Search NASA⌕ Search

SEARCH · Search NASA

Results for “Approximate inverses”

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 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Microcanonical rates from ring-polymer molecular dynamics: Direct-shooting, stationary-phase, and maximum-entropy approaches

We address the calculation of microcanonical reaction rates for processes involving significant nuclear quantum effects using ring-polymer molecular dynamics (RPMD), both with and without electronically non-adiabatic transitions. After illustrating the shortcomings of the naive free-particle direct-shooting method, in which the temperature of the internal ring-polymer modes is set to the translational energy scale, we investigate alternative strategies based on the expression for the microcanonical rate in terms of the inverse Laplace transform of the thermal reaction rate. It is shown that simple application of the stationary-phase approximation (SPA) dramatically improves the performance of the microcanonical rates using RPMD, particularly in the low-energy region where tunneling dominates. Using the SPA as a Bayesian prior, numerically exact RPMD microcanonical rates are then obtained using maximum entropy inversion of the thermal reaction rates for both electronically adiabatic and non-adiabatic model systems. Finally, the direct-shooting method is revisited using the SPA-determined temperature for the internal ring-polymer modes, leading to a simple, direct-simulation method with improved accuracy in the tunneling regime. This work suggests a general strategy for the extraction of microcanonical dynamical quantities from RPMD (or other approximate thermal) simulations.

Tao, Xuecheng↗
DOE OSTI2024

Prime VI

SAND2025-03757O Prime VI is a distribution-of-disease outbreak model calibration code based on variational inference. It accompanies a publication for submission to Statistics in Medicine journal, and the code will be maintained for open-source use on Sandia's GitLab. The software provides methods for calibrating an epidemiological model to measured case-count data for a multitude of correlated spatial regions. The code solves a Bayesian inverse problem for model calibration where the posterior over-model parameters are approximated through a custom implementation of variational inference. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

Safta, Cosmin↗
DOE OSTI2024

Inferring Stochastic Rates from Heterogeneous Snapshots of Particle Positions

Many imaging techniques for biological systems—like fixation of cells coupled with fluorescence microscopy—provide sharp spatial resolution in reporting locations of individuals at a single moment in time but also destroy the dynamics they intend to capture. In this study, these snapshot observations contain no information about individual trajectories, but still encode information about movement and demographic dynamics, especially when combined with a well-motivated biophysical model. The relationship between spatially evolving populations and single-moment representations of their collective locations is well-established with partial differential equations (PDEs) and their inverse problems. However, experimental data is commonly a set of locations whose number is insufficient to approximate a continuous-in-space PDE solution. Here, motivated by popular subcellular imaging data of gene expression, we embrace the stochastic nature of the data and investigate the mathematical foundations of parametrically inferring demographic rates from snapshots of particles undergoing birth, diffusion, and death in a nuclear or cellular domain. Toward inference, we rigorously derive a connection between individual particle paths and their presentation as a Poisson spatial process. Using this framework, we investigate the properties of the resulting inverse problem and study factors that affect quality of inference. One pervasive feature of this experimental regime is the presence of cell-to-cell heterogeneity. Rather than being a hindrance, we show that cell-to-cell geometric heterogeneity can increase the quality of inference on dynamics for certain parameter regimes. Altogether, the results serve as a basis for more detailed investigations of subcellular spatial patterns of RNA molecules and other stochastically evolving populations that can only be observed for single instants in their time evolution.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2025

Adaptive Interface-PINNs (AdaI-PINNs) for inverse problems: Determining material properties for heterogeneous systems

Here, we determine spatially varying discontinuous material properties using a domain-decomposition based physics-informed neural networks (PINNs) framework named the Adaptive Interface-PINNs or AdaI-PINNs (Roy et al., 2024). We propose the use of distinct neural networks for the field variables and material properties within each material, utilizing adaptive activation functions. While the neural networks across different materials share the same weights and biases, their activation functions are uniquely tailored using a hyperparameter that influences the slope of the activation function. The proposed framework is tested on several one-dimensional and two-dimensional benchmark examples, and its performance is compared with conventional PINNs and existing domain-decomposition PINNs frameworks, namely, the Multi-domain physics-informed neural network (M-PINN), and the eXtended physics-informed neural networks (XPINNs). The results demonstrate that the proposed approach can determine randomly distributed discontinuous material properties with an L 2 error of $\mathscr{O}$ (10 -3 ) for the material property and the root-mean-square error of $\mathscr{O}$ (10 -3 ) for the primary variable while the other approaches yield errors that are approximately two orders of magnitude larger (that is, $\mathscr{O}$ (10 -1 )). Moreover, the spatial distribution of material properties obtained using the proposed framework is in close agreement with the true distribution, whereas the other approaches fare much worse. Additionally, the proposed approach is approximately 40% faster than its competitors, indicating its potential as a robust alternative for solving inverse problems in heterogeneous materials.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Neutrino masses from low scale partial compositeness

We consider a class of models in which the neutrinos acquire Majorana masses through mixing with singlet neutrinos that emerge as composite states of a strongly coupled hidden sector. In this framework, the light neutrinos are partially composite particles that obtain their masses through the inverse seesaw mechanism. We focus on the scenario in which the strong dynamics is approximately conformal in the ultraviolet, and the compositeness scale lies at or below the weak scale. The small parameters in the Lagrangian necessary to realize the observed neutrino masses can naturally arise as a consequence of the scaling dimensions of operators in the conformal field theory. We show that this class of models has interesting implications for a wide variety of experiments, including colliders and beam dumps, searches for lepton flavor violation and neutrinoless double beta decay, and cosmological observations. At colliders and beam dumps, this scenario can give rise to striking signals involving multiple displaced vertices. The exchange of hidden sector states can lead to observable rates for flavor violating processes such as μ → eγ and μ → e conversion. If the compositeness scale lies at or below a hundred MeV, the rate for neutrinoless double beta decay is suppressed by form factors and may be reduced by an order of magnitude or more. The late decays of relic singlet neutrinos can give rise to spectral distortions in the cosmic microwave background that are large enough to be observed in future experiments.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Quasiparton distributions in massive QED2: Toward quantum computation

We analyze the quasiparton distributions of the lightest 𝜂′ meson in massive two-dimensional quantum electrodynamics (QED2) by exact diagonalization. The Hamiltonian and boost operators are mapped onto spin qubits in a spatial lattice with open boundary conditions. The lowest excited state in the exact diagonalization is shown to interpolate continuously between an anomalous 𝜂′ state at strong coupling, and a nonanomalous heavy meson at weak coupling, with a cusp at the critical point. The boosted 𝜂′ state follows relativistic kinematics but with large deviations in the luminal limit. The spatial quasiparton distribution function and amplitude for the 𝜂′ state are computed numerically for increasing rapidity both at strong and weak coupling, and compared to the exact light front results. The numerical results from the boosted form of the spatial parton distributions, compare fairly with the inverse Fourier transformation of the luminal parton distributions, derived in the lowest Fock space approximation. Our analysis points out some of the limitations facing the current lattice program for the parton distributions.

Lattice field theory↗
DOE OSTI2022

Calibration and Localization of Optically Pumped Magnetometers Using Electromagnetic Coils

In this paper, we propose a method to estimate the position, orientation, and gain of a magnetic field sensor using a set of (large) electromagnetic coils. We apply the method for calibrating an array of optically pumped magnetometers (OPMs) for magnetoencephalography (MEG). We first measure the magnetic fields of the coils at multiple known positions using a well-calibrated triaxial magnetometer, and model these discreetly sampled fields using vector spherical harmonics (VSH) functions. We then localize and calibrate an OPM by minimizing the sum of squared errors between the model signals and the OPM responses to the coil fields. We show that by using homogeneous and first-order gradient fields, the OPM sensor parameters (gain, position, and orientation) can be obtained from a set of linear equations with pseudo-inverses of two matrices. The currents that should be applied to the coils for approximating these low-order field components can be determined based on the VSH models. Computationally simple initial estimates of the OPM sensor parameters follow. As a first test of the method, we placed a fluxgate magnetometer at multiple positions and estimated the RMS position, orientation, and gain errors of the method to be 1.0 mm, 0.2°, and 0.8%, respectively. Lastly, we calibrated a 48-channel OPM array. The accuracy of the OPM calibration was tested by using the OPM array to localize magnetic dipoles in a phantom, which resulted in an average dipole position error of 3.3 mm. The results demonstrate the feasibility of using electromagnetic coils to calibrate and localize OPMs for MEG.

47 OTHER INSTRUMENTATION↗
DOE OSTI2022

A mixed, unified forward/inverse framework for earthquake problems: fault implementation and coseismic slip estimate

SUMMARY We introduce a new finite-element (FE) based computational framework to solve forward and inverse elastic deformation problems for earthquake faulting via the adjoint method. Based on two advanced computational libraries, FEniCS and hIPPYlib for the forward and inverse problems, respectively, this framework is flexible, transparent and easily extensible. We represent a fault discontinuity through a mixed FE elasticity formulation, which approximates the stress with higher order accuracy and exposes the prescribed slip explicitly in the variational form without using conventional split node and decomposition discrete approaches. This also allows the first order optimality condition, that is the vanishing of the gradient, to be expressed in continuous form, which leads to consistent discretizations of all field variables, including the slip. We show comparisons with the standard, pure displacement formulation and a model containing an in-plane mode II crack, whose slip is prescribed via the split node technique. We demonstrate the potential of this new computational framework by performing a linear coseismic slip inversion through adjoint-based optimization methods, without requiring computation of elastic Green’s functions. Specifically, we consider a penalized least squares formulation, which in a Bayesian setting—under the assumption of Gaussian noise and prior—reflects the negative log of the posterior distribution. The comparison of the inversion results with a standard, linear inverse theory approach based on Okada’s solutions shows analogous results. Preliminary uncertainties are estimated via eigenvalue analysis of the Hessian of the penalized least squares objective function. Our implementation is fully open-source and Jupyter notebooks to reproduce our results are provided. The extension to a fully Bayesian framework for detailed uncertainty quantification and non-linear inversions, including for heterogeneous media earthquake problems, will be analysed in a forthcoming paper.

58 GEOSCIENCES↗
DOE OSTI2021

Deployment of a double scatter system for directional detection of background neutron radiation

The detection of special nuclear materials (SNM) requires the understanding of nuclear signatures that allow the discrimination against background. In particular, understanding neutron background characteristics such as count rates and energies and their correlations with environmental conditions and surroundings of measurement locations is important in enhancing SNM detection capabilities. The Mobile Imager of Neutrons for Emergency Responders (MINER) was deployed for 8 weeks in downtown San Francisco (CA) to study such neutron background characteristics in an urban environment. Of specific interest was the investigation of the impact of surrounding buildings on the neutron background count rates and to answer the question whether buildings act as absorber of neutrons or as sources via the so-called ship effect. MINER consists of 16 liquid scintillator detector elements and can be operated as a neutron spectrometer, as a neutron imager, or simply as a counter of fast neutrons. As expected, the neutron background rate was found to be inversely proportional to the atmospheric pressure. In the energy range where MINER is most sensitive, approximately 1–10 MeV, it was found that the shape of the detected background spectrum is similar to that of a detected fission spectrum, indicating the limited discrimination power of the neutron energy. The similarities between the detected background neutron spectrum and fission sources makes it difficult to discriminate SNM from background based solely on the energies observed. The images produced using maximum likelihood expectation maximization revealed that neutrons preferentially are coming from areas in the environment that have open sky, indicating that the surrounding buildings act as absorbers of neutrons rather than sources as expected by the ship effect. Here, the inherent properties of a neutron scatter camera limit the achievable image quality and the effective deployment to systematically map neutron background signatures due to the low count rate.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2021

A Comparison of Exact and Model Exchange–Correlation Potentials for Molecules

Accurate exchange–correlation (XC) potentials for three-dimensional systems–via solution of the inverse density functional theory (DFT) problem–are now available to test the quality of DFT approximations. Herein, the exact XC potential for seven molecules–dihydrogen at four different bond-lengths, lithium hydride, water, and ortho-benzyne–are computed from full configuration interaction reference densities. These are compared to model XC potentials from nonlocal (B3LYP, HSE06, SCAN0, and M08-HX) and semilocal/local (SCAN, PBE, and PW92) XC functionals. Whereas for most systems, relative errors in the ground-state densities are O(10 –3 –10 –2 ) , the model XC potentials have much higher errors of O(10 –1 –10 0 ) . Among the model XC functionals, SCAN0 offers the best agreement with the exact XC potential, underlining the significance of satisfying exact conditions as well as including nonlocal effects in XC functionals. This work indicates that tests against the exact XC potential will provide a promising new direction for building more accurate XC functionals for DFT.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Inverse kinematics study of the energy levels of 21 Ne populated with the 20 Ne +𝑑 reaction

In recent years there has been significant experimental effort aimed at studying the impact of 16 O neutron poisoning on the weak 𝑠 process in rotating massive stars. Improving the understanding of energy levels in 21 Ne is crucial to reducing uncertainties in the rates of the 𝛼-induced reactions on 17 O that determine the overall efficiency of the weak 𝑠 process. This paper reports on one such experiment: a study of the 20 Ne (𝑑,𝑝)⁢ 21 Ne reaction in inverse kinematics. Deduced spin-parity assignments were made based on adiabatic distorted-wave approximation analysis and neutron partial widths were estimated by comparison with a previous experiment. Of particular significance for nuclear astrophysics is the resulting neutron partial width for the 7820-keV energy level, estimated to be 12 200 ⁢(2900)⁢ eV, and an upper limit of ≤ 9300 eV for that of the 7749-keV energy level. These results are in tension with previous studies and therefore this paper also discusses the current state of the research into the astrophysically relevant energy levels and highlights both areas of agreement and areas of disagreement between this and various other studies that have investigated this nucleus.

direct reactions↗
DOE OSTI2025

Enhancing ACPF Analysis: Integrating Newton-Raphson Method with Gradient Descent and Computational Graphs

This paper presents a new method for enhancing Alternating Current Power Flow (ACPF) analysis. The method integrates the Newton-Raphson (NR) method with Enhanced-Gradient Descent (GD) and computational graphs. The integration of renewable energy sources in power systems introduces variability and unpredictability, and this method addresses these challenges. It leverages the robustness of NR for accurate approximations and the flexibility of GD for handling variable conditions, all without requiring Jacobian matrix inversion. Furthermore, computational graphs provide a structured and visual framework that simplifies and systematizes the application of these methods. The goal of this fusion is to overcome the limitations of traditional ACPF methods and improve the resilience, adaptability, and efficiency of modern power grid analyses. We validate the effectiveness of our advanced algorithm through comprehensive testing on established IEEE benchmark systems. Furthermore, our findings demonstrate that our approach not only speeds up the convergence process but also ensures consistent performance across diverse system states, representing a significant advancement in power flow computation.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2020

Inverse Compton Cooling in the Coronae of Simulated Black Hole Accretion Flows

Here we present a formulation for a local cooling function to be employed in the diffuse, hot corona region of 3D GRMHD simulations of accreting black holes. This new cooling function calculates the cooling rate due to inverse Compton scattering by considering the relevant microphysics in each cell in the corona and approximating the radiation energy density and Compton temperature thereby integrating over the thermal seed photon flux from the disk surface. The method either assumes the ion and electron temperatures are equal (1T) or calculates them separately (2T) using an instantaneous equilibrium approach predicated on the actual relevant rate equations (Coulomb and Compton). The method is shown to be consistent with a more detailed ray-tracing calculation where the bulk of the cooling occurs, but is substantially less costly to perform. As an example, we apply these methods to a harm3d simulation of a 10M⊙, non-spinning black hole, accreting at nominally 1% the Eddington value. This new approach leads to radiative efficiency values sime65% above Novikov–Thorne, with a larger fraction of total cooling in the corona as compared to simulations performed using the original target-temperature cooling function. Time-averaged post-processing reveals that the continuum spectral observations predicted from these simulations are qualitatively similar to actual X-ray binary data, especially so for the 1T approach, which yields a harder power-law component (Γ = 2.25) compared to the 2T version (Γ = 2.53).

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

From the Great Wave of Translation to the Force between Quarks

Here, the chance observation of a novel traveling wave in a canal led over time to the formulation of a nonlinear wave equation—the Korteweg–de Vries equation—that describes strikingly robust disturbances now called solitons. The figure of an isolated soliton corresponds to a reflectionless potential that supports a single bound state in the one-dimensional Schrödinger equation. An appropriate combination of individual solitons yields a symmetric reflectionless potential that supports multiple bound states. Thus, the KdV equation opens the path to solving the inverse scattering problem for a collection of bound states. Applied to the quarkonium spectra, this formalism allows the construction of reflectionless approximations to the confining potentials that account for the force between quarks, and to tests of the flavor-independence of the interquark interaction.

Inverse Scattering↗
DOE OSTI2020

Inverse energy transfer in decaying, three-dimensional, non-helical magnetic turbulence due to magnetic reconnection

ABSTRACT It has been recently shown numerically that there exists an inverse transfer of magnetic energy in decaying, non-helical, magnetically dominated, magnetohydrodynamic turbulence in three dimensions (3D). We suggest that magnetic reconnection is the underlying physical mechanism responsible for this inverse transfer. In the two-dimensional (2D) case, the inverse transfer is easily inferred to be due to smaller magnetic islands merging to form larger ones via reconnection. We find that the scaling behaviour is similar between the 2D and 3D cases, i.e. the magnetic energy evolves as t−1, and the magnetic power spectrum follows a slope of k−2. We show that on normalizing time by the magnetic reconnection time-scale, the evolution curves of the magnetic field in systems with different Lundquist numbers collapse on to one another. Furthermore, transfer function plots show signatures of magnetic reconnection driving the inverse transfer. We also discuss the conserved quantities in the system and show that the behaviour of these quantities is similar between the 2D and 3D simulations, thus making the case that the dynamics in 3D could be approximately explained by what we understand in 2D. Lastly, we also conduct simulations where the magnetic field is subdominant to the flow. Here, too, we find an inverse transfer of magnetic energy in 3D. In these simulations, the magnetic energy evolves as t−1.4 and, interestingly, a dynamo effect is observed.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

A persistent adjoint method with dynamic time-scaling and an application to mass action kinetics

In this article, we consider an optimization problem where the objective function is evaluated at the fixed-point of a contraction mapping parameterized by a control variable, and optimization takes place over this control variable. Since the derivative of the fixed-point with respect to the parameter can usually not be evaluated exactly, an adjoint dynamical system can be used to estimate gradients. Using this estimation procedure, the optimization algorithm alternates between derivative estimation and an approximate gradient descent step. We analyze a variant of this approach involving dynamic time-scaling, where after each parameter update the adjoint system is iterated until a convergence threshold is passed. Here, we prove that, under certain conditions, the algorithm can find approximate stationary points of the objective function. We demonstrate the approach in the settings of an inverse problem in chemical kinetics, and learning in attractor networks.

97 MATHEMATICS AND COMPUTING↗