scholarly journals Intraday Load Forecasts with Uncertainty

2019 ◽  
Author(s):  
David Kozak ◽  
Scott Holladay ◽  
Gregory Fasshauer
Keyword(s):  
Gaussian Processes ◽  
Positive Definite ◽  
Weather Data ◽  
Model Combination ◽  
Positive Definite Kernel ◽  
Modeling Process ◽  
Important Benefit ◽  
Uncertainty Estimates ◽  
Comprehensive Framework ◽  
Point Forecast

We provide a comprehensive framework for forecasting five minute load using Gaussian processes with a positive definite kernel specifically designed for load forecasts. Gaussian processes are probabilistic, enabling us to draw samples from a posterior distribution and provide rigorous uncertainty estimates to complement the point forecast, an important benefit for forecast consumers. As part of the modeling process, we discuss various methods for dimension reduction and explore their use in effectively incorporating weather data to the load forecast. We provide guidance for every step of the modeling process, from model construction through optimization and model combination. We provide results on data from the PJMISO for various periods in 2018. The process is transparent, mathematically motivated, and reproducible. The resulting model provides a probability density of five-minute forecasts for 24 hours.

scholarly journals Intraday Load Forecasts with Uncertainty

Energies ◽  
2019 ◽  
Vol 12 (10) ◽  
pp. 1833
Author(s):  
David Kozak ◽  
Scott Holladay ◽  
Gregory E. Fasshauer
Keyword(s):  
Gaussian Processes ◽  
Electricity Market ◽  
Weather Data ◽  
Model Combination ◽  
Positive Definite Kernel ◽  
Modeling Process ◽  
Important Benefit ◽  
Uncertainty Estimates ◽  
Comprehensive Framework ◽  
Point Forecast

We provide a comprehensive framework for forecasting five minute load using Gaussian processes with a positive definite kernel specifically designed for load forecasts. Gaussian processes are probabilistic, enabling us to draw samples from a posterior distribution and provide rigorous uncertainty estimates to complement the point forecast, an important benefit for forecast consumers. As part of the modeling process, we discuss various methods for dimension reduction and explore their use in effectively incorporating weather data to the load forecast. We provide guidance for every step of the modeling process, from model construction through optimization and model combination. We provide results on data from the largest deregulated wholesale U.S. electricity market for various periods in 2018. The process is transparent, mathematically motivated, and reproducible. The resulting model provides a probability density of five minute forecasts for 24 h.

scholarly journals Harmonic analysis of network systems via kernels and their boundary realizations

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Palle Jorgensen ◽  
James Tian
Keyword(s):  
Gaussian Processes ◽  
Reproducing Kernel ◽  
Geometric Analysis ◽  
Iterated Function Systems ◽  
Positive Definite ◽  
Positive Definite Kernels ◽  
Network Graph ◽  
Network Systems ◽  
Positive Definite Kernel ◽  
Measure Spaces

<p style='text-indent:20px;'>With view to applications to harmonic and stochastic analysis of infinite network/graph models, we introduce new tools for realizations and transforms of positive definite kernels (p.d.) <inline-formula><tex-math id="M1">\begin{document}$ K $\end{document}</tex-math></inline-formula> and their associated reproducing kernel Hilbert spaces. With this we establish two kinds of factorizations: (i) Probabilistic: Starting with a positive definite kernel <inline-formula><tex-math id="M2">\begin{document}$ K $\end{document}</tex-math></inline-formula> we analyze associated Gaussian processes <inline-formula><tex-math id="M3">\begin{document}$ V $\end{document}</tex-math></inline-formula>. Properties of the Gaussian processes will be derived from certain factorizations of <inline-formula><tex-math id="M4">\begin{document}$ K $\end{document}</tex-math></inline-formula>, arising as a covariance kernel of <inline-formula><tex-math id="M5">\begin{document}$ V $\end{document}</tex-math></inline-formula>. (ii) Geometric analysis: We discuss families of measure spaces arising as boundaries for <inline-formula><tex-math id="M6">\begin{document}$ K $\end{document}</tex-math></inline-formula>. Our results entail an analysis of a partial order on families of p.d. kernels, a duality for operators and frames, optimization, Karhunen–Loève expansions, and factorizations. Applications include a new boundary analysis for the Drury-Arveson kernel, and for certain fractals arising as iterated function systems; and an identification of optimal feature spaces in machine learning models.</p>

scholarly journals Machine Learning Emulation of Spatial Deposition from a Multi-Physics Ensemble of Weather and Atmospheric Transport Models

Atmosphere ◽  
2021 ◽  
Vol 12 (8) ◽  
pp. 953
Author(s):  
Nipun Gunawardena ◽  
Giuliana Pallotta ◽  
Matthew Simpson ◽  
Donald D. Lucas
Keyword(s):  
Machine Learning ◽  
Logistic Regression ◽  
Initial Conditions ◽  
Atmospheric Transport ◽  
Hazardous Materials ◽  
Atmospheric Model ◽  
Weather Data ◽  
Uncertainty Estimates ◽  
Large Ensembles ◽  
Physics Ensemble

In the event of an accidental or intentional hazardous material release in the atmosphere, researchers often run physics-based atmospheric transport and dispersion models to predict the extent and variation of the contaminant spread. These predictions are imperfect due to propagated uncertainty from atmospheric model physics (or parameterizations) and weather data initial conditions. Ensembles of simulations can be used to estimate uncertainty, but running large ensembles is often very time consuming and resource intensive, even using large supercomputers. In this paper, we present a machine-learning-based method which can be used to quickly emulate spatial deposition patterns from a multi-physics ensemble of dispersion simulations. We use a hybrid linear and logistic regression method that can predict deposition in more than 100,000 grid cells with as few as fifty training examples. Logistic regression provides probabilistic predictions of the presence or absence of hazardous materials, while linear regression predicts the quantity of hazardous materials. The coefficients of the linear regressions also open avenues of exploration regarding interpretability—the presented model can be used to find which physics schemes are most important over different spatial areas. A single regression prediction is on the order of 10,000 times faster than running a weather and dispersion simulation. However, considering the number of weather and dispersion simulations needed to train the regressions, the speed-up achieved when considering the whole ensemble is about 24 times. Ultimately, this work will allow atmospheric researchers to produce potential contamination scenarios with uncertainty estimates faster than previously possible, aiding public servants and first responders.

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