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DOE OSTI2024

Asymptotic consistency of the WSINDy algorithm in the limit of continuum data

In this work we study the asymptotic consistency of the weak-form sparse identification of nonlinear dynamics algorithm (WSINDy) in the identification of differential equations from noisy samples of solutions. We prove that the WSINDy estimator is unconditionally asymptotically consistent for a wide class of models that includes the Navier–Stokes, Kuramoto–Sivashinsky and Sine–Gordon equations. We thus provide a mathematically rigorous explanation for the observed robustness to noise of weak-form equation learning. Conversely, we also show that, in general, the WSINDy estimator is only conditionally asymptotically consistent, yielding discovery of spurious terms with probability one if the noise level exceeds a critical threshold σ c . We provide explicit bounds on σ c in the case of Gaussian white noise and we explicitly characterize the spurious terms that arise in the case of trigonometric and/or polynomial libraries. Furthermore, we show that, if the data is suitably denoised (a simple moving average filter is sufficient), then asymptotic consistency is recovered for models with locally-Lipschitz, polynomial-growth nonlinearities. Our results reveal important aspects of weak-form equation learning, which may be used to improve future algorithms. We demonstrate our findings numerically using the Lorenz system, the cubic oscillator, a viscous Burgers-growth model and a Kuramoto–Sivashinsky-type high-order PDE.

asymptotic consistency↗

NASA NTRS1972

Self-consistent Pauli corrections in Brueckner-Hartree-Fock calculations

A scheme is introduced which makes it feasible to make completely self-consistent Brueckner-Hartree-Fock (BHF) and renormalized BHF calculations for spherical, closed-shell and axially-symmetric deformed nuclei. The usual requirement or orbital self-consistency has been imposed, as well as self-consistency in the starting energies and occupation probabilities. Previously, only approximate forms were used for the Pauli operator. This approximation is removed and a method for making the necessary Pauli corrections to the reaction matrix during the approach to self-consistency is presented. A discussion of the symmetries which reduce the problem to one of manageable proportions is included.

Braley, R. C.↗

NASA NTRS1992

Numerical experiments on consistent horizontal and vertical resolution for atmospheric models and observing systems

Simple numerical experiments are performed in order to determine the effects of inconsistent combinations of horizontal and vertical resolution in both atmospheric models and observing systems. In both cases, we find that inconsistent spatial resolution is associated with enhanced noise generation. A rather fine horizontal resolution in a satellite data observing system seems to be excessive when combined with the usually available relatively coarse vertical resolution. Using different strength horizontal filters, adjusted in such a way as to render the effective horizontal resolution more consistent with vertical resolution for the observing system, may result in improvement of the analysis accuracy. However, the increase of vertical resolution for a satellite data observing system is desirable. For the conventional data observing system with better vertically resolved data, the results are different in that little or no horizontal filtering is needed to make spatial resolution more consistent for the system. The obtained experimental estimates of consistent vertical and effective horizontal resolution are in a general agreement with consistent resolution estimates previously derived theoretically by the authors.

Fox-Rabinovitz, Michael S.↗

NASA NTRS1993

Numerical experiments on consistent horizontal and vertical resolution for atmospheric models and observing systems

Simple numerical experiments are performed in order to determine the effects of inconsistent combinations of horizontal and vertical resolution in both atmospheric models and observing systems. In both cases, we find that inconsistent spatial resolution is associated with enhanced noise generation. A rather fine horizontal resolution in a satellite-data observing system seems to be excessive when combined with the usually available relatively coarse vertical resolution. Using horizontal filters of different strengths, adjusted in such a way as to render the effective horizontal resolution more consistent with vertical resolution for the observing system, may result in improvement of the analysis accuracy. The increase of vertical resolution for a satellite data observing system with better vertically resolved data, the results are different in that little or no horizontal filtering is needed to make spatial resolution more consistent for the system. The obtained experimental estimates of consistent vertical and effective horizontal resolution are in a general agreement with consistent resolution estimates previously derived theoretically by the authors.

Fox-Rabinovitz, Michael S.↗

NASA NTRS1993

Accuracy of the Generalized Self-Consistent Method in Modelling the Elastic Behaviour of Periodic Composites

Local stress and strain fields in the unit cell of an infinite, two-dimensional, periodic fibrous lattice have been determined by an integral equation approach. The effect of the fibres is assimilated to an infinite two-dimensional array of fictitious body forces in the matrix constituent phase of the unit cell. By subtracting a volume averaged strain polarization term from the integral equation we effectively embed a finite number of unit cells in a homogenized medium in which the overall stress and strain correspond to the volume averaged stress and strain of the constrained unit cell. This paper demonstrates that the zeroth term in the governing integral equation expansion, which embeds one unit cell in the homogenized medium, corresponds to the generalized self-consistent approximation. By comparing the zeroth term approximation with higher order approximations to the integral equation summation, both the accuracy of the generalized self-consistent composite model and the rate of convergence of the integral summation can be assessed. Two example composites are studied. For a tungsten/copper elastic fibrous composite the generalized self-consistent model is shown to provide accurate, effective, elastic moduli and local field representations. The local elastic transverse stress field within the representative volume element of the generalized self-consistent method is shown to be in error by much larger amounts for a composite with periodically distributed voids, but homogenization leads to a cancelling of errors, and the effective transverse Young's modulus of the voided composite is shown to be in error by only 23% at a void volume fraction of 75%.

Walker, Kevin P.↗

NASA NTRS2001

Our Sun V: A Bright Young Sun Consistent with Helioseismology and Warm Temperatures on Ancient Earth and Mars

The relatively warm temperatures required on early Earth and Mars have been difficult to account for with warming from greenhouse gases. A slightly more massive young Sun would be brighter than predicted by the standard solar model, simultaneously resolving this problem for both Earth and Mars. We computed high-precision solar models with seven initial masses, from Mi = 1.01 to 1.07 solar mass - the latter being the maximum permitted if the early Earth is not to lose its water via a moist greenhouse effect. The relatively modest early mass loss that is required remains consistent with observational limits on mass loss from young stars and with estimates of the past solar wind obtained from lunar rocks. We considered three types of mass loss rates: (1) a reasonable choice of a simple exponential decline, (2) an extreme step-function case that gives the maximum effect consistent with observations, and (3) the radical case of a linear decline which is inconsistent with the solar wind mass loss estimates from lunar rocks. Our computations demonstrated that mass loss leaves a fingerprint oil the Sun's internal structure large enough to be detectable with helioseismic observations. All of our mass-losing solar models were consistent with the helioseismic observations; in fact, our preferred mass-losing cases were in marginally better agreement with the helioseismology than the standard solar model was, although this difference was smaller than the effects of other uncertainties in the input physics and in the solar composition. Mass loss has only a relatively minor effect on the predicted lithium depletion; the major portion of the solar lithium depletion must still be due to rotational mixing. Thus the modest mass loss cases considered here cannot be ruled out by observed lithium depletions. For the three mass loss types considered, the preferred initial masses were 1.07 solar mass for the exponential case and 1.04 solar mass for the step-function and linear cases; all of these provided high enough solar fluxes at Mars 3.8 Gyr ago to be consistent with the existence of liquid water. For a more massive early Sun, the planets would have had to be closer to the young Sun in order to end up in their present orbits; the orbital radii of the planets would vary inversely with the solar mass. Both of these effects contribute to the fact that the early solar flux at the planets would have been considerably higher than that of the standard solar model at that time. In fact, the 1.07 solar mass exponential case has a flux at birth 5% higher than the present solar flux, while the radical 1.04 solar mass linear case has a nearly constant flux over the first 3 Gyr only about 10% lower than at present. The early solar evolution would be in the opposite direction in the H-R diagram to that of the standard Sun.

Sackmann, I.-Juliana↗

NASA NTRS2002

Self-Consistent Magnetosphere-Ionosphere Coupling: Theoretical Studies

A self-consistent ring current (RC) model has been developed that couples electron and ion magnetospheric dynamics with the calculation of the electric field. Two new features were taken into account in order to close the self-consistent magnetosphere- ionosphere coupling loop. First, in addition to the RC ions, we solve an electron kinetic equation in our model. Second, using the relation of Galand and Richmond [2001], we calculate the height integrated ionospheric conductances as a function of the precipitated high energy magnetospheric electrons and ions that are produced by our code. To validate the results of our model we simulate the magnetic storm of May 2, 1986, a storm that has has been comprehensively studied, and compare our results with different theoretical approaches. The self-consistent inclusion of the hot electrons and, their effect on the conductance results in deeper penetration of the magnetospheric electric field. In addition, a slight westward rotation of the potential pattern (compared to previous self-consistent results) is evident in the inner magnetosphere. This changes the hot plasma distribution, especially by allowing increased access of plasma sheet ions and electrons to low L shells.

Khazanov, G. V.↗

NASA NTRS2002

Self-Consistent Magnetosphere-Ionosphere Coupling

A self-consistent ring current (RC) model has been developed that couples electron and ion magnetospheric dynamics with the calculation of the electric field. Two new features were taken into account in order to close the self-consistent magnetosphere-ionosphere coupling loop. First, in addition to the RC ions, we have solved an electron kinetic equation in our model. Second, using the relation of Galand and Richmond, we have calculated the height integrated ionospheric conductances as a function of the precipitated high energy magnetospheric electrons and ions that are produced by our model. To validate the results of our model we simulate the magnetic storm of May 2, 1986, a storm that has been comprehensively studied by Fok et al., and have compared our results with different theoretical approaches. The self-consistent inclusion of the hot electrons and their effect on the conductance results in deeper penetration of the magnetospheric electric field. In addition, a slight westward rotation of the potential pattern (compared to previous self-consistent results) is evident in the inner magnetosphere. These effects change the hot plasma distribution, especially by allowing increased access of plasma sheet ions and electrons to low L shells.

Six, N. Frank↗

NASA NTRS2003

Self-Consistent Model of Magnetospheric Ring Current and Electromagnetic Ion Cyclotron Waves: The May 2-7, 1998, Storm

Complete description of a self-consistent model for magnetospheric ring current interacting with electromagnetic ion cyclotron waves is presented. The model is based on the system of two kinetic equations; one equation describes the ring current ion dynamics, and another equation describes the wave evolution. The effects on ring current ions interacting with electromagnetic ion cyclotron waves, and back on waves, are considered self-consistently by solving both equations on a global magnetospheric scale under non steady-state conditions. In the paper by Khazanov et al. [2002] this self-consistent model has only been shortly outlined, and discussions of many the model related details have been omitted. For example, in present study for the first time a new algorithm for numerical finding of the resonant numbers for quasilinear wave-particle interaction is described, or it is demonstrated that in order to describe quasilinear interaction in a multi-ion thermal plasma correctly, both e and He(+) modes of electromagnetic ion cyclotron waves should be employed. The developed model is used to simulate the entire May 2-7, 1998 storm period. Trapped number fluxes of the ring current protons are calculated and presented along with their comparison with the data measured by the 3D hot plasma instrument Polar/HYDRA. Examining of the wave (MLT, L shell) distributions produced during the storm progress reveals an essential intensification of the wave emissions in about two days after main phase of storm. This result is well consistent with the earlier ground-based observations. Also the theoretical shapes and the occurrence rates for power spectral densities of electromagnetic ion cyclotron waves are studied. It is found that in about 2 days after the storm main phase on May 4, mainly non Gaussian shapes of power spectral densities are produced.

Khazanov, G. V.↗

NASA NTRS2009

Self-Consistent Model of Magnetospheric Electric Field, Ring Current, Plasmasphere, and Electromagnetic Ion Cyclotron Waves: Initial Results

Further development of our self-consistent model of interacting ring current (RC) ions and electromagnetic ion cyclotron (EMIC) waves is presented. This model incorporates large scale magnetosphere-ionosphere coupling and treats self-consistently not only EMIC waves and RC ions, but also the magnetospheric electric field, RC, and plasmasphere. Initial simulations indicate that the region beyond geostationary orbit should be included in the simulation of the magnetosphere-ionosphere coupling. Additionally, a self-consistent description, based on first principles, of the ionospheric conductance is required. These initial simulations further show that in order to model the EMIC wave distribution and wave spectral properties accurately, the plasmasphere should also be simulated self-consistently, since its fine structure requires as much care as that of the RC. Finally, an effect of the finite time needed to reestablish a new potential pattern throughout the ionosphere and to communicate between the ionosphere and the equatorial magnetosphere cannot be ignored.

Gamayunov, K. V.↗

NASA NTRS2015

High Ice Water Content at Low Radar Reflectivity near Deep Convection: Consistency of In Situ and Remote-Sensing Observations with Stratiform Rain Column Simulations - Part I

Occurrences of jet engine power loss and damage have been associated with flight through fully glaciated deep convection at -10 to -50 degrees Centigrade. Power loss events commonly occur during flight through radar reflectivity (Zeta (sub e)) less than 20-30 decibels relative to Zeta (dBZ - radar returns) and no more than moderate turbulence, often overlying moderate to heavy rain near the surface. During 2010-2012, Airbus carried out flight tests seeking to characterize the highest ice water content (IWC) in such low-radar-reflectivity regions of large, cold-topped storm systems in the vicinity of Cayenne, Darwin, and Santiago. Within the highest IWC regions encountered, at typical sampling elevations (circa 11 kilometers), the measured ice size distributions exhibit a notably narrow concentration of mass over area-equivalent diameters of 100-500 micrometers. Given substantial and poorly quantified measurement uncertainties, here we evaluate the consistency of the Airbus in situ measurements with ground-based profiling radar observations obtained under quasi-steady, heavy stratiform rain conditions in one of the Airbus-sampled locations. We find that profiler-observed radar reflectivities and mean Doppler velocities at Airbus sampling temperatures are generally consistent with those calculated from in situ size-distribution measurements. We also find that column simulations using the in situ size distributions as an upper boundary condition are generally consistent with observed profiles of radar reflectivity (Ze), mean Doppler velocity (MDV), and retrieved rain rate. The results of these consistency checks motivate an examination of the microphysical pathways that could be responsible for the observed size-distribution features in Ackerman et al. (2015).

Rain↗

NASA NTRSDate not supplied

Toward Consistent Long-term Records of Cloud Fraction from MODIS and VIIRS for CERES

In order to produce a long-term and stable climate record of Earth’s energy budget for NASA’s Clouds and Earth’s Radiant Energy System (CERES) project, a consistent cloud fraction record across different measurement platforms is a crucial first step. As Aqua satellite is approaching the end of its operational lifetime, NOAA-20 VIIRS observations on the JPSS-2 spacecraft will be used for cloud detection to continue the long-term Earth energy budget record. Two steps are designed to achieve this goal. The first step is a quick approach that revises the CERES NOAA-20 VIIRS Edition 1 A (CV Ed1A) cloud mask to incorporate Cross-track Infrared Sounder (CrIS) water vapor and CO_2 channels into the VIIRS cloud mask (CV Ed1B) to produce a consistent cloud fraction with CERES MODIS Edition 4 (CM Ed4) to avoid potential discontinuity when Aqua orbit drifts beyond tolerance before the next Edition is completed. The second step is to develop, as part of CERES next edition (Ed5), a unified MODIS and VIIRS cloud mask using common channels to produce consistent cloud products with improved radiative transfer models, refined clear sky predictions, new GMAO reanalysis products, and the latest radiance collections of MODIS and VIIRS data. This poster will present cloud fraction comparison between CV Ed1B and CM Ed4, as well as the preliminary results of ongoing Ed5 including pixel level cloud mask results, monthly global cloud fraction differences between MODIS and VIIRS (consistency), and initial validation using CALIPSO data (accuracy).

CERES↗

NASA NTRSDate not supplied

Development of a Consistent GEOsat Cloud Property Dataset for the CERES Climate Data Record

Cloud properties are critical for understanding the Earth’s radiation budget and cloud feedbacks. At NASA Langley Research Center, the Satellite ClOud and Radiative Property retrieval System (SatCORPS) provides real-time and historical analyses of clouds derived from Geostationary satellite (GEOsat) data for weather and climate applications. For the Clouds and the Earth’s Radiant Energy System (CERES) program, the global constellation of GEOsats has been analyzed since 2000 to help characterize and account for the diurnal cycle of clouds and their radiative impacts in the CERES climate data record. Obtaining consistent cloud properties over the GEOsat data record during the CERES era is a major objective but a significant challenge considering the diversity of imaging capabilities deployed during that time. The GEOsat data analysis approach for the current CERES Edition-4 (Ed4) data products was focused on accuracy and consistency with MODIS by employing as much spectral information as possible from each satellite. However, the inconsistent use of spectral information across GEOsats led to marked discontinuities in the spatial and temporal record of cloud properties that had to be accounted for post facto in downstream CERES processing. This paper reports progress in developing a new GEOsat analysis system for the next CERES edition (Ed5) that has potential to improve cross-platform consistency and continuity. In this approach, the spectral channel complement is limited to just 3-channels during daytime, ~0.65 µm (VIS), ~3.9 µm (NIR), and ~10.8 µm (IR), common to nearly all of the satellites in the record. At night, a 2-channel approach is taken with the NIR and IR, and ~6.7 µm bands that includes a machine learning approach for optically thick cloud properties. A tradeoff is the potential for reduced accuracy particularly using data from the more advanced satellites that have more spectral channels (e.g. SEVIRI, AHI and ABI) that are known to help improve thin cirrus detection, cloud-aerosol discrimination and estimates in other difficult conditions that challenge cloud remote sensing. The new continuity approach is applied to one month of global GEOSat data for each year of the CERES record since 2000 and compared with the Ed4 GEO and MODIS cloud property time series in order to evaluate the level of improved consistency in the GEOsat record and to assess the accuracy impacts. Cloud fraction will also be assessed with CALIPSO data. Outstanding issues and challenges will be discussed. The results are expected to guide future work needed to develop a more robust GEOsat cloud data record for CERES.

CERES CDR↗

DOE OSTI2025

A thermodynamically consistent discretization of 1D thermal-fluid models using their metriplectic 4-bracket structure

Thermodynamically consistent models in continuum physics, i.e. models which satisfy the first and second laws of thermodynamics, may be expressed using the metriplectic formalism. In this work, we leverage the structures underlying this modeling formalism to preserve thermodynamic consistency in discretizations of a fluid model. The procedure relies (1) on ensuring that the spatial semi-discretization retains certain symmetries and degeneracies of the Poisson and metriplectic 4-brackets, and (2) on the use of an appropriate energy conserving time-stepping method. Here, the minimally simple yet nontrivial example of a one-dimensional thermal-fluid model is treated. It is found that preservation of the requisite symmetries and degeneracies of the 4-bracket is relatively simple to ensure in Galerkin spatial discretizations, suggesting a path forward for thermodynamically consistent discretizations of more complex fluid models using more specialized Galerkin methods.

Hamiltonian structure↗

DOE OSTI2025

Lowering the Scaling of Self-Consistent Field Methods by Combining Tensor Hypercontraction and a Density Difference Ansatz

We present the tensor hypercontraction difference self-consistent field (SCF) method, an approach that reduces the formal computational scaling of traditional naive self-consistent field methods from 𝑂(𝑁 4 ) to 𝑂(𝑁 3 ) with system size 𝑁. The scaling reduction is achieved by developing a new technique for constructing the tensor hypercontraction decomposition based on the fundamental approximation made in density fitting. Combining this scheme with the difference self-consistent field methodology, we achieve a method that enables 𝑂(𝑁 3 ) scaling SCF calculations with only 𝑂(𝑁 2 ) storage requirements. In conclusion, our proof-of-concept numerical tests demonstrate robust performance with errors in total energies below 8 × 10 –4 E h and with sub 1 kcal/mol errors for relative energies.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Thermodynamic consistency and fluctuations in mesoscopic stochastic simulations of reactive gas mixtures

It is essential that mesoscopic simulations of reactive systems reproduce the correct statistical distributions at thermodynamic equilibrium. By considering a compressible fluctuating hydrodynamics (FHD) simulation method of ideal gas mixtures undergoing reversible reactions described by the chemical Langevin equations, we show that thermodynamic consistency in reaction rates and the use of instantaneous temperatures for the evaluation of reaction rates is required for fluctuations for the overall system to be correct. We then formulate the required properties of a thermodynamically consistent reaction (TCR) model. As noted in the literature, while reactions are often discussed in terms of forward and reverse rates, these rates should not be modeled independently because they must be compatible with thermodynamic equilibrium for the system. Using a simple TCR model where each chemical species has constant heat capacity, we derive the explicit condition that the forward and reverse reaction rate constants must satisfy in order for the system to be thermodynamically consistent. We perform equilibrium and non-equilibrium simulations of ideal gas mixtures undergoing a reversible dimerization reaction to measure the fluctuational behavior of the system numerically. We confirm that FHD simulations with the TCR model give the correct static structure factor of equilibrium fluctuations. For the statistically steady simulation of a gas mixture between two isothermal walls with different temperatures, we show using the TCR model that the temperature variance agrees with the corresponding thermodynamic-equilibrium temperature variance in the interior of the system, whereas noticeable deviations are present in regions near walls, where chemistry is far from equilibrium.

Polimeno, Matteo [University of California, Merced↗

DOE OSTI2026

Influence of Markovianity and self-consistency on time-resolved spectral functions of driven quantum systems

We present a systematic comparison of the real-time Dyson expansion (RTDE) with established nonequilibrium Green's function (GF) approaches for simulating driven, interacting quantum systems. Focusing on density matrix dynamics, time-off-diagonal GFs, and time-resolved photoemission spectra, we benchmark RTDE against fully self-consistent Kadanoff-Baym equation (KBE) calculations, the generalized Kadanoff-Baym ansatz, and exact diagonalization for small systems using second-order many-body perturbation theory. Using a driven two-band Hubbard model, we show that mean-field single-particle density matrix trajectories provide a reliable baseline for RTDE across a broad range of interaction strengths and excited-carrier populations. Further, RTDE accurately captures correlation effects in the GFs, including long-lived oscillations and revivals that are strongly suppressed by the overdamping inherent to self-consistent KBE schemes. As a consequence, RTDE resolves rich nonequilibrium spectral structure in time-resolved photoemission, such as interaction- and population-dependent quasiparticle splittings and band gap renormalization, which are largely washed out in self-consistent approaches yet are present in exact solutions. Furthermore, our results demonstrate that RTDE bridges the gap between mean-field propagation and full two-time KBE simulations, retaining favorable linear scaling while capturing essential dynamical correlations relevant for ultrafast spectroscopy.

Electronic structure↗

DOE OSTI2025

Self-Consistent Relativistic Electron Scattering using the Sherlock Scattering Model for X-ray Diagnostics

We present on a new, self-consistent, arbitrary-temperature Romberg integration scheme for modeling electron scattering in materials in a LANL Lagrangian Shock Hydro (LSH) code. Electron beam-target interactions are fundamental to a wide range of scientific and technological applications. When high-energy electron beams hit their target, they may scatter, deposit energy, or ionize the source. These processes govern the behavior and outcomes in nanotechnology manufacturing, electron microscopy, and modern X-ray diagnostics. Simulating these interactions is essential for interpreting experimental results, predicting material responses, and designing efficient tools and experiments. At Los Alamos, this is done using a LSH code, which is a multi-dimension, multi-material, massively parallel, multi-physics code used to simulate applications from asteroid impacts to electron beam interactions. By effectively and efficiently modeling the way that electrons scatter from the beam we can bolster these simulations and more accurately predict experimental outcomes. The model currently implemented in the LSH of interest is based on work by Papp and does not self-consistently preserve momentum in the slightly relativistic regime; here we adopt a model proposed by Braams and Karney and implement a Romberg integration scheme to compute the diffusion tensor. In this paper we will provide background on the Braams-Karney diffusion tensor as well as the Romberg integration scheme we employed to numerically solve for it. We will show that our integration scheme is accurate in solving for the set of scalar potentials used to re-express the diffusion tensor in differential form, and in solving for the diffusion coefficients in the larger LSH code. By using this diffusion tensor rather than the existing Papp one, and numerically integrating it with a Romberg method, we produce much more accurate, self-consistent results.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗