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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 OSTI2024

Calculation of tearing mode stability in an inverse aspect-ratio expanded tokamak plasma equilibrium

The tearing mode stability of an inverse aspect-ratio expanded tokamak plasma equilibrium of general shape is investigated using asymptotic matching techniques. Particular emphasis is placed on the conservation of toroidal electromagnetic angular momentum. The TJ code, which is a specific implementation of the results of the investigation, is described.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

Calculation of Critical Heat Flux Using an Inverse Heat Transfer Method to Support TREAT Experiment Analysis

Heat transfer between cladding and coolant during transient scenarios remains a critical area of uncertainty in understanding nuclear reactor safety. To advance the understanding of transient and accident scenarios involving critical heat flux (CHF), an in-pile experiment for the Transient Reactor Test (TREAT) facility at Idaho National Laboratory was developed. The experiment named CHF-Static Environment Rodlet Transient Test Apparatus (CHF-SERTTA), consists of a hollow borated stainless steel heater rod submerged in a static water pool which is heated via the (n, a) reaction in boron-10. This paper presents a novel inverse heat transfer method to determine CHF by using the optimization and uncertainty software DAKOTA to calibrate a RELAP5-3D model of CHF-SERTTA to temperature measurements obtained from a thermocouple welded to the surface of the rod.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2024

Improved Earthquake Source Parameters with 3D Wavespeed Models in California and Nevada

Seismic tomography harnesses earthquake data to explore the inaccessible structure of the Earth. Adjoint waveform tomography (AWT), a method of seismic tomography, updates the tomographic model by optimizing the fit between observed earthquake data and synthetic waveforms. The synthetic data are calculated by solving the wave equation through a given 3D model. An important requirement to calculating synthetics is the source information (location, centroid time, depth, and moment tensor). Errors in source information affect the quality of the synthetics produced, which in turn can limit how structure can be inferred in the AWT workflow. Here, to test the effect of updating source information, we used MTTime (Chiang, 2020), a time-domain full-waveform moment tensor inversion code, to calculate the moment tensors and depths of 118 earthquakes that occurred in California and Nevada over a 20-yr period. We calculated 3D Green’s functions using a 3D seismic wavespeed model of California and Nevada (Doody et al., 2023b). We show that the inverted solutions provide better waveform fits than the Global Centroid Moment Tensor catalog and increase usable, well-correlated data by up to 7%. Therefore, we argue that recalculating source parameters should be considered in AWT workflows, particularly for smaller magnitude events (⁠M w > 5.0).

58 GEOSCIENCES↗

NASA NTRS2011

Inverse Design of Low-Boom Supersonic Concepts Using Reversed Equivalent-Area Targets

A promising path for developing a low-boom configuration is a multifidelity approach that (1) starts from a low-fidelity low-boom design, (2) refines the low-fidelity design with computational fluid dynamics (CFD) equivalent-area (Ae) analysis, and (3) improves the design with sonic-boom analysis by using CFD off-body pressure distributions. The focus of this paper is on the third step of this approach, in which the design is improved with sonic-boom analysis through the use of CFD calculations. A new inverse design process for off-body pressure tailoring is formulated and demonstrated with a low-boom supersonic configuration that was developed by using the mixed-fidelity design method with CFD Ae analysis. The new inverse design process uses the reverse propagation of the pressure distribution (dp/p) from a mid-field location to a near-field location, converts the near-field dp/p into an equivalent-area distribution, generates a low-boom target for the reversed equivalent area (Ae,r) of the configuration, and modifies the configuration to minimize the differences between the configuration s Ae,r and the low-boom target. The new inverse design process is used to modify a supersonic demonstrator concept for a cruise Mach number of 1.6 and a cruise weight of 30,000 lb. The modified configuration has a fully shaped ground signature that has a perceived loudness (PLdB) value of 78.5, while the original configuration has a partially shaped aft signature with a PLdB of 82.3.

Li, Wu↗

DOE OSTI2021

Efficient Precoding for Single Carrier Modulation in Multi-User Massive MIMO Networks

Abstract—Frequency domain (FD) multi-user detection (MUD) and precoding has been shown to be an effective means of approaching the theoretical per-user capacity for single carrier modulation (SCM) schemes in massive MIMO scenarios with highly dispersive channels. When a cyclic prefix is added to the SCM waveform, the circulant structures of the resulting convolutional channel matrix allows for relatively simple expressions for the FD detection and precoding. In this paper, we further refine the computationally efficient minimum mean squared error (MMSE) FD-MUD technique in a time-division duplexing (TDD) massive MIMO setup by pre-computing the scale factor needed to produce an unbiased estimate. The resulting scale factor and the matrix inverse that was calculated for the uplink is then reused for the downlink to form a computationally efficient precoding scheme with superior performance compared to zero-forcing (ZF) precoding. Performance analysis is provided and confirmed through simulation results.

5G and Beyond Communications↗

DOE OSTI2020

Extended Lagrangian Born–Oppenheimer molecular dynamics using a Krylov subspace approximation

It is shown how the electronic equations of motion in extended Lagrangian Born–Oppenheimer molecular dynamics simulations can be integrated using low-rank approximations of the inverse Jacobian kernel. This kernel determines the metric tensor in the harmonic oscillator extension of the Lagrangian that drives the evolution of the electronic degrees of freedom. The proposed kernel approximation is derived from a pseudoinverse of a low-rank estimate of the Jacobian, which is expressed in terms of a generalized set of directional derivatives with directions that are given from a Krylov subspace approximation. The approach allows a tunable and adaptive approximation that can take advantage of efficient preconditioning techniques. The proposed kernel approximation for the integration of the electronic equations of motion makes it possible to apply extended Lagrangian first-principles molecular dynamics simulations to a broader range of problems, including reactive chemical systems with numerically sensitive and unsteady charge solutions. This can be achieved without requiring exact full calculations of the inverse Jacobian kernel in each time step or relying on iterative non-linear self-consistent field optimization of the electronic ground state prior to the force evaluations as in regular direct Born–Oppenheimer molecular dynamics. We note the low-rank approximation of the Jacobian is directly related to Broyden’s class of quasi-Newton algorithms and Jacobian-free Newton–Krylov methods and provides a complementary formulation for the solution of nonlinear systems of equations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1999

A Neural Network Aero Design System for Advanced Turbo-Engines

An inverse design method calculates the blade shape that produces a prescribed input pressure distribution. By controlling this input pressure distribution the aerodynamic design objectives can easily be met. Because of the intrinsic relationship between pressure distribution and airfoil physical properties, a Neural Network can be trained to choose the optimal pressure distribution that would meet a set of physical requirements. Neural network systems have been attempted in the context of direct design methods. From properties ascribed to a set of blades the neural network is trained to infer the properties of an 'interpolated' blade shape. The problem is that, especially in transonic regimes where we deal with intrinsically non linear and ill posed problems, small perturbations of the blade shape can produce very large variations of the flow parameters. It is very unlikely that, under these circumstances, a neural network will be able to find the proper solution. The unique situation in the present method is that the neural network can be trained to extract the required input pressure distribution from a database of pressure distributions while the inverse method will still compute the exact blade shape that corresponds to this 'interpolated' input pressure distribution. In other words, the interpolation process is transferred to a smoother problem, namely, finding what pressure distribution would produce the required flow conditions and, once this is done, the inverse method will compute the exact solution for this problem. The use of neural network is, in this context, highly related to the use of proper optimization techniques. The optimization is used essentially as an automation procedure to force the input pressure distributions to achieve the required aero and structural design parameters. A multilayered feed forward network with back-propagation is used to train the system for pattern association and classification.

Sanz, Jose M.↗

DOE OSTI2023

Performance-Portable GPU Acceleration of the EFIT Tokamak Plasma Equilibrium Reconstruction Code

This paper presents the steps followed to GPU-offload parts of the core solver of EFIT-AI, an equilibrium reconstruction code suitable for tokamak experiments and burning plasmas. For this work, we will focus on the fitting procedure that consists of a Grad–Shafranov (GS) equation inverse solver that calculates equilibrium reconstructions on a grid. We will show profiling results of the original code (CPU-baseline), as well as the directives used to GPU-offload the most time-consuming function, initially to compare OpenACC and OpenMP on NVIDIA and AMD GPUs and later on to assess OpenMP performance portability on NVIDIA, AMD and Intel GPUs. We will make a performance comparison for different spatial grid sizes and show the speedup achieved on NVIDIA A100 (Perlmutter-NERSC), AMD MI250X (Frontier-OLCF) and Intel PVC GPUs (Sunspot-ALCF). Finally, we will draw some conclusions and recommendations to achieve high-performance portability for an equilibrium reconstruction code on the new HPC architectures

GPU↗

NASA NTRS1972

The mathematical-physical problem of P prime(f) to N(h) inversion for anisotropic media

The requirements for a numerical inversion method to calculate electron density profiles from ionograms are discussed. A systematic investigation about the independence of the two magnetoionic components shows that the extent to which the range of ambiguity can be reduced depends mainly on the magnetic latitude. Error estimates and first-order corrections for less elaborate methods are included.

Paul, A. K.↗

NASA NTRS1975

Nozzle Free Jet Flows Within the Strong Curved Shock Regime

A study based on inviscid analysis was conducted to examine the flow field produced from a convergent-divergent nozzle when a strong curved shock occurs. It was found that a certain constraint is imposed on the flow solution of the problem which is the unique feature of the flow within this flow regime, and provides the reason why the inverse method of calculation cannot be employed for these problems. An approximate method was developed to calculate the flow field, and results were obtained for two-dimensional flows. Analysis and calculations were performed for flows with axial symmetry. It is shown that under certain conditions, the vorticity generated at the jet boundary may become infinite and the viscous effect becomes important. Under other conditions, the asymptotic free jet height as well as the corresponding shock geometry were determined.

Shih, Tso-Shin↗

NASA NTRS1978

A cesium plasma TELEC device for conversion of laser radiation to electric power

Tests of the thermoelectronic laser energy converter (TELEC) concept are reported. This device has been devised as a means to convert high-average-power laser radiation into electrical energy, a crucial element in any space laser power transmission scheme using the available high-power/efficiency infrared lasers. Theoretical calculations, based upon inverse bremsstrahlung absorption in a cesium plasma, indicate internal conversion efficiency up to 50% with an overall system efficiency of 42%. The experiments reported were made with a test cell designed to confirm the theoretical model rather than demonstrate efficiency; 10.6-micron laser-beam absorption was limited to about 0.001 of the incident beam by the short absorption region. Nevertheless, confirmatory results were obtained, and the conversion of absorbed radiation to electric power is estimated to be near 10%.

Britt, E. J.↗

NASA NTRS1982

Map projections for larger-scale mapping

For the U.S. Geological Survey maps at 1:1,000,000-scale and larger, the most common projections are conformal, such as the Transverse Mercator and Lambert Conformal Conic. Projections for these scales should treat the Earth as an ellipsoid. In addition, the USGS has conceived and designed some new projections, including the Space Oblique Mercator, the first map projection designed to permit low-distortion mapping of the Earth from satellite imagery, continuously following the groundtrack. The USGS has programmed nearly all pertinent projection equations for inverse and forward calculations. These are used to plot maps or to transform coordinates from one projection to another. The projections in current use are described.

Snyder, J. P.↗

NASA NTRS1988

Analysis of LIMS data by potential vorticity inversion

This paper analyzes LIMS data for a minor warming of January 1979 by potential vorticity inversion, to investigate how flows in the middle atmosphere were determined. The inversion problem of calculating the flow from the potential vorticity is solved repeatedly, including and excluding different portions of the potential vorticity, thus revealing which bits of potential vorticity were important in determining the flow at a time and location of interest. The results of the analysis of LIMS data indicate that the middle stratospheric flow is dominated by potential vorticity that is local in height and in latitude, while planetary-scale mesospheric flows are primarily induced by potential vorticity in the stratosphere. A possible explanation for this difference is proposed.

Robinson, Walter A.↗

NASA NTRS1990

The aerodynamic design of the oblique flying wing supersonic transport

The aerodynamic design of a supersonic oblique flying wing is strongly influenced by the requirement that passengers must be accommodated inside the wing. It was revealed that thick oblique wings of very high sweep angle can be efficient at supersonic speeds when transonic normal Mach numbers are allowed on the upper surface of the wing. The goals were motivated by the ability to design a maximum thickness, minimum size oblique flying wing. A 2-D Navier-Stokes solver was used to design airfoils up to 16 percent thickness with specified lift, drag and pitching moment. A new method was developed to calculate the required pressure distribution on the wing based on the airfoil loading, normal Mach number distribution and theoretical knowledge of the minimum drag of oblique configurations at supersonic speeds. The wing mean surface for this pressure distribution was calculated using an inverse potential flow solver. The lift to drag ratio of this wing was significantly higher than that of a comparable delta wing for cruise speeds up to Mach 2.

Vandervelden, Alexander J. M.↗

NASA NTRS1990

Gamma-ray bursts from magnetospheric plasma oscillations. II - Model spectra

Several mechanisms for the primary release of energy in gamma-ray bursts (GRBs) may result in the excitation of relativistic, magnetospheric plasma oscillations above the polar cap of a neutron star. This paper presents a survey of detailed calculations of the inverse Compton scattering interaction between the sinusoidally accelerated particles in relativistic, magnetospheric plasma oscillations and the self-consistently determined thermal radiation from the stellar surface. The upscattered photons are boosted to gamma-ray energies and a Monte Carlo simulation is used to obtain the spectrum for different viewing angles relative to the magnetic field in the oscillating region. It is shown that several GRB spectral characteristics may be understood in the context of a model wherein the overall spectrum changes with aspect angle as a result of the superposition of four components with different angular distributions.

Melia, Fulvio↗

NASA NTRS1995

Prospect redux

The remote estimation of leaf biochemical content from spaceborne platforms has been the subject of many studies aimed at better understanding of terrestrial ecosystem functioning. The major ecological processes involved in exchange of matter and energy, like photosynthesis, primary production, evaportranspiration, respiration, and decomposition can be related to plant properties e.g., chlorophyll, water, protein, cellulose and lignin contents. As leaves represent the most important plant surfaces interacting with solar energy, a top priority has been to relate optical properties to biochemical constituents. Two different approaches have been considered: first, statistical correlations between the leaf reflectance (or transmittance) and biochemical content, and second, physically based models of leaf scattering and absorption developed using the laws of optics. Recently reviewed by Verdebout et al., the development of models of leaf optical properties has resulted in better understanding of the interaction of light with plant leaves. Present radiative transfer models mainly use chlorophyll and/or water contents as input parameters to calculate leaf reflectance. Inversion of these models allows to retrieve these constituents from spectrophotometric measurements. Conel et al. recently proposed a two-stream Kubelka-Munk model to analyze the influence of protein, cellulose, lignin, and starch on leaf reflectance, but in fact, the estimation of leaf biochemistry from remote sensing is still an open question. In order to clarify it, a laboratory experiment associating visible/infrared spectra of plan leaves both with physical measurements and biochemical analyses was conducted at the Joint Research Center during the summer of 1993. This unique data set has been used to upgrade the PROSPECT model, by including leaf biochemistry.

Jacquemoud, S.↗

NASA NTRS1999

A Neural Network Aero Design System for Advanced Turbo-Engines

Sanz, Jose M.↗