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At least 433 records · Page 24
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Scrambling Dynamics with Imperfections in a Solvable Model

We study how probes of quantum scrambling dynamics respond to two kinds of imperfections -- unequal forward and backward evolutions and decoherence -- in a solvable Brownian circuit model. We calculate a ``renormalized'' out-of-time-order correlator (ROTOC) in the model with $N$ qubits, and we show that the circuit-averaged ROTOC is controlled by an effective probability distribution in operator weight space which obeys a system of $N$ non-linear equations of motion. These equations can be easily solved numerically for large system sizes which are beyond the reach of exact methods. Moreover, for an operator initially concentrated on weight one $w_0=1$, we provide an exact solution to the equations in the thermodynamic limit of many qubits that is valid for all times, all non-vanishing perturbation strengths $p\gtrsim 1/\sqrt{N}$, and all decoherence strengths. We also show that a generic initial condition $w_0 >1$ leads to a metastable state that eventually collapses to the $w_0=1$ case after a lifetime $\sim \log(N/w_0)$. Our results highlight situations where it is still possible to extract the unperturbed chaos exponent even in the presence of imperfections, and we comment on the applications of our results to existing experiments with nuclear spins and to future scrambling experiments.

FOS: Physical sciences↗
DOE OSTI2022

Long- and short-term temporal variability in cloud condensation nuclei spectra over a wide supersaturation range in the Southern Great Plains site

Abstract. When aerosol particles seed the formation of liquid water droplets in the atmosphere, they are called cloud condensation nuclei (CCN). Different aerosols will act as CCN under different degrees of water supersaturation (relative humidity above 100 %), depending on their size and composition. In this work, we build and analyze a best-estimate CCN spectrum product, tabulated at ∼ 45 min resolution, generated using high quality data from seven independent instruments at the U.S. Department of Energy Atmospheric Radiation Measurement (ARM) Southern Great Plains site. The data product spans a large supersaturation range, from 0.0001 % to ∼ 30 %, and time period of 5 years, from 2009–2013, and is available on the ARM data archive. We leverage this added statistical power to examine relationships that are unclear in smaller datasets. Our analysis is performed in three main areas. First, probability distributions of many aerosol and CCN metrics are found to exhibit skewed log-normal distribution shapes. Second, clustering analyses of CCN spectra reveal that the primary drivers of CCN differences are aerosol number size distributions, rather than hygroscopicity or composition, especially at supersaturations above 0.2 %, while also allowing for a simplified understanding of seasonal and diurnal variations in CCN behavior. The predictive ability of using limited hygroscopicity data with accurate number size distributions to estimate CCN spectra is investigated, and the uncertainties of this approach are estimated. Third, the dynamics of CCN spectral clusters and concentrations are examined with cross-correlation and autocorrelation analyses. We find that CCN concentrations change rapidly on the timescale of 1–3 h, with some conservation beyond that which is greatest for the lower supersaturation region of the spectrum.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Evaluation of four ground-based retrievals of cloud droplet number concentration in marine stratocumulus with aircraft in situ measurements

Abstract. Cloud droplet number concentration (Nd) is crucial for understanding aerosol–cloud interactions (ACI) and associated radiative effects. We present evaluations of four ground-based Nd retrievals based on comprehensive datasets from the Atmospheric Radiation Measurement (ARM) Aerosol and Cloud Experiments in the Eastern North Atlantic (ACE-ENA) field campaign. The Nd retrieval methods use ARM ENA observatory ground-based remote sensing observations from a micropulse lidar, Raman lidar, cloud radar, and the ARM NDROP (Droplet Number Concentration) value-added product (VAP), all of which also retrieve cloud effective radius (re). The retrievals are compared against aircraft measurements from the fast cloud droplet probe (FCDP) and the cloud and aerosol spectrometer (CAS) obtained from low-level marine boundary layer clouds on 12 flight days during summer and winter seasons. Additionally, the in situ measurements are used to validate the assumptions and characterizations used in the retrieval algorithms. Statistical comparisons of the probability distribution function (PDF) of the Nd and cloud re retrievals with aircraft measurements demonstrate that these retrievals align well with in situ measurements for overcast clouds, but they may substantially differ for broken clouds or clouds with low liquid water path (LWP). The retrievals are applied to 4 years of ground-based remote sensing measurements of overcast marine boundary layer clouds at the ARM ENA observatory to find that Nd (re) values exhibit seasonal variations, with higher (lower) values during the summer season and lower (higher) values during the winter season. The ensemble of various retrievals using different measurements and retrieval algorithms such as those in this paper can help to quantify Nd retrieval uncertainties and identify reliable Nd retrieval scenarios. Of the retrieval methods, we recommend using the micropulse lidar-based method. This method has good agreement with in situ measurements, less sensitivity to issues arising from precipitation and low cloud LWP and/or optical depth, and broad applicability by functioning for both daytime and nighttime conditions.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Carbon cycle extremes accelerate weakening of the land carbon sink in the late 21st century

Increasing surface temperature could lead to enhanced evaporation, reduced soil moisture availability, and more frequent droughts and heat waves. The spatiotemporal co-occurrence of such effects further drives extreme anomalies in vegetation productivity and net land carbon storage. However, the impacts of climate change on extremes in net biospheric production (NBP) over longer time periods are unknown. Using the percentile threshold on the probability distribution curve of NBP anomalies, we computed negative and positive extremes in NBP. Here we show that due to climate warming, about 88% of global regions will experience a larger magnitude of negative NBP extremes than positive NBP extremes toward the end of 2100, which accelerate the weakening of the land carbon sink. Our analysis indicates the frequency of negative extremes associated with declines in biospheric productivity was larger than positive extremes, especially in the tropics. While the overall impact of warming at high latitudes is expected to increase plant productivity and carbon uptake, high-temperature anomalies increasingly induce negative NBP extremes toward the end of the 21st century. Using regression analysis, we found soil moisture anomalies to be the most dominant individual driver of NBP extremes. The compound effect of hotness, dryness, and fire caused extremes at more than 50% of the total grid cells. The larger proportion of negative NBP extremes raises a concern about whether the Earth is capable of increasing vegetation production with a growing human population and rising demand for plant material for food, fiber, fuel, and building materials. The increasing proportion of negative NBP extremes highlights the consequences not only of reduction in total carbon uptake capacity but also of conversion of land to a carbon source.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Evaluation of Four Ground-based Retrievals of Cloud Droplet Number Concentration in Marine Stratocumulus with Aircraft In Situ Measurements

Cloud droplet number concentration (N d ) is crucial for understanding aerosol-cloud interactions (ACI) and associated radiative effects. We present evaluations of four ground-based N d retrievals based on comprehensive datasets from the Atmospheric Radiation Measurements (ARM) Aerosol and Cloud Experiments in the Eastern North Atlantic (ACE-ENA) field campaign. The N d retrieval methods use ARM ENA observatory ground-based remote sensing observations from a Micropulse lidar, Raman lidar, cloud radar, and the ARM NDROP Value-added Product (VAP), all of which also retrieve cloud effective radius (r e ). The retrievals are compared against aircraft measurements from the Fast-Cloud Droplet Probe (FCDP) and the Cloud and Aerosol Spectrometer (CAS) obtained from low-level marine boundary layer clouds on 12 flight days during summer and winter seasons. Additionally, the in situ measurements are used to validate the assumptions and characterizations used in the retrieval algorithms. Statistical comparisons of the probability distribution function (PDF) of the N d and cloud r e retrievals with aircraft measurements demonstrate that these retrievals align well with in situ measurements for overcast clouds, but they may substantially differ for broken clouds or clouds with low liquid water path (LWP). The retrievals are applied to four years of ground-based remote sensing measurements of overcast marine boundary layer clouds at the ARM ENA observatory to find that N d (r e ) values exhibit seasonal variations, with higher (lower) values during the summer season and lower (higher) values during the winter season. The ensemble of various retrievals using different measurements and retrieval algorithms such as those in this paper can help to quantify N d retrieval uncertainties and identify reliable N d retrieval scenarios. Of the retrieval methods, we recommend using the using the Micropulse lidar-based method given its good agreement with in situ measurements, it has less sensitivity to issues arising from precipitation and low cloud LWP/optical depth, and it has broad applicability by functioning for both day and nighttime conditions.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Effects of coupling a stochastic convective parameterization with the Zhang–McFarlane scheme on precipitation simulation in the DOE E3SMv1.0 atmosphere model

Abstract. A stochastic deep convection parameterization is implemented into the US Department of Energy (DOE) Energy Exascale Earth System Model (E3SM) Atmosphere Model version 1.0 (EAMv1). This study evaluates its performance in simulating precipitation. Compared to the default model, the probability distribution function (PDF) of rainfall intensity in the new simulation is greatly improved. The well-known problem of “too much light rain and too little heavy rain” is alleviated, especially over the tropics. As a result, the contribution from different rain rates to the total precipitation amount is shifted toward heavier rain. The less frequent occurrence of convection contributes to suppressed light rain, while more intense large-scale and convective precipitation contributes to enhanced heavy total rain. The synoptic and intraseasonal variabilities of precipitation are enhanced as well to be closer to observations. The sensitivity of the rainfall intensity PDF to the model vertical resolution is examined. The relationship between precipitation and dilute convective available potential energy in the stochastic simulation agrees better with that in the Atmospheric Radiation Measurement (ARM) observations compared with the standard model simulation. The annual mean precipitation is largely unchanged with the use of the stochastic scheme except over the tropical western Pacific, where a moderate increase in precipitation represents a slight improvement. The responses of precipitation and its extremes to climate warming are similar with or without the stochastic deep convection scheme.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Sensitivity of fatigue reliability in wind turbines: effects of design turbulence and the Wöhler exponent

Fatigue assessment of wind turbines involves three main sources of uncertainty: material resistance, load, and the damage accumulation model. Many studies focus on increasing the accuracy of fatigue load assessment to improve the fatigue reliability. Probabilistic modeling of the wind's turbulence standard deviation is an example of an approach used for this purpose. Editions 3 and 4 of the IEC standard for the design of wind energy generation systems (IEC 61400-1) suggest different probability distributions as alternatives for the representative turbulence in the normal turbulence model (NTM) of edition 1. There are debates on whether the suggested distributions provide conservative reliability levels, as the established design safety factors are calibrated based on the representative turbulence approach. The current study addresses the debate by comparing annual reliability based on different scenarios of NTM using a probabilistic approach. More importantly, it elaborates on the relative importance of load assessment accuracy in defining the fatigue reliability. Using the DTU 10 MW reference wind turbine and the first-order reliability method (FORM), we study the changes in the annual reliability level and its sensitivity to the three main random inputs. We perform the study considering the blade root flapwise and the tower base fore–aft moments, assuming different fatigue exponents in each load channel. The results show that integration over distributions of turbulence in each mean wind speed results in less conservative annual reliability levels than representative turbulence. The difference in the reliability levels varies according to turbulence distribution and the fatigue exponent. In the case of the tower base, the difference in the annual reliability index after 20 years can be up to 50 %. However, the model and material uncertainty have much higher effects on the reliability levels compared to load uncertainty. Knowledge about such differences in the reliability levels due to the choice of turbulence distribution is especially important, as it impacts the extent of lifetime extension through reliability reassessments.

17 WIND ENERGY↗
DOE OSTI2022

EGS Stimulation Design with Uncertainty Quantification at the EGS Collab Site

Engineering a robust hydraulic connection between wells is one of the most difficult aspects of enhanced geothermal systems (EGS). Designing and constructing such hydraulic connections requires and understanding of the in situ state of stress and the heterogeneities and discontinuities that naturally exist and may control the stimulation. Even with comprehensive stress and formation characterization programs substantial uncertainty remains in these key parameters. This is especially the case in high-temperature EGS environments where drilling conditions are often difficult and a far fewer logging and testing options are available. This paper presents a new approach for explicitly quantifying the uncertainties in the state of stress using a Bayesian Markov Chain Monte Carlo method. This approach produces a probability distribution for the stress tensor, including a general 3D orientation, that reflects the uncertainties in all the observations or indicators used to constrain the stress state. This method is demonstrated on the characterization data for the EGS Collab Experiment 2 site. The output of the analysis is used to guide the design of the planned stimulations. In the case of research projects like EGS Collab, explicitly quantifying the uncertainties in the stress state allow for more rigorous hypothesis testing by allowing conclusions drawn from the experiments to be interpreted in the context of the uncertain knowledge about conditions in the test bed.

Burghardt, Jeffrey A.↗
DOE OSTI2024

Reference Site Condition Datasets for Floating Wind Arrays in the United States

Floating offshore wind farm design is highly site-specific, requiring detailed information about the specific conditions of a project area for realistic design studies. Unfortunately, publicly available site condition data for potential floating offshore wind project sites in the United States is scarce. To support U.S. offshore wind research, we developed reference site condition datasets, including metocean and seabed information, for four potential floating wind project areas in the U.S.: Humboldt Bay, Morro Bay, the Gulf of Maine, and the Gulf of Mexico. These datasets were compiled using publicly available data. Our metocean analysis, covering wind, waves, and surface currents, utilized measurement data from 2000 to 2020. Sources included the National Renewable Energy Laboratory’s National Offshore Wind Dataset for wind data, National Data Buoy Center buoys for wave data, and the High Frequency Radar Network for surface currents. These data were integrated into hourly time series used to compute extreme return periods up to 500 years, monthly statistics, and joint probability clusters for fatigue analysis. Soil conditions were evaluated using the usSEABED database and bathymetry grids were interpolated from the NCEI Digital Elevation Model Global Mosaic. Further information on the datasets and how they were created can be found in: Biglu, M., M. Hall, E. Lozon, S. Housner. 2024. Reference Site Conditions for Floating Wind Arrays in the United States. Golden, CO: National Renewable Energy Laboratory (NREL). NREL/TP-5000-89897. The data are also available at: https://github.com/FloatingArrayDesign/SiteConditions The content of each dataset is as follows: _NOW23_wind.txt: Hourly NOW-23 wind data up to a height of 400 meter. _metocean_1hr.txt: Hourly time series including wind, wave, surface current and temperature data. _Summary.xlsx: Metocean data, including extreme values, joint probability distributions and monthly statistics. _usSEABED_soil.csv: Extract of the usSEABED database for this specific site. _bathymetry_200m.txt (and 500m, 1000m): Gridded seabed depth data.

16 TIDAL AND WAVE POWER↗
DOE OSTI2021

Generalized Bayesian Framework for Evaluation of Integral Benchmark Experiments

A recently published generalized Bayesian optimization framework has provided a way to retract any or all of the three common assumptions underlying the conventional Generalized Linear Least Squares (GLLS) optimization method based on the concepts introduced in reference two. These assumptions are: 1. Perfection: The model used for data evaluation and the prior probability distribution function (PDF) of generalized* data are perfect; 2. Normality: The prior and posterior PDF are normal; and 3. Linearity: The model is linear. In this work we outline how the framework in 1 could be directly adopted for improved evaluation of nuclear criticality integral benchmark experiments (IBEs) by: 1. Removing the first assumption alone by utilizing the concept of imperfections introduced in 1 to enable evaluation in the presence of discrepancies between the data and model or of missing covariance information by a GLLS method that will be seen as a generalization of the conventional GLLS method employed by the TSURFER code, and by 2. Removing the remaining two assumptions by implement- ing a Markov Chain Monte Carlo method for computation of the posterior PDF in the SAMPLER code, where TSURFER and SAMPLER are the uncertainty quantification (UQ) codes for IBEs in the SCALE code system based on the GLLS, and the stochastic method, respectively.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Rapid Generation of a Macroscopic Schrödinger Cat State of Atoms with Parity-Independent Orientation

We show that using the process of one-axis-twist squeezing in an echo configuration, it is possible to control the orientation of the macroscopic magnetic moment of a large number of atoms by manipulating the quantum state of a single atom that is physically isolated from the ensemble. With this control technique, it is also possible to entangle an ensemble with a single atom deterministically, which mimics the thought experiment known as the Schrödinger cat. In addition, this technique would make it possible to generate a mesoscopic Schrödinger cat state for a large number of atoms far more rapidly that the conventional process for generating such a state, with an orientation that is independent of the parity of the number of atoms. Apart from the echo configuration, we have also investigated the behavior of one-axis-twist squeezing for some special values of the squeezing parameter. We find that the squeezing propagator can be expressed as the sum of n rotation operators if the product of n and the squeezing parameter equals pi, where n is a non-zero integer. A direct consequence of this property of one-axis-twist squeezing is that there is a hidden order in a squeezed state generated under this condition even if its Husimi quasi-probability distribution looks irregular.

Li, Jinyang↗
DOE OSTI2022

Bayesian Monte Carlo Evaluation Framework for Imperfect Data and Models [Abstract]

Nuclear data evaluation methods conventionally make the following assumptions: prior and posterior probability distribution functions (PDFs) of all model parameters and data are normal (Gaussian); the linear approximation is sufficiently accurate for minimization of a cost function (even for non-linear models); and that both the model (of, e.g., neutron cross section) and experimental data (including their covariance data) are perfect. These assumptions are inherent to the well-known generalized linear least squares (GLLS) minimization method commonly used for evaluations of resolved resonance region (RRR) neutron cross sections. However, these assumptions are often not justified due to the presence of non-normal PDFs, non-linear models (e.g. R -matrix formalism), and inherent imperfections in data and models (e.g. discrepant data sets, discrepancies between the previous evaluation and newly measured data, or imperfect covariance data). We remove the said assumptions in a mathematical framework of Bayes’ theorem, and implement it using the Metropolis-Hastings Monte Carlo method. Parameters of a new kind are introduced to parameterize inherent imperfections, e.g. , any discrepancies between the theoretical model and measured data. These new parameters enable evaluators to quantify their expert judgement about any discrepancies or imperfections in a reproducible manner. We demonstrate the framework with an ongoing evaluation of 233 U in the eV region using the ENDF-B/VIII library and transmission data measured by Guber, et al. , and compare the posterior parameters to those obtained by conventional evaluation methods.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Computational framework for modeling of physical process

Techniques, systems, and devices are described for providing a computational frame for estimating high-dimensional stochastic behaviors. In one exemplary aspect, a method for performing numerical estimation includes receiving a set of measurements of a stochastic behavior. The set of correlated measurements follows a non-standard probability distribution and is non-linearly correlated. Also, a non-linear relationship exists between a set of system variables that describes the stochastic behavior and a corresponding set of measurements. The method includes determining, based on the set of measurements, a numerical model of the stochastic behavior. The numerical model comprises a feature space comprising non-correlated features corresponding to the stochastic behavior. The non-correlated features have a dimensionality of M and the set of measurements has a dimensionality of N, M being smaller than N. The method includes generating a set of approximated system variables corresponding to the set of measurements based on the numerical model.

Chen, Xiao↗
DOE OSTI2021

On the Stochastic Stability of Deep Markov Models

Deep Markov models (DMM) are generative models which are scalable and expressive generalization of Markov models for representation, learning, and inference problems. DMMs using deep neural networks to parametrize the transition of Markov probability distributions have recently been shown to provide more expressiveness in modeling sequential data and dynamical system responses. However, the fundamental stochastic stability guarantees of such models have not been thoroughly investigated. In this paper, we present a rigorous analytical method to prove the necessary and sufficient conditions of DMM's stochastic stability. This task is achieved by spectral analysis of the efficiently computed Jacobians of probabilistic maps modeled by deep neural networks. We make theoretical connections between the eigenvalues of neural network's weights and the different activation function types used on the stability and overall dynamic behavior of DMMs with Gaussian distributions. We empirically substantiate our theoretical results on stochastic stability and eigenvalue spectra via several numerical experiments. Formal stability guarantees of DMMs can substantially improve their robustness and trustworthiness, necessary for reliable use in safety-critical real-world applications.

Drgona, Jan↗
DOE OSTI2023

Λ Baryon Production in ν¯µ Interactions in the MicroBooNE Detector

The Cabibbo suppressed production of $\Lambda$ baryons in anti-neutrino interactions with nuclei is a rare process that is yet to be measured with a modern neutrino detector with automated reconstruction. The cross section for this process is sensitive to a number of unique nuclear effects, most notably the secondary interactions of the produced hyperon while attempting to escape from the nucleus. Other interactions within the nuclear remnant can impact the estimation of neutrino energy in oscillation measurements, and thus an accurate description of the nuclear environment is required. The strangeness violating hyperon production process is only available to anti-neutrinos. The model of this interaction is implemented into the NuWro neutrino interaction Monte Carlo simulation, and some predictions are presented, focusing on the role of nuclear effects. This model introduces a hyperon-nucleus potential, which calculations from hypernuclear theory permit to be strongly repulsive in th e case of $\Sigma$ baryons. The presence of this potential is found to sculpt the shape of the differential cross section in some variables. The MicroBooNE detector will be described, followed by a description of a measurement of the flux averaged, restricted phase space cross section of Cabibbo suppressed $\Lambda$ baryon production. A sophisticated event selection is employed, as a very large quantity of background neutrino interactions must be removed to perform the measurement with any sensitivity. This selection introduces some novel techniques such as the island finding method, and achieves a background reduction of $\sim 10^6$, with an efficiency of around 7\%. The calculation of the systematic uncertainties will be explained, including two procedures explored to handle sources of background with extremely poor simulation statistics: an in-situ constraint using data from sidebands, and a visual inspection of the data and simulation to remove the troublesome background events. The sensitivity to the $\Lambda$ baryon production cross section is calculated in the form of Bayesian posterior probability distributions, combining the systematic uncertainties with data and simulation statistical uncertainties. As a rare process, the statistical uncertainties are highly non-Gaussian, and the Bayesian approach is applied to include the full shapes of these uncertainties. Data corresponding to $2.2 \times 10^{20}$ protons on target of neutrino mode running and $4.9 \times 10^{20}$ protons on target of anti-neutrino running is analysed. When the data was unblinded, five $\Lambda$ production candidates were selected from the data, consistent with the MC simulation prediction of $5.3 \pm 1.1$ events. The final estimated cross section is $1.8^{+2.0}_{-1.6} \times 10^{-40}$cm$^2/$Ar when employing the sideband constraint procedure. A similar result of $2.0^{+2.2}_{-1.8} \times 10^{-40}$cm$^2/$Ar is obtained when performing the visual scan instead. The methods used in t his analysis are intended to be easily exported to other LArTPC detectors such as the Short Baseline Near Detector.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Status of Error Correction Studies in Support of FFA@CEBAF

In this work, we examine the beam correction requirements for the FFA@CEBAF energy upgrade. Both hardware and software diagnostic and corrector components are under investigation; in particular the relationship between hardware and software optimization will be developed. To generate a representative sample of errors---from the machine lattice and other beam properties---we construct a Markov Chain Monte Carlo (MCMC) sampler which considers different probability distributions for different types of errors. This sample is used to investigate the statistical sensitivity of the beam to various diagnostic and corrective schema. Once statistics are acquired, we plan to use a variety of optimization techniques to minimize correction time for the electron beam in the FFA arcs designed for the CEBAF upgrade.

Benesch, J.↗
DOE OSTI2024

Model Gap Quantification and Evaluation

In the real world, model gaps always exist because models cannot perfectly match the objective physical plants. Model gaps reflect the integrity of models, which is vital for model validation and calibration. This letter proposes a novel approach for model gap quantification and evaluation. First, a comprehensive metric is developed to quantify dynamic model gaps. Next, the model gaps are evaluated from a panoramic view of the probability distribution of the comprehensive metric for multiple scenarios. Finally, we demonstrate the proposed quantification and evaluation approach through synchronous machine models.

Wang, Shaobu↗
DOE OSTI2024

Computational framework for modeling of physical process

Techniques, systems, and devices are described for providing a computational frame for estimating high-dimensional stochastic behaviors. In one exemplary aspect, a method for performing numerical estimation includes receiving a set of measurements of a stochastic behavior. The set of correlated measurements follows a non-standard probability distribution and is non-linearly correlated. Also, a non-linear relationship exists between a set of system variables that describes the stochastic behavior and a corresponding set of measurements. The method includes determining, based on the set of measurements, a numerical model of the stochastic behavior. The numerical model comprises a feature space comprising non-correlated features corresponding to the stochastic behavior. The non-correlated features have a dimensionality of M and the set of measurements has a dimensionality of N, M being smaller than N. The method includes generating a set of approximated system variables corresponding to the set of measurements based on the numerical model.

Chen, Xiao↗