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Results for “Order restricted regression”

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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Qualitative trend analysis based on a mixed-integer representation

Shape constrained spline fitting is a useful method to impose prior knowledge onto flexible semi-parametric models during parameter estimation. Most typically, the function shape is imposed through order restrictions on the regression coefficients. The intended shape is considered known or selected based on heuristic rules. In this study, we present a method to estimate the optimal set of order restrictions to segment a univariate data series into episodes with distinct shapes. This is also known as the qualitative trend analysis (QTA) problem. The obtained solution uses a trade-off between lack-of-fit and model complexity. Further, our practical implementation takes inspiration from the generalized order restricted information criterion (GORIC) for inequality-constrained model selection. From this, one learns (a) that QTA can be formulated as a mixed-integer quadratic program (MIQP) and (b) that the newly proposed mixed order restricted information criterion (MORIC) enables optimal segmentation. This is illustrated through didactic case studies.

42 ENGINEERING↗
DOE OSTI2022

Photometry on Structured Backgrounds: Local Pixel-wise Infilling by Regression

Photometric pipelines struggle to estimate both the flux and flux uncertainty for stars in the presence of structured backgrounds such as filaments or clouds. However, it is exactly stars in these complex regions that are critical to understanding star formation and the structure of the interstellar medium. We develop a method, similar to Gaussian process regression, which we term local pixel-wise infilling (LPI). Using a local covariance estimate, we predict the background behind each star and the uncertainty of that prediction in order to improve estimates of flux and flux uncertainty. We show the validity of our model on synthetic data and real dust fields. We further demonstrate that the method is stable even in the crowded field limit. While we focus on optical-IR photometry, this method is not restricted to those wavelengths. We apply this technique to the 34 billion detections in the second data release of the Dark Energy Camera Plane Survey. In addition to removing many >3σ outliers and improving uncertainty estimates by a factor of ~2–3 on nebulous fields, we also show that our method is well behaved on uncrowded fields. The entirely post-processing nature of our implementation of LPI photometry allows it to easily improve the flux and flux uncertainty estimates of past as well as future surveys.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Impacts of COVID-19 related stay-at-home restrictions on residential electricity use and implications for future grid stability

“Stay-at-home” orders and other health precautions enacted during the COVID-19 pandemic have led to substantial changes in residential electricity usage. Here, we conduct a case study to analyze data from 390 apartments in New York City (NYC) to examine the impacts of two key drivers of residential electricity usage: COVID-19 case-loads and the outdoor temperature. We develop a series of regression models to predict two characteristics of residential electricity usage on weekdays: The average occupied apartment’s consumption (kWh) over a 9am-5pm window and the hourly peak demand (Watt) over a 12pm-5pm window. Via a Monte Carlo simulation, we forecast the two usage characteristics under a possible scenario in which stay-at-home orders in NYC, or a similar metropolitan region, coincide with warm summer weather. Under the scenario, the 9am-5pm residential electricity usage on weekdays is predicted to be 15% – 24% higher than under prior, pre-pandemic conditions. This could lead to substantially higher utility costs for residents. Additionally, we predict that the residential hourly peak demand between 12pm and 5pm on weekdays could be 35% – 53% higher than that under pre-pandemic conditions. We conclude that the projected increase in peak demand - which might arise if stay-at-home guidelines coincided with hot weather conditions - could pose grid management challenges, especially for residential feeders. We also note that, if there is a longer lasting shift towards work and study-from-home, utilities will have to rethink load profile considerations. The applications of our predictive models to managing future smart-grid technology are also highlighted.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2025

Toward the Analytic Bootstrap of Energy Correlators

In this paper, we present a framework for the analytic bootstrap of three-point energy correlators, a crucial observable in N = 4 N=4 super Yang-Mills theory and quantum chromodynamics (QCD). Our approach combines spherical contour techniques, general physical constraints such as pole cancellations, and power correction data in the singular limits to determine its analytic expression. In contrast to previous bootstrap studies restricted to scattering amplitudes for supersymmetric theories, our framework makes use of the properties of Feynman integrals, marking a significant step toward bootstrapping realistic QCD observables. Using this method, we derive analytic expressions for leading-order three-point energy correlators with equal and unequal energy weights, where the latter are crucial ingredients for projected N N-point energy correlators. We also apply the recently developed technique of analytic regression with lattice reduction as a way to bypass needing explicit expressions for the singular limits. Bridging theoretical advances in scattering amplitudes with the renewed interest in weighted cross-sections, our work opens the door to precision tests of QCD dynamics through analytic event-shape predictions.

Gong, Jianyu [State Key Laboratory]↗
DOE OSTI2026

Toward the analytic bootstrap of energy correlators

In this paper, we present a framework for the analytic bootstrap of three-point energy correlators, a crucial observable in $\mathcal{N}$ = 4 super Yang-Mills theory and quantum chromodynamics (QCD). Our approach combines spherical contour techniques, general physical constraints such as pole cancellations, and power correction data in the singular limits to determine its analytic expression. In contrast to previous bootstrap studies restricted to scattering amplitudes for supersymmetric theories, our framework makes use of the properties of Feynman integrals, marking a significant step toward bootstrapping realistic QCD observables. Using this method, we derive analytic expressions for leading-order three-point energy correlators in the multi-collinear limit with equal and unequal energy weights, where the latter are crucial ingredients for projected N -point energy correlators. We also apply the recently developed technique of analytic regression with lattice reduction as a way to bypass needing explicit expressions for the singular limits. Bridging theoretical advances in scattering amplitudes with the renewed interest in weighted cross-sections, our work opens the door to precision tests of QCD dynamics through analytic event-shape predictions.

jet substructure↗
DOE OSTI2022

Cost function for low-dimensional manifold topology assessment

Abstract In reduced-order modeling, complex systems that exhibit high state-space dimensionality are described and evolved using a small number of parameters. These parameters can be obtained in a data-driven way, where a high-dimensional dataset is projected onto a lower-dimensional basis. A complex system is then restricted to states on a low-dimensional manifold where it can be efficiently modeled. While this approach brings computational benefits, obtaining a good quality of the manifold topology becomes a crucial aspect when models, such as nonlinear regression, are built on top of the manifold. Here, we present a quantitative metric for characterizing manifold topologies. Our metric pays attention to non-uniqueness and spatial gradients in physical quantities of interest, and can be applied to manifolds of arbitrary dimensionality. Using the metric as a cost function in optimization algorithms, we show that optimized low-dimensional projections can be found. We delineate a few applications of the cost function to datasets representing argon plasma, reacting flows and atmospheric pollutant dispersion. We demonstrate how the cost function can assess various dimensionality reduction and manifold learning techniques as well as data preprocessing strategies in their capacity to yield quality low-dimensional projections. We show that improved manifold topologies can facilitate building nonlinear regression models.

42 ENGINEERING↗