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At least 73 records · Page 4

Learning robust parameter inference and density reconstruction in flyer plate impact experiments

Estimating physical parameters or material properties from experimental observations is a common objective in many areas of physics and material science. In many experiments, especially in shock physics, radiography is the primary means of observing the system of interest. However, radiography does not provide direct access to key state variables, such as density, which prevents the application of traditional parameter estimation approaches. Here we focus on flyer plate impact experiments on porous materials, and resolving the underlying parameterized equation of state (EoS) and crush porosity model parameters given radiographic observation(s). We use machine learning as a tool to demonstrate with high confidence that using only high impact velocity data does not provide sufficient information to accurately infer both EoS and crush model parameters, even with fully resolved density fields or a dynamic sequence of images. We thus propose an observable data set consisting of low and high impact velocity experiments/simulations that capture different regimes of compaction and shock propagation, and proceed to introduce a generative machine learning approach which produces a posterior distribution of physical parameters directly from radiographs. We demonstrate the effectiveness of the approach in estimating parameters from simulated flyer plate impact experiments, and show that the obtained estimates of EoS and crush model parameters can then be used in hydrodynamic simulations to obtain accurate and physically admissible density reconstructions. Finally, we examine the robustness of the approach to model mismatches, and find that the learned approach can provide useful parameter estimates in the presence of out-of-distribution radiographic noise and previously unseen physics, thereby promoting a potential breakthrough in estimating material properties from experimental radiographic images.

97 MATHEMATICS AND COMPUTING

Qualitative Risk Assessment of Legacy Wells within the Estimated Prairie State Generating Company Area of Review

This report details the digitization of a legacy wellbore database, including data processing assumptions, parameter estimation, and risk assessment methodology. The database, comprising 6,454 documents, was provided by ISGS. It includes valuable data from the Prairie State Generating Company (PSGC) and One Earth Energy (OEE) sites of the CarbonSAFE Phase III – Illinois Storage Corridor project. The report focuses on wells within a 15-mile radius from the Lively Grove #1 (LG#1) well at PSGC site, evaluating subsurface conditions and potential risks. A total of 4,386 wellbores within 15 miles of the LG#1 well were filtered based on depth and formation codes. LG#1 is the stratigraphic well at the PSGC site drilled in 2021. Ninety-four (94) wells penetrating the Maquoketa Shale Group (the primary confining unit) within the estimated area-of-review (AoR) for the PSGC site were evaluated using a qualitative risk assessment (QRA) methodology. The QRA developed by Arbad et al. 2022 focuses on legacy wells within the AoR and categorizes them based on well construction details. The QRA identifies wells that need immediate attention by categorizing them based on penetration depth and protection. Wells within the AoR were categorized into nine groups based on penetrations and protections. These categories range from Type 1 wells, with no documentation, to Type 9 wells, which do not penetrate the primary confining unit or storage reservoir (unit). Well accessibility within the AoR varies based on well status, including Dry & Abandoned (DA), Plugged & Abandoned (PA), Injection (INJ), Oil/Gas Producing (PROD), and Observation (Obs) wells. Accessibility levels were determined by well construction, with DA wells being the least accessible and Observation wells the most accessible, impacting gas leakage detection possibilities. Remedial action priority of wells decreases from Type 1 to Type 9 wells. Type 1 to Type 6 wells with status DA and PA require immediate attention, while Type 7 and Type 8 wells are low priority. A risk matrix used to prioritize corrective actions for legacy wells is proposed to categorize wells within an AoR based on penetrations, protections, and accessibility. The methodology involves data acquisition, well categorization into nine types, and determining CO 2 leakage pathways using well schematics and geospatial mapping. This approach is particularly useful for managing the integrity of legacy wells throughout the lifecycle of a Carbon Capture and Storage (CCS) project. A qualitative risk assessment of 94 wells within the AoR of the PSGC site identified 54 wells with high priority for corrective action due to penetration of the primary containment seal. The assessment utilizes color-coded maps to categorize well types and prioritize corrective actions, providing a comprehensive analysis. Schematics of wells penetrating the primary confining unit were drawn, and leakage pathways were identified. Details of all wells penetrating the confining zone are provided in the appendix, including information on well types, plugging, and casing status.

01 COAL, LIGNITE, AND PEAT

Blueprints for Training Information Bottlenecks for Collider Analyses

Dimensionality reduction is a crucial aspect of data analysis in high energy physics, even if accompanied by information loss. Several methods, including histogram- and kernel-based analyses, are only computationally feasible for low-dimensional data. Furthermore, simulation models used in HEP can often only be validated for low-dimensional data. We provide several blueprints for using machine learning to create low-dimensional data representations (continuous event variables and discrete classification labels) for use in signal discovery and parameter estimation tasks. We also describe how to design the learned representation to facilitate a) searches with unknown model parameters and b) validation of simulation models in data control regions.

43 PARTICLE ACCELERATORS

Applying Gaussian Process Machine Learning and Modern Probabilistic Programming to Satellite Data to Infer CO 2 Emissions

Satellite data provides essential insights into the spatiotemporal distribution of CO 2 concentrations. However, many atmospheric inverse models fail to adequately incorporate the spatial and temporal correlations inherent in satellite observations and often lack rigorous methods for estimating parameters like spatial length scales. We introduce an inference model that processes the spatiotemporal covariance in satellite data and estimates hyperparameters such as covariance length scales. Our approach uses the Gaussian process (GP) machine learning (ML) and modern probabilistic programming languages (PPLs) to perform atmospheric inversions of emissions from satellite data. We develop a GP ML inversion system based on modern PPLs and the GEOS-Chem chemical transport model, simulating atmospheric CO 2 concentrations corresponding to the Orbiting Carbon Observatory-2/3 (OCO-2/3) data for July 2020. In our supervised learning framework, we treat the GEOS-Chem simulated data set as the target, with predictors derived by scaling the target with sector-specific factors hidden from the GP machine. Our results show that the GP model, combined with GPU-enabled PPLs, effectively retrieves true emission scaling factors and infers noise levels concealed within the data. This suggests that our method could be applied over larger areas with more complex covariance structures, enabling comprehensive analysis of the spatiotemporal patterns observed in OCO-2/3 and similar satellite data sets.

54 ENVIRONMENTAL SCIENCES

Can Neutron Star Tidal Effects Obscure Deviations from General Relativity?

Abstract One of the main goals of gravitational-wave astrophysics is to study gravity in the strong-field regime and constrain deviations from general relativity (GR). Any such deviation affects not only binary dynamics and gravitational-wave emission but also the structure and tidal properties of compact objects. In the case of neutron stars, masses, radii, and tidal deformabilities can all differ significantly between different theories of gravity. Currently, the measurement uncertainties in neutron star radii and tidal deformabilities are quite large. However, much less is known about how the large uncertainty in the nuclear equation of state (EOS) might affect tests of GR using binary neutron star mergers. Conversely, using the wrong theory of gravity might lead to incorrect constraints on the nuclear EOS. Here, we study this problem within scalar–tensor (ST) theory. We apply the recently derived ℓ = 2 tidal Love numbers in this theory to parameter estimation of GW170817. Correspondingly, we test if physics beyond GR could bias measurements of the nuclear EOS and neutron star radii. We find that parameter inference for both the GR and ST cases returns consistent component masses and tidal deformabilities. The radius and the EOS posteriors, however, differ between the two theories, but neither is excluded by current observational limits. This indicates that measurements of the nuclear EOS may be biased and that deviations from GR could go undetected when analyzing current binary neutron star mergers.

79 ASTRONOMY AND ASTROPHYSICS

Towards constraining cosmological parameters with SPT-3G observations of 25% of the sky

The South Pole Telescope (SPT), using its third-generation camera, SPT-3G, is conducting observations of the cosmic microwave background (CMB) in temperature and polarization across approximately 10 000 deg$^2$ of the sky at 95, 150, and 220 GHz. This comprehensive dataset should yield stringent constraints on cosmological parameters. In this work, we explore its potential to address the Hubble tension by forecasting constraints from temperature, polarization, and CMB lensing on early dark energy (EDE) and the variation in electron mass in spatially flat and curved universes. For this purpose, we investigate first whether analyzing the distinct SPT-3G observation fields independently, as opposed to as a single, unified region, results in a loss of information relevant to cosmological parameter estimation. We develop a realistic temperature and polarization likelihood pipeline capable of analyzing these fields in these two ways, and subsequently forecast constraints on cosmological parameters. Our findings indicate that any loss of constraining power from analyzing the fields separately is primarily concentrated at low multipoles ($\ell$ < 50) and the overall impact on the relative uncertainty on standard $Λ$ cold dark matter parameters is minimal (< 3%). Our forecasts suggest that SPT-3G data should improve by more than a factor of 90 and 190 the figure of merit of the EDE and the varying electron mass models, respectively, when combined with Planck data. The likelihood pipeline developed and used in this work is made publicly available online.

Vitrier, A. [Paris, Inst. Astrophys.]

Benchmarking optimization methods for materials research: Gradient descent and Bayesian optimization for lithium-ion battery aging diagnostics

Accurate and efficient parameter estimation is essential for battery diagnostics and aging analysis. Here, in this study, we compare two optimization-based approaches—gradient descent and Bayesian optimization—for extracting parameters from differential voltage analysis in lithium-ion batteries. While these techniques are widely used, their relative strengths and limitations for this application are not well understood. The study evaluates the trade-offs between these methods in terms of result quality, computational cost, and reliability within this specific application. The diagnostic results from our battery data suggest adopting gradient descent as an initial method for rapid and efficient analysis, while employing more stable optimization techniques, such as Bayesian optimization, as a verification step to mitigate potential instability. Comparing the two methods provides information on algorithmic choice, while inspiring further discussions on selecting appropriate techniques for specific research tasks.

Zhao, Ziqing [Boston Univ., MA (United States)] (O

Rejection Sampling with Autodifferentiation -- Case study: Fitting a Hadronization Model

We present an autodifferentiable rejection sampling algorithm termed Rejection Sampling with Autodifferentiation (RSA). In conjunction with reweighting, we show that RSA can be used for efficient parameter estimation and model exploration. Additionally, this approach facilitates the use of unbinned machine-learning-based observables, allowing for more precise, data-driven fits. To showcase these capabilities, we apply an RSA-based parameter fit to a simplified hadronization model.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Entanglement Requirements for Coherent Enhancement in Detectors

Coherent enhancement is a powerful mechanism for improving the sensitivity of a wide range of detectors, but its practical use is often limited by the difficulty of preparing the required quantum states. We show that this difficulty has a fundamental origin: coherent enhancement of a signal interacting with a detector is quantitatively constrained by entanglement. We prove general bounds on how the strength of coherent effects can scale with system size, as a function of the single-mode entanglement entropy of the detector. These bounds smoothly interpolate between the incoherent and fully coherent regimes, and apply both to parameter-estimation problems and to scattering processes. We discuss these results from two complementary perspectives: First, they appear as bounds on the quantum Fisher information of many-body states, which translate directly into limits on parameter sensitivity via the quantum Cramér-Rao bound. Second, they can be interpreted as limits on a class of scattering cross sections, leading to predictions for how minimum detectable interaction strengths scale with target size. Together, these results provide a unified view of coherent enhancement in metrology and scattering experiments, and motivate the development of new techniques for generating entangled detector states.

Bogorad, Zachary [Fermilab] (ORCID:000000019913647

Lambda-PFLOTRAN 1.0: a workflow for incorporating organic matter chemistry informed by ultra high resolution mass spectrometry into biogeochemical modeling

Abstract. Organic matter (OM) composition plays a central role in microbial respiration of dissolved organic matter and subsequent biogeochemical reactions. Here, a direct connection of organic matter chemistry and thermodynamics to reactive transport simulators has been achieved through the newly developed Lambda-PFLOTRAN workflow tool that succinctly incorporates carbon chemistry data generated from Fourier transform ion cyclotron resonance mass spectrometry (FTICR-MS) into reaction networks to simulate organic matter degradation and the resulting biogeochemistry. Lambda-PFLOTRAN is a Python-based workflow, executed through a Jupyter notebook interface, that digests raw FTICR-MS data, develops a representative reaction network based on substrate-explicit thermodynamic modeling (also termed lambda modeling due to its key thermodynamic parameter λ used therein), and completes a biogeochemical simulation with the open source, reactive flow and transport code PFLOTRAN. The workflow consists of the following five steps: configuration, thermodynamic (lambda) analysis, sensitivity analysis, parameter estimation, and simulation output and visualization. Two test cases are provided to demonstrate the functionality of the Lambda-PFLOTRAN workflow. The first test case uses laboratory incubation data of temporal oxygen depletion to fit lambda parameters (i.e., maximum utilization rate and microbial carrying capacity). A slightly more complex second test case fits multiple lambda formulation and soil organic matter release parameters to temporal greenhouse gas generation measured during a soil incubation. Overall, the Lambda-PFLOTRAN workflow facilitates upscaling by using molecular-scale characterization to inform biogeochemical processes occurring at larger scales.

58 GEOSCIENCES

A numerical study of process complexity in permafrost dominated regions

Numerical modeling of permafrost dynamics requires adequate representation of atmospheric and surface processes, a reasonable parameter estimation strategy, and site-specific model development. The three main research objectives of the study are: (i) to propose a novel methodology that determines the required level of surface process complexity of permafrost models by conducting parameter sensitivity and calibration, (ii) to design and compare three numerical models of increasing surface process complexity, and (iii) to calibrate and validate the numerical models at the Yakou catchment on the Qinghai-Tibet Plateau as an exemplary study site. The calibration was carried out by coupling the Advanced Terrestrial Simulator (numerical model) and PEST (calibration tool). Simulation results showed that (i) A simple numerical model that considers only subsurface processes can simulate active layer development with the same accuracy as other more complex models that include surface processes. (ii) Peat and mineral soil layer permeability, Van Genuchten alpha, and porosity are highly sensitive. (iii) Liquid precipitation aids in increasing the rate of permafrost degradation. (iv) Deposition of snow insulated the subsurface during the thaw initiation period. We have developed and released an integrated code that couples the numerical software ATS to the calibration software PEST. The numerical model can be further used to determine the impacts of climate change on permafrost degradation.

Calibration

Efficient First-Order Algorithms for Large-Scale, Non-Smooth Maximum Entropy Models with Application to Wildfire Science

Maximum entropy (MaxEnt) models are a class of statistical models that use the maximum entropy principle to estimate probability distributions from data. Due to the size of modern data sets, MaxEnt models need efficient optimization algorithms to scale well for big data applications. State-of-the-art algorithms for MaxEnt models, however, were not originally designed to handle big data sets; these algorithms either rely on technical devices that may yield unreliable numerical results, scale poorly, or require smoothness assumptions that many practical MaxEnt models lack. In this paper, we present novel optimization algorithms that overcome the shortcomings of state-of-the-art algorithms for training large-scale, non-smooth MaxEnt models. Our proposed first-order algorithms leverage the Kullback–Leibler divergence to train large-scale and non-smooth MaxEnt models efficiently. For MaxEnt models with discrete probability distribution of n elements built from samples, each containing m features, the stepsize parameter estimation and iterations in our algorithms scale on the order of O(mn) operations and can be trivially parallelized. Moreover, the strong ℓ1 convexity of the Kullback–Leibler divergence allows for larger stepsize parameters, thereby speeding up the convergence rate of our algorithms. To illustrate the efficiency of our novel algorithms, we consider the problem of estimating probabilities of fire occurrences as a function of ecological features in the Western US MTBS-Interagency wildfire data set. Our numerical results show that our algorithms outperform the state of the art by one order of magnitude and yield results that agree with physical models of wildfire occurrence and previous statistical analyses of wildfire drivers.

Physics

Jipole: A Differentiable ipole-based Code for Radiative Transfer in Curved Spacetimes

Recent imaging of supermassive black holes by the Event Horizon Telescope has relied on exhaustive parameter-space searches, matching observations to large, precomputed libraries of theoretical models. As observational data become increasingly precise, the limitations of this computationally expensive approach grow more acute, creating a pressing need for more efficient methods. In this work, we present Jipole, an automatically differentiable (AD), ipole-based code for radiative transfer in curved spacetimes, designed to compute image gradients with respect to underlying model parameters. These gradients quantify how parameter changes—such as the black hole’s spin or the observer’s inclination—affect the image, enabling more efficient parameter estimation and reducing the number of required images. We validate Jipole against ipole in two analytical tests and then compare pixelwise intensity derivatives from AD with those from finite-difference methods. We then demonstrate the utility of these gradients by performing parameter recovery for an analytical model in three increasingly complex cases for the injected image: ideal, blurred, and blurred with added noise. In most cases, high-accuracy fits are obtained in only a few optimization steps, failing only in cases with extremely low signal-to-noise ratios. These results highlight the potential of AD-based methods to accelerate robust, high-fidelity model-data comparisons in current and future black hole imaging efforts.

79 ASTRONOMY AND ASTROPHYSICS

Constraining Cosmology with Simulation-based inference and Optical Galaxy Cluster Abundance

We test the robustness of simulation-based inference (SBI) in the context of cosmological parameter estimation from galaxy cluster counts and masses in simulated optical datasets. We construct ``simulations'' using analytical models for the galaxy cluster halo mass function (HMF) and for the observed richness (number of observed member galaxies) to train and test the SBI method. We compare the SBI parameter posterior samples to those from an MCMC analysis that uses the same analytical models to construct predictions of the observed data vector. The two methods exhibit comparable performance, with reliable constraints derived for the primary cosmological parameters, ($\Omega_m$ and $\sigma_8$), and richness-mass relation parameters. We also perform out-of-domain tests with observables constructed from galaxy cluster-sized halos in the Quijote simulations. Again, the SBI and MCMC results have comparable posteriors, with similar uncertainties and biases. Unsurprisingly, upon evaluating the SBI method on thousands of simulated data vectors that span the parameter space, SBI exhibits worsened posterior calibration metrics in the out-of-domain application. We note that such calibration tests with MCMC is less computationally feasible and highlight the potential use of SBI to stress-test limitations of analytical models, such as in the use for constructing models for inference with MCMC.

79 ASTRONOMY AND ASTROPHYSICS

Emulator-based Bayesian calibration of a subglacial drainage model

Subglacial drainage models, often motivated by the relationship between hydrology and ice flow, sensitively depend on numerous unconstrained parameters. We explore using borehole water-pressure time series to calibrate the uncertain parameters of a popular subglacial drainage model, taking a Bayesian perspective to quantify the uncertainty in parameter estimates and in the calibrated model predictions. To reduce the computation time associated with Markov Chain Monte Carlo sampling, we construct a fast Gaussian process emulator to stand in for the subglacial drainage model. We first carry out a calibration experiment using synthetic observations consisting of model simulations with hidden parameter values as a demonstration of the method. Using real borehole water pressures measured in western Greenland, we find meaningful constraints on four of the eight model parameters and a factor-of-three reduction in uncertainty of the calibrated model predictions. These experiments illustrate Gaussian process-based Bayesian inference as a useful tool for calibration and uncertainty quantification of complex glaciological models using field data. However, significant differences between the calibrated model and the borehole data suggest that structural limitations of the model, rather than poorly constrained parameters or computational cost, remain the most important constraint on subglacial drainage modelling.

58 GEOSCIENCES

The Profiled Feldman-Cousins Method for Confidence Interval Construction for the Nova 3-Flavor Oscillation Analysis

The small interaction cross-section of neutrinos makes experimental neutrino physics particularly responsive to technological advancements. A significant development leveraged by the NOvA experiment is large-scale parallel processing, enabling novel computational approaches to longstanding experimental challenges. Central to managing the resulting high-throughput data is NOvA’s implementation of the Freight Train model, designed for efficient data production and handling.This dissertation details the methodology and execution of the NOvA 2024 3-Flavor Oscillation Analysis, supported by a comprehensive dataset spanning ten years. It emphasizes frequentist results refined through the Feldman-Cousins (FC) technique, specifically addressing confidence interval corrections in parameter estimation. The computational intensity associated with Feldman-Cousins arises from extensive Monte Carlo simulations, which were substantially mitigated through parallel computing on the Perlmutter supercomputer at the National Energy Research Scientific Computing Center (NERSC), employing the MPI framework.To further enhance computational efficiency, an Importance Sampling method is introduced and evaluated, demonstrating significant potential to reduce complexity, particularly in exploring extreme parameter space regions. This thesis presents both the successful application of advanced computational resources and the development of sophisticated statistical techniques, aiming to enhance the precision and scope of neutrino oscillation analyses.

Dye ajdye11190@gmail.com, Andrew Joseph [Mississip

Videos, photos, and AI-derived grain size data associated with “High-throughput AI Video Surveys Enable Reproducible Multiscale Sediment Size Mapping, with Implications for Hydrobiogeochemical Parameterization”

NOTE: The manuscript associated with this data package is currently in review. The data may be revised based on reviewer feedback. Upon manuscript acceptance, this data package will be updated with the final dataset and additional metadata. This data package is associated with the manuscript “High-throughput AI Video Surveys Enable Reproducible Multiscale Sediment Size Mapping, with Implications for Hydrobiogeochemical Parameterization” under review. This data package includes five data types: 1) raw photos and videos from drone survey and walking smartphone surveys; 2) images derived from raw videos; 3) manual labeling of reference scales; 4) metadata for all images and photo resolution derived from artificial intelligence (AI) models or manual labels, 5) grain size data obtained from AI models for all photos, 6) metadata and grain size data after quality control, 7) summaries of sample efficiency for all data, and 8) computational fluid dynamics (CFD) data used to support hydro-biogeochemical (HBGC) parameter estimation. Such data is used to 1) demonstrate significant improvements in accuracy, efficiency, and quality control for grain size data collection with the help of AI models, 2) study the spatial heterogeneity of grain size and observation reproducibility based on tens of thousands of data points generated by the AI models, and 3) evaluate the impacts of grain size heterogeneity on key HBGC parameters across sediment-to-reach and hourly-to-yearly scales. In particular, the data package contains 116 folders and 179696 files. The files include 41 videos in .mov format, 64047 photos in .jpg format, 13541 video-derived photos in .png format, 12747 segmentation mask data in .tif format, 12747 segmentation data in .json format, 24771 .csv files that with metadata and grain size for each individual photo as well as water depth and velocity data from CFD and observation, 51791 .txt files of raw AI predicted labels, and 11 flight record data in .srt format. The summary for all metadata and grain size statistics information is included in “Scales_V3_NG.csv” and “Statistics_V3_NG.csv”. The summary for data that pass data quality control (QC) level 0-2 is included in “QCStatistics_V3_NG.csv”. The QC level 0 represents photos whose photo resolution is positive, excluding photos that miss reference scale. The QC level 1 means reference scale circularity uncertainty is less than 5% for smartphone images while representing photo resolution is larger than 0.44 mm/pixel for drone images. The QC level 2 means excluding photos whose grain number is less than 100, a minimum number of grains recommended by classic literature. The summary for each video’s name, length, frame rates, survey area, grain number, survey efficiency, etc. can be found in “QCSummary_V3_NG.csv”. The summary for site name, GPS coordinates, and number of images at each site can be found in “SitesSummary_V3_*.csv” files. Overall computational efficiency summary is reported in Table 4 of accompanying manuscript. Additionally, the nitrate concentration data used in this work was downloaded from an existing dataset published on ESS-DIVE (Boat-Dragged Sensor Hanford Reach.csv; Conner A. et al., 2020). We thank the United States Forest Service, Washington Department of Fish and Wildlife, Washington Department of Natural Resources, Cowiche Canyon Conservatory, Port of Benton, and the Confederated Tribes and Bands of the Yakama Nation for access to field locations where the data were collected. We also thank the Yakama Nation Tribal Council and Yakama Nation Fisheries for working with us to facilitate data collection and optimization of data usage according to their values and worldview.

54 ENVIRONMENTAL SCIENCES

Variance-Reduced Accelerated First-Order Methods: Central Limit Theorems and Confidence Statements

In this paper, we consider a strongly convex stochastic optimization problem and propose three classes of variable sample-size stochastic first-order methods: (i) the standard stochastic gradient descent method, (ii) its accelerated variant, and (iii) the stochastic heavy-ball method. In each scheme, the exact gradients are approximated by averaging across an increasing batch size of sampled gradients. We prove that when the sample size increases at a geometric rate, the generated estimates converge in mean to the optimal solution at an analogous geometric rate for schemes (i)–(iii). Based on this result, we provide central limit statements, whereby it is shown that the rescaled estimation errors converge in distribution to a normal distribution with the associated covariance matrix dependent on the Hessian matrix, the covariance of the gradient noise, and the step length. If the sample size increases at a polynomial rate, we show that the estimation errors decay at a corresponding polynomial rate and establish the associated central limit theorems (CLTs). Under certain conditions, we discuss how both the algorithms and the associated limit theorems may be extended to constrained and nonsmooth regimes. As a result, we provide an avenue to construct confidence regions for the optimal solution based on the established CLTs and test the theoretical findings on a stochastic parameter estimation problem.

Lei, Jinlong