHEMATICS AND COMPUTING↗
Comparison of various methods for mathematical analysis of the Foucault knife edge test pattern to determine optical imperfections
The linearized integral equation for the Foucault test of a solid mirror was solved by various methods: power series, Fourier series, collocation, iteration, and inversion integral. The case of the Cassegrain mirror was solved by a particular power series method, collocation, and inversion integral. The inversion integral method appears to be the best overall method for both the solid and Cassegrain mirrors. Certain particular types of power series and Fourier series are satisfactory for the Cassegrain mirror. Numerical integration of the nonlinear equation for selected surface imperfections showed that results start to deviate from those given by the linearized equation at a surface deviation of about 3 percent of the wavelength of light. Several possible procedures for calibrating and scaling the input data for the integral equation are described.
Gatewood, B. E.↗
Procedures utilized for obtaining direct and remote atmospheric carbon monoxide measurements over the lower Lake Michigan Basin in August of 1976
In order to establish the applicability of a gas filter correlation radiometer, GFCR, to remote carbon monoxide, CO, measurements on a regional and worldwide basis, Old Dominion University has been engaged in the development of accurate and cost effective techniques for inversion of GFCR CO data and in the development of an independent gas chromatographic technique for measuring CO. This independent method is used to verify the results and the associated inversion method obtained from the GFCR. A description of both methods (direct and remote) will be presented. Data obtained by both techniques during a flight test over the lower Lake Michigan Basin in August of 1976 will also be discussed.
Casas, J. C.↗
The double universal joint wrist on a manipulator: Solution of inverse position kinematics and singularity analysis
This paper presents three methods to solve the inverse position kinematics position problem of the double universal joint attached to a manipulator: (1) an analytical solution for two specific cases; (2) an approximate closed form solution based on ignoring the wrist offset; and (3) an iterative method which repeats closed form position and orientation calculations until the solution is achieved. Several manipulators are used to demonstrate the solution methods: cartesian, cylindrical, spherical, and an anthropomorphic articulated arm, based on the Flight Telerobotic Servicer (FTS) arm. A singularity analysis is presented for the double universal joint wrist attached to the above manipulator arms. While the double universal joint wrist standing alone is singularity-free in orientation, the singularity analysis indicates the presence of coupled position/orientation singularities of the spherical and articulated manipulators with the wrist. The cartesian and cylindrical manipulators with the double universal joint wrist were found to be singularity-free. The methods of this paper can be implemented in a real-time controller for manipulators with the double universal joint wrist. Such mechanically dextrous systems could be used in telerobotic and industrial applications, but further work is required to avoid the singularities.
Williams, Robert L., III↗
Comparative evolution of the inverse problems (Introduction to an interdisciplinary study of the inverse problems)
The progressive realization of the consequences of nonuniqueness imply an evolution of both the methods and the centers of interest in inverse problems. This evolution is schematically described together with the various mathematical methods used. A comparative description is given of inverse methods in scientific research, with examples taken from mathematics, quantum and classical physics, seismology, transport theory, radiative transfer, electromagnetic scattering, electrocardiology, etc. It is hoped that this paper will pave the way for an interdisciplinary study of inverse problems.
Sabatier, P. C.↗
Inverse airfoil design procedure using a multigrid Navier-Stokes method
The Modified Garabedian McFadden (MGM) design procedure was incorporated into an existing 2-D multigrid Navier-Stokes airfoil analysis method. The resulting design method is an iterative procedure based on a residual correction algorithm and permits the automated design of airfoil sections with prescribed surface pressure distributions. The new design method, Multigrid Modified Garabedian McFadden (MG-MGM), is demonstrated for several different transonic pressure distributions obtained from both symmetric and cambered airfoil shapes. The airfoil profiles generated with the MG-MGM code are compared to the original configurations to assess the capabilities of the inverse design method.
Malone, J. B.↗
The inverse scattering problem for transmission lines
A number of exact and approximate methods for solving the inverse scattering problem for transmission lines are reviewed. In particular, the application to transmission lines of Marcenko's version of the Gelfand-Levitan exact method for the quantum mechanical problem is compared with a more direct approach based on a different version of the Gelfand-Levitan method. In addition, some aspects of the lack of uniqueness of solutions are discussed, and some open questions related to the inverse scattering problem are suggested.
Kay, I.↗
Proton radiography inversions with source extraction and comparison to mesh methods
In this article, proton radiography is a central diagnostic technique for measuring electromagnetic (EM) fields in high-energy-density, laser-produced plasmas. In this technique, protons traverse the plasma where they accumulate small EM deflections which lead to variations in the proton fluence pattern on a detector. Path-integrated EM fields can then be extracted from the fluence image through an inversion process. In this work, experiments of laser-driven foils were conducted on the OMEGA laser and magnetic field reconstructions were performed using both “fluence-based” techniques and high-fidelity “mesh-based” methods. We implement nonzero boundary conditions into the inversion and show their importance by comparing against mesh measurements. Good agreement between the methods is found only when nonzero boundary conditions are used. We also introduce an approach to determine the unperturbed proton source profile, which is a required input in fluence reconstruction algorithms. In this approach, a fluence inversion is embedded inside of a mesh region, which provides overconstrained magnetic boundary conditions. A source profile is then iteratively optimized to satisfy the boundary information. This method substantially enhances the accuracy in recovering EM fields. Lastly, we propose a scheme to quantify uncertainty in the final inversion that is introduced through errors in the source retrieval.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Revisiting matrix-based inversion of scanning mobility particle sizer (SMPS) and humidified tandem differential mobility analyzer (HTDMA) data
Abstract. Tikhonov regularization is a tool for reducing noise amplification during data inversion. This work introduces RegularizationTools.jl, a general-purpose software package for applying Tikhonov regularization to data. The package implements well-established numerical algorithms and is suitable for systems of up to ∼ 1000 equations. Included is an abstraction to systematically categorize specific inversion configurations and their associated hyperparameters. A generic interface translates arbitrary linear forward models defined by a computer function into the corresponding design matrix. This obviates the need to explicitly write out and discretize the Fredholm integral equation, thus facilitating fast prototyping of new regularization schemes associated with measurement techniques. Example applications include the inversion involving data from scanning mobility particle sizers (SMPSs) and humidified tandem differential mobility analyzers (HTDMAs). Inversion of SMPS size distributions reported in this work builds upon the freely available software DifferentialMobilityAnalyzers.jl. The speed of inversion is improved by a factor of ∼ 200, now requiring between 2 and 5 ms per SMPS scan when using 120 size bins. Previously reported occasional failure to converge to a valid solution is reduced by switching from the L-curve method to generalized cross-validation as the metric to search for the optimal regularization parameter. Higher-order inversions resulting in smooth, denoised reconstructions of size distributions are now included in DifferentialMobilityAnalyzers.jl. This work also demonstrates that an SMPS-style matrix-based inversion can be applied to find the growth factor frequency distribution from raw HTDMA data while also accounting for multiply charged particles. The outcome of the aerosol-related inversion methods is showcased by inverting multi-week SMPS and HTDMA datasets from ground-based observations, including SMPS data obtained at Bodega Marine Laboratory during the CalWater 2/ACAPEX campaign and co-located SMPS and HTDMA data collected at the US Department of Energy observatory located at the Southern Great Plains site in Oklahoma, USA. Results show that the proposed approaches are suitable for unsupervised, nonparametric inversion of large-scale datasets as well as inversion in real time during data acquisition on low-cost reduced-instruction-set architectures used in single-board computers. The included software implementation of Tikhonov regularization is freely available, general, and domain-independent and thus can be applied to many other inverse problems arising in atmospheric measurement techniques and beyond.
54 ENVIRONMENTAL SCIENCES↗
Interpreting strain tensor data to characterize and monitor reservoirs for CO2 storage and other applications
Recent advances in instrumentation have made it feasible to measure the transient strain tensor caused by small changes in fluid volume or pressure in the subsurface and this has opened the door to new opportunities for characterization and monitoring. We have deployed strainmeters and then conducted injection well tests in an underlying reservoir at 530m depth. The resulting data indicated that the horizontal strain at shallow strainmeters (30 to 40m depth) was tensile and the vertical strain was compressive. The radial strain was less than the horizontal strain, and the strain rates decreased from 100 nanostrain/day to roughly 10 n/d over a few days. The signal at two strainmeters at shallow depth were consistent, although the magnitude of the horizontal strains were different reflecting the different radial directions from the well. The signal at a deep strainmeter deployed at reservoir depth was much different, with tensile vertical strains and compressive horizontal strains. These data can be interpreted by inverting poroelastic forward models developed using numerical and analytical methods. The average horizontal strain in the caprock resembles the transient pressure in the underlying reservoir and classic type-curve methods from transient well testing can be used for preliminary interpretations of strain data. We have developed closed-form analytical solutions to a pressurized poroelastic inclusion and inhomogeneity in a half-space. This model is fast and can be inverted to estimate reservoir stiffness and geometry. Numerical models developed using finite element methods allow more details of the subsurface to be included in the inversion, but they require much longer run times and this makes inversion cumbersome using standard methods. We have developed an inversion approach that uses a proxy model created using machine learning to do most of the forward calculations. The proxy model is periodically updated and refined using the finite element model to ensure accuracy. This approach significantly reduces the computational requirements and makes it feasible to use Bayesian inversion with large numerical models. We have shown that the strain tensor in the caprock is sensitive to pressure in the reservoir, boundaries in the reservoir, and pressure in the caprock caused by leaks. These results indicate that coupling strain tensor data with inversion has the potential to help evaluate reservoirs during initial characterization, and to monitor them during the CO2 injection and storage process.
Murdoch, Larry↗
Quantitatively Monitoring Bubble-Flow at a Seep Site Offshore Oregon: Field Trials and Methodological Advances for Parallel Optical and Hydroacoustical Measurements
Two lander-based devices, the Bubble-Box and GasQuant-II, were used to investigate the spatial and temporal variability and total gas flow rates of a seep area offshore Oregon, United States. The Bubble-Box is a stereo camera–equipped lander that records bubbles inside a rising corridor with 80 Hz, allowing for automated image analyses of bubble size distributions and rising speeds. GasQuant is a hydroacoustic lander using a horizontally oriented multibeam swath to record the backscatter intensity of bubble streams passing the swath plain. The experimental set up at the Astoria Canyon site at a water depth of about 500 m aimed at calibrating the hydroacoustic GasQuant data with the visual Bubble-Box data for a spatial and temporal flow rate quantification of the site. For about 90 h in total, both systems were deployed simultaneously and pressure and temperature data were recorded using a CTD as well. Detailed image analyses show a Gaussian-like bubble size distribution of bubbles with a radius of 0.6–6 mm (mean 2.5 mm, std. dev. 0.25 mm); this is very similar to other measurements reported in the literature. Rising speeds ranged from 15 to 37 cm/s between 1- and 5-mm bubble sizes and are thus, in parts, slightly faster than reported elsewhere. Bubble sizes and calculated flow rates are rather constant over time at the two monitored bubble streams. Flow rates of these individual bubble streams are in the range of 544–1,278 mm 3 /s. One Bubble-Box data set was used to calibrate the acoustic backscatter response of the GasQuant data, enabling us to calculate a flow rate of the ensonified seep area (~1,700 m 2 ) that ranged from 4.98 to 8.33 L/min (5.38 × 10 6 to 9.01 × 10 6 CH 4 mol/year). Such flow rates are common for seep areas of similar size, and as such, this location is classified as a normally active seep area. For deriving these acoustically based flow rates, the detailed data pre-processing considered echogram gridding methods of the swath data and bubble responses at the respective water depth. The described method uses the inverse gas flow quantification approach and gives an in-depth example of the benefits of using acoustic and optical methods in tandem.
54 ENVIRONMENTAL SCIENCES↗
Forced Component Estimation Statistical Method Intercomparison Project (ForceSMIP)
Anthropogenic climate change is unfolding rapidly, yet its regional manifestation can be obscured by internal variability. A primary goal of climate science is to identify the externally forced climate response from among the noise of internal variability. Separating the forced response from internal variability can be addressed in climate models by using a large ensemble to average over different possible realizations of internal variability. However, with only one realization of the real world, it is a major challenge to isolate the forced response directly in observations. In the Forced Component Estimation Statistical Method Intercomparison Project (ForceSMIP), contributors used existing and newly developed statistical and machine learning methods to estimate the forced response over 1950–2022 within individual realizations of the climate system. Participants used neural networks, linear inverse models, fingerprinting methods, and low-frequency component analysis, among other approaches. These methods were trained using large ensembles from multiple climate models and then applied to observations. Here, we evaluate method performance within large ensembles and investigate the estimates of the forced response in observations. Our results show that many different types of methods are skillful for estimating the forced response in climate models, though the relative skill of individual methods varies depending on the variable and evaluation metric. Methods with comparable skill in models can give a wide range of estimates of the forced response pattern in observations, illustrating the epistemic uncertainty in forced response estimates. ForceSMIP gives new insights into the forced response in observations, its uncertainty, and methods for its estimation.
Climate attribution↗
Fast Computation of the Inverse CMH Model
A fast computational method based on differential equation approach for inverse DOK model has been extended for the inverse CMH model. Also, a cobweb technique for calculating the inverse CMH model is also presented. The two techniques are differed from the point of view of flexibility and computation time.
Patel, Umesh D.↗