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N-particle irreducible actions for stochastic fluids
We construct one- and two-particle irreducible (1PI and 2PI) effective actions for the stochastic fluid dynamics of a conserved density undergoing diffusive motion. We compute the 1PI action in one-loop order and the 2PI action in two-loop approximation. We derive a set of Schwinger-Dyson equations and regularize the resulting equations using Pauli-Villars fields. We numerically solve the Schwinger-Dyson equations for a non-critical fluid. We find that higher-loop effects summed by the Schwinger-Dyson renormalize the non-linear coupling. We also find indications of a diffuson-cascade, the appearance of n-loop correction with smaller and smaller exponential suppression.
Generating realistic building electrical load profiles through the Generative Adversarial Network (GAN)
Building electrical load profiles can improve understanding of building energy efficiency, demand flexibility, and building-grid interactions. Current approaches to generating load profiles are time-consuming and not capable of reflecting the dynamic and stochastic behaviors of real buildings; some approaches also trigger data privacy concerns. In this study, we proposed a novel approach for generating realistic electrical load profiles of buildings through the Generative Adversarial Network (GAN), a machine learning technique that is capable of revealing an unknown probability distribution purely from data. The proposed approach has three main steps: (1) normalizing the daily 24-hour load profiles, (2) clustering the daily load profiles with the k-means algorithm, and (3) using GAN to generate daily load profiles for each cluster. The approach was tested with an open-source database – the Building Data Genome Project. We validated the proposed method by comparing the mean, standard deviation, and distribution of key parameters of the generated load profiles with those of the real ones. The KL divergence of the generated and real load profiles are within 0.3 for majority of parameters and clusters. Additionally, results showed the load profiles generated by GAN can capture not only the general trend but also the random variations of the actual electrical loads in buildings. We report the proposed GAN approach can be used to generate building electrical load profiles, verify other load profile generation models, detect changes to load profiles, and more importantly, anonymize smart meter data for sharing, to support research and applications of grid-interactive efficient buildings.
Time irreversibility as an indicator of approaching tipping points in Earth subsystems
With shifting environmental trends, many Earth system elements may be poised to undergo critical transitions or ‘tipping’. Reliable anticipation of these tipping elements is vital to inform policy decisions. Many of the current methods for tipping point detection are based on loss of resilience or ‘critical slowdown’ of the system as it approaches a tipping point. However, these methods are prone to false alarms; the detected slowdown may be an artifact of nonstationary noise unrelated to tipping behavior. Here, we explore the efficacy of early warning signs based on a nonequilibrium thermodynamics framework. The model-free detection method relies on the increased intrinsic time-irreversibility due to detailed balance breaking, preceding the onset of tipping or instabilities. We demonstrate that these EWSs are effective for tipping point detection and robust against false alarms due to nonstationary noise, using idealized models for two key elements of the Earth system that are prone to tipping: the Atlantic Meridional Overturning Circulation and Arctic sea-ice loss.
Vehicle to Grid Frequency Regulation Capacity Optimal Scheduling for Battery Swapping Station Using Deep Q-Network
Battery swapping stations (BSSs) are ideal candidates for fast frequency regulation services (FFRS) due to their large battery stock capacity. In addition, BSSs can precharge batteries for customers and the batteries that are not in charging can provide a stable regulation capacity to the market. However, uncertainties, such as ACE signals and the EV per-hour visit counts, introduce stochastic nonlinear dynamics into the operation of a BSS-based FFRS. Currently, there is no quantification method to ensure its optimal economical operation. To close this gap, in this article, we propose a novel deep Q-learning-based FFRS capacity dynamic scheduling strategy. This method can autonomously schedule the hourly regulation capacity in real time to maximize the BSSx0027;s revenue for providing FFRS. Case studies using real-world data verify the efficacy of the proposed work.
Exponential Decay of Sensitivity in Graph-Structured Nonlinear Programs
We study solution sensitivity for nonlinear programs (NLPs) whose structures are induced by graphs. These NLPs arise in many applications such as dynamic optimization, stochastic optimization, optimization with partial differential equations, and network optimization. We illustrate that for a given pair of nodes, the sensitivity of the primal-dual solution at one node against a data perturbation at the other node decays exponentially with respect to the distance between these two nodes on the graph. In other words, the solution sensitivity decays as one moves away from the perturbation point. This result, which we call exponential decay of sensitivity, holds under the strong second-order sufficiency condition and the linear independence constraint qualification. We also present conditions under which the decay rate remains uniformly bounded; this allows us to characterize the sensitivity behavior of NLPs defined over subgraphs of infinite graphs. The theoretical developments are illustrated with numerical examples.
A Bayesian Approach to Regional Decadal Predictability: Sparse Parameter Estimation in High-Dimensional Linear Inverse Models of High-Latitude Sea Surface Temperature Variability
Stochastic reduced models are an important tool in climate systems whose many spatial and temporal scales cannot be fully discretized or underlying physics may not be fully accounted for. One form of reduced model, the linear inverse model (LIM), has been widely used for regional climate predictability studies—typically focusing more on tropical or midlatitude studies. However, most LIM fitting techniques rely on point estimation techniques deriving from fluctuation–dissipation theory. In this methodological study we explore the use of Bayesian inference techniques for LIM parameter estimation of sea surface temperature (SST), to quantify the skillful decadal predictability of Bayesian LIM models at high latitudes. We show that Bayesian methods, when compared to traditional point estimation methods for LIM-type models, provide better calibrated probabilistic skill, while simultaneously providing better point estimates due to the regularization effect of the prior distribution in high-dimensional problems. We compare the effect of several priors, as well as maximum likelihood estimates, on 1) estimating parameter values on a perfect model experiment and 2) producing calibrated 1-yr SST anomaly forecast distributions using a preindustrial control run of the Community Earth System Model (CESM). Finally, we employ a host of probabilistic skill metrics to determine the extent to which an LIM can forecast SST anomalies at high latitudes. We find that the choice of prior distribution has an appreciable impact on estimation outcomes, and priors that emphasize physically relevant properties enhance the model’s ability to capture variability of SST anomalies.
NREL CITIES Support (CRADA CRD-14-00558 Final Report)
The Technical University of Denmark has received a Grant from the Danish Council for Strategic Research for the project "CITIES - Centre for IT-Intelligent Energy Systems in Cities", a strategic research centre, which involves industrial partners and universities. The Alliance for Sustainable Energy, LLC will participate with DTU as an industrial partner in "CITIES" under this Cooperative Research and Development Agreement (CRADA). The Centre for IT based Intelligent Energy Systems in Cities (CITIES) Project is a Danish national research center focused on work in building short-term operational integrated energy system models that feed longer term plam1ing models, considering the spatio-temporal variations, interactions, dynamics and stochastics in the energy system, from production to consumption. CITIES will harness the extensive expertise and experience of its industrial and academic partners to conduct meaningful research with tangible outputs, including a roadmap to a fossil free future. Decision support tools will be developed to inform stakeholders of the impact of investment, control and policy measures and to identify further opportunities for energy system efficiency. Dissemination and transferring knowledge is a key value to this CRADA, and the use of results by Danish policymakers, industry and society is vital. All participants in the Centre for IT based Intelligent Energy Systems in Cities (CITIES) Project are therefore encouraged to use all means to communicate their findings to society. Wherever possible, and compatible with applicable intellectual property regulations, publications should be produced and disseminated under Open Science, Data, Source and Access principles.
Stochastic Optimization of Power System Dynamics for Grid Resilience Presentation.
Abstract not provided.
Understanding and Controlling Photoexcited Molecules in Complex Environments (Final Technical Report)
Predicting the outcome of a photochemical reaction is complicated by factors outside the scope of tradition theoretical chemistry. On such small scales, fluctuations of the environment render outcomes stochastic, nonadiabatic dynamics blur the separation between nuclear and electronic motion, and ultrafast relaxation renders typical assumptions of equilibrium inappropriate. This project aimed to elucidate and control nonadiabatic molecular dynamics in condensed phases. We developed accurate, efficient simulation tools to study irreversible molecular processes computational across a range of scales. We applied these methodological advances to study electron transfer under exotic conditions where spin and topology opened new pathways for reactivity. We also brought these ideas to bare on light harvesting systems, where energy and charge transport are coupled, and where long lifetimes can be deleterious to function. These advances helped to establish general principles for chemical efficiency and guide the design of nanoscale energy materials, molecular machines, and related technologies.
Stochastic Optimization of Power System Dynamics for Grid Resilience.
Abstract not provided.
On the separation theorem of stochastic control.
Optimal control and filtering problem for stochastic linear dynamic system reduced to independent equations
Stochastic models of cover class dynamics
Investigations related to satellite remote sensing of vegetation have been concerned with questions of signature identification and extension, cover inventory accuracy, and change detection and monitoring. Attention is given to models of ecological succession, present directions in successional modeling and analysis, nondynamic spatial models, issues in the analysis of spatial data, and aspects of spatial modeling. Issues in time-series analysis are considered along with dynamic spatial models, and problems of model specification and identification.
Supercomputer optimizations for stochastic optimal control applications
Supercomputer optimizations for a computational method of solving stochastic, multibody, dynamic programming problems are presented. The computational method is valid for a general class of optimal control problems that are nonlinear, multibody dynamical systems, perturbed by general Markov noise in continuous time, i.e., nonsmooth Gaussian as well as jump Poisson random white noise. Optimization techniques for vector multiprocessors or vectorizing supercomputers include advanced data structures, loop restructuring, loop collapsing, blocking, and compiler directives. These advanced computing techniques and superconducting hardware help alleviate Bellman's curse of dimensionality in dynamic programming computations, by permitting the solution of large multibody problems. Possible applications include lumped flight dynamics models for uncertain environments, such as large scale and background random aerospace fluctuations.
Multifractal characterizations of nonstationarity and intermittency in geophysical fields: Observed, retrieved, or simulated
Geophysical data rarely show any smoothness at any scale, and this often makes comparison with theoretical model output difficult. However, highly fluctuating signals and fractal structures are typical of open dissipative systems with nonlinear dynamics, the focus of most geophysical research. High levels of variability are excited over a large range of scales by the combined actions of external forcing and internal instability. At very small scales we expect geophysical fields to be smooth, but these are rarely resolved with available instrumentation or simulation tools; nondifferentiable and even discontinuous models are therefore in order. We need methods of statistically analyzing geophysical data, whether measured in situ, remotely sensed or even generated by a computer model, that are adapted to these characteristics. An important preliminary task is to define statistically stationary features in generally nonstationary signals. We first discuss a simple criterion for stationarity in finite data streams that exhibit power law energy spectra and then, guided by developments in turbulence studies, we advocate the use of two ways of analyzing the scale dependence of statistical information: singular measures and qth order structure functions. In nonstationary situations, the approach based on singular measures seeks power law behavior in integrals over all possible scales of a nonnegative stationary field derived from the data, leading to a characterization of the intermittency in this (gradient-related) field. In contrast, the approach based on structure functions uses the signal itself, seeking power laws for the statistical moments of absolute increments over arbitrarily large scales, leading to a characterization of the prevailing nonstationarity in both quantitative and qualitative terms. We explain graphically, step by step, both multifractal statistics which are largely complementary to each other. The geometrical manifestations of nonstationarity and intermittency, 'roughness' and 'sparseness', respectively, are illustrated and the associated analytical (differentiability and continuity) properties are discussed. As an example, the two techniques are applied to a series of recent measurements of liquid water distributions inside marine stratocumulus decks; these are found to be multifractal over scales ranging from approximately 60 m to approximately 60 km. Finally, we define the 'mean multifractal plane' and show it to be a simple yet comprehensive tool with many applications including data intercomparison, (dynamical or stochastic) model and retrieval validations.
Dynamic Theory of Relativistic Electrons Stochastic Heating by Whistler Mode Waves with Application to the Earth Magnetosphere
In the Hamiltonian approach an electron motion in a coherent packet of the whistler mode waves propagating along the direction of an ambient magnetic field is studied. The physical processes by which these particles are accelerated to high energy are established. Equations governing a particle motion by group symmetries of the problem were transformed in to a closed pair of nonlinear difference equations. The solutions of these equations have shown there exists the energetic threshold below that the electron motion is regular, and when the initial energy is above the threshold an electron moves stochastically. It is proved that the upper boundary of particle stochastic heating is conditioned by intrinsic property of the particle chaotic motion. Particle energy spectra and pitch angle electron scattering are described by the Fokker-Planck-Kolmogorov equations. It is shown that significant pitch angle diffusion occurs for the Earth radiation belt electrons with energies from a few keV up to a few MeV.
Dynamic Theory of Relativistic Electrons Stochastic Heating by Whistler Mode Waves with Application to the Earth Magnetosphere
In the Hamiltonian approach an electron motion in a coherent packet of the whistler mode waves propagating along the direction of an ambient magnetic field is studied. The physical processes by which these particles are accelerated to high energy are established. Equations governing a particle motion were transformed in to a closed pair of nonlinear difference equations. The solutions of these equations have shown there exists the energetic threshold below that the electron motion is regular, and when the initial energy is above the threshold an electron moves stochastically. Particle energy spectra and pitch angle electron scattering are described by the Fokker-Planck-Kolmogorov equations. Calculating the stochastic diffusion of electrons due to a spectrum of whistler modes is presented. The parametric dependence of the diffusion coefficients on the plasma particle density, magnitude of wave field, and the strength of magnetic field is studies. It is shown that significant pitch angle diffusion occurs for the Earth radiation belt electrons with energies from a few keV up to a few MeV.