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At least 37 records · Page 2

Data-driven probability concentration and sampling on manifold

A new methodology is proposed for generating realizations of a random vector with values in a finite-dimensional Euclidean space that are statistically consistent with a dataset of observations of this vector. The probability distribution of this random vector, while a priori not known, is presumed to be concentrated on an unknown subset of the Euclidean space. A random matrix is introduced whose columns are independent copies of the random vector and for which the number of columns is the number of data points in the dataset. The approach is based on the use of (i) the multidimensional kernel-density estimation method for estimating the probability distribution of the random matrix, (ii) a MCMC method for generating realizations for the random matrix, (iii) the diffusion-maps approach for discovering and characterizing the geometry and the structure of the dataset, and (iv) a reduced-order representation of the random matrix, which is constructed using the diffusion-maps vectors associated with the first eigenvalues of the transition matrix relative to the given dataset. The convergence aspects of the proposed methodology are analyzed and a numerical validation is explored through three applications of increasing complexity. The proposed method is found to be robust to noise levels and data complexity as well as to the intrinsic dimension of data and the size of experimental datasets. Both the methodology and the underlying mathematical framework presented in this paper contribute new capabilities and perspectives at the interface of uncertainty quantification, statistical data analysis, stochastic modeling and associated statistical inverse problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Data-Conforming Data-Driven Control: Avoiding Premature Generalizations Beyond Data

Data-driven and adaptive control approaches face the problem of introducing sudden distributional shifts beyond the distribution of data encountered during learning. Therefore, they are prone to invalidating the very assumptions used in their own construction. This is due to the linearity of the underlying system, inherently assumed and formulated in most data-driven control approaches, which may falsely generalize the behavior of the system beyond the behavior experienced in the data. This article seeks to mitigate these problems by enforcing consistency of the newly designed closed-loop systems with data and slowing down any distributional shifts in the joint state-input space. This is achieved through incorporating affine regularization terms and linear matrix inequality constraints to data-driven approaches, resulting in convex semi-definite programs that can be efficiently solved by standard software packages. We discuss the optimality conditions of these programs and then conclude this article with a numerical example that further highlights the problem of premature generalization beyond data and shows the effectiveness of our proposed approaches in enhancing the safety of data-driven control methods.

97 MATHEMATICS AND COMPUTING↗

AGGREGATE: dAta-driven modelinG preservinG contRollable dEr for outaGe mAnagemenT and rEsiliency (Report for Task 9: Viability of Data-Driven Approach for Outage Management (Deliverable D6))

This technical report is provided to US Department of Energy for progress made on the AGGERGATE project led by the Washington State University. This report is specifically related to the deliverable: ’D6: Technical report discussing the viability of the developed data-driven models and co-simulation architecture for models for operation in a real-world operational setting and the results of Tasks 1 to 8, summarizing the project findings and accomplishments to date’.

42 ENGINEERING↗

Creating Accurate Methane Emission Inventories through Data-Driven Airborne Survey Strategies

Because natural gas emits less carbon than other fossil fuels, it holds promise as a green energy transition fuel. However, the overall carbon footprint of natural gas is significantly elevated by methane emissions that occur during its production and transmission (Cusworth et al. 2022). Methane “super-emitters,” while comprising only about 1% of sites, are responsible for the majority of oil- and gas-sourced methane emissions, making their detection and mitigation critical in reducing the climate impact of natural gas and in meeting national and global sustainability goals (Sherwin et al. 2024). Yet, despite advancements in detection, significant uncertainties remain regarding the size, frequency, and duration distributions of methane emissions (e.g., Frankenberg et al. 2016, Cusworth et al. 2022, Chen, Sherwin et al. 2022, Conrad et al. 2023, Johnson et al. 2023, Sherwin et al. 2024) underscoring the need for comprehensive emissions inventories segmented by basin across the US. Airborne surveys are well-suited for collecting data to build these comprehensive, basin-level inventories because they allow for extensive spatial coverage, and have the spatial resolution, and the sensitivity to pinpoint individual methane sources. As remote sensing technologies enable rapid basin-scale surveys, it is imperative to establish scientifically and statistically robust standards to generate reliable and actionable emissions inventories. Recent work has shown that differences in airborne sampling strategies, detection technologies, and analysis can lead to large differences between survey conclusions if not correctly accounted for (Chen et al. 2024). This elevates the importance of incorporating proper sampling and analysis techniques when designing a methane emissions monitoring campaign to produce accurate results and facilitate cross-study comparisons. In this paper, we describe a survey strategy designed using the latest conclusions from the literature to align results from different aerial surveys. We identify several sampling and analysis principles, including large sample sizes, balanced sampling across oil and gas production, careful survey area definition, and a unified protocol for analysis, to be vital to producing an unbiased estimate of basin-scale emissions. We present results from a Department of Energy-funded project that deployed this survey strategy in two understudied oil and gas- producing regions in the United States: the Haynesville Basin in Texas and Louisiana, and the Woodford Shale in the Anadarko Basin in Oklahoma.

03 NATURAL GAS↗

DeePKS: A Comprehensive Data-Driven Approach toward Chemically Accurate Density Functional Theory

We propose a general machine learning-based framework for building an accurate and widely applicable energy functional within the framework of generalized Kohn–Sham density functional theory. To this end, we develop a way of training self-consistent models that are capable of taking large datasets from different systems and different kinds of labels. Here, we demonstrate that the functional that results from this training procedure gives chemically accurate predictions on energy, force, dipole, and electron density for a large class of molecules. It can be continuously improved when more and more data are available.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Joint physics-based and data-driven time-lapse seismic inversion: Mitigating data scarcity

In carbon capture and sequestration (CCS), developing rapid and effective imaging techniques is crucial for real-time monitoring of the spatial and temporal dynamics of CO 2 propagation during/after injection. With continuing improvements in computational power and data storage, data-driven techniques based on machine learning (ML) have been effectively applied to seismic inverse problems. In particular, ML helps alleviate the ill-posedness and high computational cost of full-waveform inversion (FWI). However, such data-driven inversion techniques require massive high-quality training data sets to ensure prediction accuracy, which hinders their application to time-lapse monitoring of CO 2 sequestration. We propose an efficient “hybrid” time-lapse workflow that combines physics-based FWI and data-driven ML inversion. The scarcity of the available training data is addressed by developing a new data-generation technique with physics constraints. The method is vali dated on a synthetic CO 2 -sequestration model based on the Kimberlina storage reservoir in California. The proposed approach is shown to synthesize a large volume of high-quality, physically realistic training data, which is critically important in accurately characterizing the CO 2 movement in the reservoir. In conclusion, the developed hybrid methodology can also simultaneously predict the variations in velocity and saturation and achieve high spatial resolution in the presence of realistic noise in the data.

58 GEOSCIENCES↗

Data-Driven Chance-Constrained Design of Voltage Droop Control for Distribution Networks: Preprint

This paper addresses the design of local control methods for voltage control in distribution networks with high level of distributed energy resources (DERs). The designed control methods adapt the active and reactive power output of distributed energy resources proportional to the deviation of the local measured voltage magnitudes from a reference voltage, which is referred to as droop control. Thus, the design focuses on determining the droop characteristics which satisfy network-wide voltage magnitude constraints. The uncertainty and variability of DERs renders the design of optimal droop controls very challenging. Hence, this paper proposes chance constraints to limit the risk from intermittent DERs, by designing droop control coefficients that guarantee the satisfaction of network operational constraints with a specific probability. In addition, the proposed approach relies entirely on historical data rather than assuming knowledge of the probability distributions that characterize the uncertainty of DERs. The efficacy of the proposed method is demonstrated on a 37-bus distribution feeder.

chance-constrained optimization↗