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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.

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At least 307 records · Page 17
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Spatial pattern of lake evaporation increases under global warming linked to regional hydroclimate change

Abstract Lakes are critical natural resources that are vulnerable to climate change. In a warmer climate, lake evaporation is projected to increase globally, but with substantial variation between regions. Here, based on ensemble projections of climate and lake models and an attribution method, we show that future lake evaporation increase is strongly modulated by regional hydroclimate change. Specifically, a drying hydroclimate will amplify evaporation increase by enlarging surface vapor pressure deficit and reducing cloud shortwave reflection. Future lake evaporation increase is amplified in tropical America, the Mediterranean and Southeast China with drier future hydroclimates, and dampened in high latitudes and the Tibetan Plateau with wetter future hydroclimates. Such spatially coupled changes in lake evaporation and hydroclimate have important implications on regional lake water balance and volume change, which can aggravate water scarcity and flood risks.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Penalized ensemble Kalman filters for high dimensional non-linear systems

The ensemble Kalman filter (EnKF) is a data assimilation technique that uses an ensemble of models, updated with data, to track the time evolution of a usually non-linear system. It does so by using an empirical approximation to the well-known Kalman filter. However, its performance can suffer when the ensemble size is smaller than the state space, as is often necessary for computationally burdensome models. This scenario means that the empirical estimate of the state covariance is not full rank and possibly quite noisy. To solve this problem in this high dimensional regime, we propose a computationally fast and easy to implement algorithm called the penalized ensemble Kalman filter (PEnKF). Under certain conditions, it can be theoretically proven that the PEnKF will be accurate (the estimation error will converge to zero) despite having fewer ensemble members than state dimensions. Further, as contrasted to localization methods, the proposed approach learns the covariance structure associated with the dynamical system. These theoretical results are supported with simulations of several non-linear and high dimensional systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Systems and methods for modeling water quality

A system, method, device and computer-readable medium for creating an ensemble model of water quality. The ensemble model is generated by determining a set of optimal component models for spectral regions of a body of water, and combining the optimal models. The optimal models can be based on remote sensing data, including satellite imagery. A K-fold partition approach or a global approach can be used to determine the optimal component models, and the optimal component models can be combined through spectral space partition rules to generate an ensemble model of water quality. The ensemble model not only has improved water quality prediction ability, but also has strong spatial and temporal extensibility. The spatial and temporal extensibility of the ensemble model is fundamentally important and desirable for long-term and large-scale remote sensing monitoring and assessment of water quality.

Liu, Hongxing↗
DOE OSTI2020

Calibration and Uncertainty Estimation Using the Ensemble Kalman Filter with a Large Subsurface Flow and Transport Model - 20321

At routinely monitored groundwater contamination sites, periodically measured environmental conditions such as groundwater levels and contaminant concentrations are used to inform and confirm a conceptual site model (CSM) and guide the development and calibration of a numerical groundwater flow and transport model. The calibration of groundwater flow and transport models after each measurement (sampling) event can illuminate deficiencies in a CSM, identify areas where additional monitoring is warranted, and predict the behavior of the system to guide decision making. However, manual and automated (e.g. PEST) model calibration tools can be time-consuming and computationally expensive to implement after each sampling event. Perhaps as a result, such calibration tools generally utilize all available monitoring data simultaneously rather than sequentially assimilating monitoring data one sampling event at a time as the results from sampling become available. A more real-time data assimilation approach may reduce parameter uncertainty, quantify the value of additional monitoring data, and produce a usable model more quickly and with less effort. To mitigate the potential time-consuming aspects of manual and widely applied automated calibration techniques, a data assimilation algorithm called the ensemble Kalman filter (EnKF) was evaluated as a relatively efficient method of model calibration and uncertainty assessment via the sequential integration of monitoring data into a model. The EnKF was able to successfully and efficiently assimilate monitoring and modeling data to calibrate a complex flow and transport model at a real-world site with significant subsurface heterogeneity, uncertainty, and 12 years of monitoring data (over 4,000 individual measurements of groundwater levels and over 2,500 measurements of contaminant concentrations). Starting with an uncalibrated model data from annual sampling events were sequentially assimilated, and the resultant predication errors and estimated parameter uncertainties were tracked. After all monitoring data were assimilated, both flow and transport residuals at the end of the EnKF process were comparable to those produced via a concurrent PEST calibration effort but required fewer model simulations. Both uncertainty and prediction errors decreased over time. In a real-time application, the adequacy of the model could be assessed after each sampling event. The benefits of such a real-time approach to utilizing monitoring data include reduced costs (in the form of model updates or site characterization efforts), early flagging of possible errors in the CSM, and a reduced risk of overfitting and corresponding increased confidence in model predictions. This tool may be particularly useful compared to other calibration techniques (e.g. manual, PEST) when model runtimes are long, calibration parameters are many, or parameter uncertainty is large. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2024

Bayesian reduced-order deep learning surrogate model for dynamic systems described by partial differential equations

We propose a reduced-order deep-learning surrogate model for dynamic systems described by time-dependent partial differential equations. This method employs space–time Karhunen–Loève expansions (KLEs) of the state variables and space-dependent KLEs of space-varying parameters to identify the reduced (latent) dimensions. Subsequently, a deep neural network (DNN) is used to map the parameter latent space to the state variable latent space. An approximate Bayesian method is developed for uncertainty quantification (UQ) in the proposed KL-DNN surrogate model. The KL-DNN method is tested for the linear advection–diffusion and nonlinear diffusion equations, and the Bayesian approach for UQ is compared with the deep ensembling (DE) approach, commonly used for quantifying uncertainty in DNN models. It was found that the approximate Bayesian method provides a more informative distribution of the PDE solutions in terms of the coverage of the reference PDE solutions (the percentage of nodes where the reference solution is within the confidence interval predicted by the UQ methods) and log predictive probability. The DE method is found to underestimate uncertainty and introduce bias. For the nonlinear diffusion equation, we compare the KL-DNN method with the Fourier Neural Operator (FNO) method and find that KL-DNN is 10% more accurate and needs less training time than the FNO method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Physics-Based Machine Learning Methods for U-235 Forensics Signatures

Signatures of low-intensity U-235 sources have been recently studied by utilizing a variety of machine learning (ML) classifiers using features derived from gamma spectral measurements collected under structured campaigns. Several ML classifiers, such as ensemble of tress and classification trees, revealed misleadingly-optimistic training error due to over-fitting, and furthermore, their performance is not directly relatable to the physical properties due to their data-driven, opaque designs. We present a regression-based ML method that first estimates the inverse distance to the source and then utilizes a threshold to infer its presence, by representing the background as a source located at an infinite distance. For the inverse distance estimation, we study the ensemble of trees and Gaussian process regression methods, and a hyper parameter auto-tuning and selection method that employs five regression estimators. These methods avoid the over-fitting observed in several ML classifiers, while providing the classification error nearly comparable to them based on independent test data. Their error is directly related to estimates of the inverse physical distance to source, and the precision of error determines the seperability property that determines the false alarm and missed detection rates. The property of monotonic decrease of the source strength with increasing detector distance combined with Poisson distribution of measurements is utilized to analytically validate these methods by deriving the generalization equations of underlying regression methods.

Rao, Nageswara↗
DOE OSTI2020

Ensembles of Networks Produced from Neural Architecture Search

Neural architecture search (NAS) is a popular topic at the intersection of deep learning and high performance computing. NAS focuses on optimizing the architecture of neural networks along with their hyperparameters in order to produce networks with superior performance. Much of the focus has been on how to produce a single best network to solve a machine learning problem, but as NAS methods produce many networks that work very well, this affords the opportunity to ensemble these networks to produce an improved result. Additionally, the diversity of network structures produced by NAS drives a natural bias towards diversity of predictions produced by the individual networks. This results in an improved ensemble over simply creating an ensemble that contains duplicates of the best network architecture retrained to have unique weights.

Herron, Emily↗
DOE OSTI2021

Are 100 Ensemble Members Enough to Capture the Remote Atmospheric Response to +2°C Arctic Sea Ice Loss?

This study presents results from the Polar Amplification Multimodel Intercomparison Project (PAMIP) single-year time-slice experiments that aim to isolate the atmospheric response to Arctic sea ice loss at global warming levels of +2°C. Using two general circulation models (GCMs), the ensemble size is increased up to 300 ensemble members, beyond the recommended 100 members. After partitioning the response in groups of 100 ensemble members, the reproducibility of the results is evaluated, with a focus on the response of the midlatitude jet streams in the North Atlantic and North Pacific. Both atmosphere-only and coupled ocean–atmosphere PAMIP experiments are analyzed. Substantial differences in the midlatitude response are found among the different experiment subsets, suggesting that 100-member ensembles are still significantly influenced by internal variability, which can mislead conclusions. Despite an overall stronger response, the coupled ocean–atmosphere runs exhibit greater spread due to additional ENSO-related internal variability when the ocean is interactive. The lack of consistency in the response is true for anomalies that are statistically significant according to Student’s t and false discovery rate tests. This is problematic for the multimodel assessment of the response, as some of the spread may be attributed to different model sensitivities whereas it is due to internal variability. Here, we propose a method to overcome this consistency issue that allows for more robust conclusions when only 100 ensemble members are used.

58 GEOSCIENCES↗
DOE OSTI2024

On the uncertainty of long-period return values of extreme daily precipitation

Methods for calculating return values of extreme precipitation and their uncertainty are compared using daily precipitation rates over the Western U.S. and Southwestern Canada from a large ensemble of climate model simulations. The roles of return-value estimation procedures and sample size in uncertainty are evaluated for various return periods. We compare two different generalized extreme value (GEV) parameter estimation techniques, namely L-moments and maximum likelihood (MLE), as well as empirical techniques. Even for very large datasets, confidence intervals calculated using GEV techniques are narrower than those calculated using empirical methods. Furthermore, the more efficient L-moments parameter estimation techniques result in narrower confidence intervals than MLE parameter estimation techniques at small sample sizes, but similar best estimates. It should be noted that we do not claim that either parameter fitting technique is better calibrated than the other to estimate long period return values. While a non-stationary MLE methodology is readily available to estimate GEV parameters, it is not for the L-moments method. Comparison of uncertainty quantification methods are found to yield significantly different estimates for small sample sizes but converge to similar results as sample size increases. Finally, practical recommendations about the length and size of climate model ensemble simulations and the choice of statistical methods to robustly estimate long period return values of extreme daily precipitation statistics and quantify their uncertainty.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Direct evaluation of the phase diagrams of dense multicomponent plasmas by integration of the Clapeyron equations

Accurate phase diagrams of multicomponent plasmas are required for the modeling of dense stellar plasmas, such as those found in the cores of white dwarf stars and the crusts of neutron stars. Those phase diagrams have been computed using a variety of standard techniques, which suffer from physical and computational limitations. Here we present an efficient and accurate method that overcomes the drawbacks of previously used approaches. In particular, finite-size effects are avoided as each phase is calculated separately; the plasma electrons and volume changes are explicitly taken into account; and arbitrary analytic fits to simulation data as well as particle insertions are avoided. Furthermore, no simulations at “uninteresting” state conditions, i.e., away from the phase coexistence curves, are required, which improves the efficiency of the technique. The method consists of an adaptation of the so-called Gibbs-Duhem integration approach to electron-ion plasmas, where the coexistence curve is determined by direct numerical integration of its underlying Clapeyron equation. The thermodynamics properties of the coexisting phases are evaluated separately using Monte Carlo simulations in the isobaric semigrand canonical ensemble (NPT Δ μ ). We describe this Monte Carlo-based Clapeyron integration method, including its basic physical and numerical principles, our extension to electron-ion plasmas, and our numerical implementation. We illustrate its applicability and benefits with the calculation of the melting curve of dense carbon-oxygen plasmas under conditions relevant for the cores of white dwarf stars and provide analytic fits to implement this new melting curve in white dwarf models. While this work focuses on the liquid-solid phase boundary of dense two-component plasmas, a wider range of physical systems and phase boundaries are within the scope of the Clapeyron integration method, which had until now only been applied to simple model systems of neutral particles.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Positive- and negative-frequency noise from an ensemble of two-level fluctuators

The analysis of charge noise based on the Bloch-Redfield treatment of an ensemble of dissipative two-level fluctuators generally results in a violation of the fluctuation-dissipation theorem. The standard Markov approximation (when applied to the two-level fluctuators coupled to a bath) can be identified as the main origin of this failure. The resulting decoherence rates only involve the bath response at the fluctuator frequency, and thus completely neglect the effects of frequency broadening. A systematic and computationally convenient way to overcome this issue is to employ the spectator-qubit method: by coupling an auxiliary qubit to the two-level fluctuator ensemble, an analytical approximation for S(ω) fully consistent with the fluctuation-dissipation theorem can be obtained. We discuss the resulting characteristics of the noise which exhibits distinct behavior over several frequency ranges, including a 1/f to 1/f2 crossover with a T3 temperature dependence of the crossover frequency.

2-dimensional systems↗
DOE OSTI2022

Automated Stellar Spectra Classification with Ensemble Convolutional Neural Network

Large sky survey telescopes have produced a tremendous amount of astronomical data, including spectra. Machine learning methods must be employed to automatically process the spectral data obtained by these telescopes. Classification of stellar spectra by applying deep learning is an important research direction for the automatic classification of high-dimensional celestial spectra. In this paper, a robust ensemble convolutional neural network (ECNN) was designed and applied to improve the classification accuracy of massive stellar spectra from the Sloan digital sky survey. We designed six classifiers which consist six different convolutional neural networks (CNN), respectively, to recognize the spectra in DR16. Then, according the cross-entropy testing error of the spectra at different signal-to-noise ratios, we integrate the results of different classifiers in an ensemble learning way to improve the effect of classification. The experimental result proved that our one-dimensional ECNN strategy could achieve 95.0% accuracy in the classification task of the stellar spectra, a level of accuracy that exceeds that of the classical principal component analysis and support vector machine model.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Permafrost Region Greenhouse Gas Budgets Suggest a Weak CO 2 Sink and CH 4 and N 2 O Sources, But Magnitudes Differ Between Top-Down and Bottom-Up Methods

Large stocks of soil carbon (C) and nitrogen (N) in northern permafrost soils are vulnerable to remobilization under climate change. However, there are large uncertainties in present-day greenhouse gas (GHG) budgets. We compare bottom-up (data-driven upscaling and process-based models) and top-down (atmospheric inversion models) budgets of carbon dioxide (CO 2 ), methane (CH 4 ) and nitrous oxide (N 2 O) as well as lateral fluxes of C and N across the region over 2000–2020. Bottom-up approaches estimate higher land-to-atmosphere fluxes for all GHGs. Both bottom-up and top-down approaches show a sink of CO 2 in natural ecosystems (bottom-up: -29 (-709, 455), top-down: -587 (-862, -312) Tg CO 2 -C yr -1 ) and sources of CH 4 (bottom-up: 38 (22, 53), top-down: 15 (11, 18) Tg CH 4 -C y -1 ) and N 2 O (bottom-up: 0.7 (0.1, 1.3), top-down: 0.09 (-0.19, 0.37) Tg N 2 O-N yr -1 ). The combined global warming potential of all three gases (GWP-100) cannot be distinguished from neutral. Over shorter timescales (GWP-20), the region is a net GHG source because CH 4 dominates the total forcing. The net CO 2 sink in Boreal forests and wetlands is largely offset by fires and inland water CO 2 emissions as well as CH 4 emissions from wetlands and inland waters, with a smaller contribution from N 2 O emissions. Priorities for future research include the representation of inland waters in process-based models and the compilation of process-model ensembles for CH 4 and N 2 O. Discrepancies between bottom-up and top-down methods call for analyses of how prior flux ensembles impact inversion budgets, more and well-distributed in situ GHG measurements and improved resolution in upscaling techniques.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Standardising the “Gregory method” for calculating equilibrium climate sensitivity

The equilibrium climate sensitivity (ECS) – the equilibrium global mean temperature response to a doubling of atmospheric CO 2 – is a high-profile metric for quantifying the Earth system's response to human-induced climate change. A widely applied approach to estimating the ECS is the “Gregory method” (Gregory et al., 2004), which uses an ordinary least squares (OLS) regression between the net radiative flux, N, and surface air temperature anomalies, ΔT, from a 150 year experiment in which atmospheric CO 2 concentrations are quadrupled. The ECS is determined by extrapolating the linear fit to N=0, i.e. the ΔT-intercept, indicating the point at which the system is back in equilibrium. This method has been used to compare ECS estimates across the CMIP5 and CMIP6 ensembles and will likely be a key diagnostic for CMIP7. Despite its widespread application, there is little consistency or transparency between studies in how the climate model data is processed prior to the regression, leading to potential discrepancies in ECS estimates. We identify 32 alternative data processing pathways, varying by differences in global mean weighting, net radiative flux variable, anomaly calculation method, and linear regression fit. Using 44 CMIP6 models, we systematically assess the impact of these choices on ECS estimates and calculate uncertainty ranges using two bootstrap approaches. While the inter-model ECS range is insensitive to the data processing pathway, individual outlier models exhibit notable differences. Approximating a model's native grid cell area (if irregular) with cosine of the latitude can decrease the ECS by 11 %, the choice of N-variable can change the ECS by 6 %, and some anomaly calculation methods can introduce spurious temporal correlations in the processed data. Beyond data processing choices, we also evaluate an alternative linear regression method – total least squares (TLS) – which has a more statistically robust basis than OLS. However, for consistency with previous literature, and given TLS may reduce the ECS compared to OLS (by up to 24 %), thereby making a known bias in the Gregory method worse, we do not feel there is sufficient clarity to recommend a transition to TLS in all cases. To improve reproducibility and comparability in future studies, we recommend a standardised Gregory method: weighting the global mean by cell area, using the top of the atmosphere (as opposed to the top of model) N-variable, and calculating anomalies by first applying a rolling average to the preindustrial control timeseries then subtracting from the raw CO 2 quadrupling experiment. This approach accounts for model drift while reducing noise in the data to best meet the pre-conditions of the linear regression. While CMIP6 results of the multi-model mean ECS appear insensitive to these processing choices, similar assumptions may not hold for CMIP7, underscoring the need for standardised data preparation in future climate sensitivity assessments.

Geosciences↗
DOE OSTI2026

Enhanced accuracy through ensembling of randomly initialized auto-regressive models for dynamical systems

Computational mechanics simulations using traditional finite element methods (FEM) require prohibitively expensive computational resources for real-time engineering applications, design optimization, and digital twin implementations. While machine learning (ML) surrogate models offer significant computational speedups, autoregressive ML models for time-dependent mechanical systems suffer from error accumulation that compromises long-term prediction reliability - a critical concern for engineering applications where accuracy over extended time horizons is essential for safety and performance assessments. Here, we propose a deep ensemble framework specifically designed to address this challenge in computational mechanics applications, where multiple ML surrogate models with random weight initializations are trained in parallel and their predictions aggregated during inference. This approach leverages statistical diversity to maximize information gain from a fixed set of training data and to mitigate error propagation, while maintaining the computational efficiency that makes ML surrogates attractive for engineering practice. We validate the framework on three representative problems spanning critical areas of computational mechanics: stress field evolution in heterogeneous microstructures under complex loading (relevant to advanced materials design and composite analysis), planetary-scale shallow water dynamics (applicable to environmental and geotechnical engineering), and Gray-Scott reaction-diffusion systems (relevant to mass transport and chemical process engineering). Across all test cases, the ensemble approach demonstrates consistent error reduction of 15-33% compared to individual models. The codes for this work are available on GitHub (https://github.com/Graham-Brady-Research-Group/AutoregressiveEnsemble_SpatioTemporal_Evolution).

autoregressive prediction↗
DOE OSTI2023

Knowledge-informed deep learning for hydrological model calibration: an application to Coal Creek Watershed in Colorado

Abstract. Deep learning (DL)-assisted inverse mapping has shown promise in hydrological model calibration by directly estimating parameters from observations. However, the increasing computational demand for running the state-of-the-art hydrological model limits sufficient ensemble runs for its calibration. In this work, we present a novel knowledge-informed deep learning method that can efficiently conduct the calibration using a few hundred realizations. The method involves two steps. First, we determine decisive model parameters from a complete parameter set based on the mutual information (MI) between model responses and each parameter computed by a limited number of realizations (∼50). Second, we perform more ensemble runs (e.g., several hundred) to generate the training sets for the inverse mapping, which selects informative model responses for estimating each parameter using MI-based parameter sensitivity. We applied this new DL-based method to calibrate a process-based integrated hydrological model, the Advanced Terrestrial Simulator (ATS), at Coal Creek Watershed, CO. The calibration is performed against observed stream discharge (Q) and remotely sensed evapotranspiration (ET) from the water year 2017 to 2019. Preliminary MI analysis on 50 realizations resulted in a down-selection of 7 out of 14 ATS model parameters. Then, we performed a complete MI analysis on 396 realizations and constructed the inverse mapping from informative responses to each of the selected parameters using a deep neural network. Compared with calibration using observations covering all time steps, the new inverse mapping improves parameter estimations, thus enhancing the performance of ATS forward model runs. The Nash–Sutcliffe efficiency (NSE) of streamflow predictions increases from 0.53 to 0.8 when calibrating against Q alone. Using ET observations, on the other hand, does not show much improvement on the performance of ATS modeling mainly due to both the uncertainty of the remotely sensed product and the insufficient coverage of the model ET ensemble in capturing the observation. By using observed Q only, we further performed a multiyear analysis and show that Q is best simulated (NSE > 0.8) by including in the calibration the dry-year flow dynamics that show more sensitivity to subsurface characteristics than the other wet years. Moreover, when continuing the forward runs till the end of 2021, the calibrated models show similar simulation performances during this evaluation period as the calibration period, demonstrating the ability of the estimated parameters in capturing climate sensitivity. Our success highlights the importance of leveraging data-driven knowledge in DL-assisted hydrological model calibration.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Deficient precipitation sensitivity to Sahel land surface forcings among CMIP5 models

Abstract The overall performance of the simulated seasonal precipitation response to local terrestrial forcings, namely vegetation abundance and soil moisture, in the Sahel among the Coupled Model Intercomparison Project Phase Five (CMIP5) Earth System Models (ESMs) is systematically investigated and compared with its observational counterpart using a multivariate statistical method. The observed seasonal precipitation response is evaluated against a large ensemble of observational, reanalysis, and satellite data sets to provide quantification of uncertainties. The behaviour of models with and without a Dynamic Global Vegetation Model (DGVM) component is also explored, along with the mechanisms responsible for terrestrial feedback on rainfall. In general, the CMIP5 models can reasonably capture the seasonal evolution of Sahel precipitation and soil moisture, albeit with wet biases during the pre‐monsoon period and dry biases during the peak monsoon period. The non‐DGVM ESMs simulate comparable leaf area indices (LAIs) with observations, while DGVM‐enabled ESMs simulate too much year‐round LAI. The variance of precipitation that is attributed to oceanic forcings in CMIP5 is comparable with observations; however, the variance of precipitation that is attributed to terrestrial forcings is smaller in CMIP5 models than observed, especially for non‐DGVM ESMs. CMIP5 models, especially those without DGVMs, undervalue precipitation's observed response strength to soil moisture anomalies. In both observations and CMIP5 models, none of the atmospheric variables show significant responses to direct vegetation forcing, except for the response in transpiration. Although vegetation has minimal direct effect on the atmospheric state, it can affect the atmosphere by modifying soil moisture and transpiration rate indirectly, which helps explain the more realistic simulation of rainfall in DGVM‐enabled ESMs than non‐DGVM ESMs. Coupling of an ESM to a DGVM is critical in generating reasonable land–atmosphere feedback and examining future ecological and climatic changes over the Sahel.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Preparation of metrological states in dipolar-interacting spin systems

Abstract Spin systems are an attractive candidate for quantum-enhanced metrology. Here we develop a variational method to generate metrological states in small dipolar-interacting spin ensembles with limited qubit control. For both regular and disordered spatial spin configurations the generated states enable sensing beyond the standard quantum limit (SQL) and, for small spin numbers, approach the Heisenberg limit (HL). Depending on the circuit depth and the level of readout noise, the resulting states resemble Greenberger-Horne-Zeilinger (GHZ) states or Spin Squeezed States (SSS). Sensing beyond the SQL holds in the presence of finite spin polarization and a non-Markovian noise environment. The developed black-box optimization techniques for small spin numbers ( N ≤ 10) are directly applicable to diamond-based nanoscale field sensing, where the sensor size limits N and conventional squeezing approaches fail.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗