Multi-Fidelity Dynamic Line Rating Fusion for System Load Margin Enhancement with Large-Scale Offshore Wind Generations
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Energy↗
Engineering topics
Constantinescu, Emil
Publications and source records attributed to Constantinescu, Emil.
Electron dynamics in extended systems within real-time time-dependent density-functional theory
Due to a beneficial balance of computational cost and accuracy, real-time time-dependent density-functional theory has emerged as a promising first-principles framework to describe electron real-time dynamics. Here we discuss recent implementations around this approach, in particular in the context of complex, extended systems. Results include an analysis of the computational cost associated with numerical propagation and when using absorbing boundary conditions. Here we extensively explore the shortcomings for describing electron–electron scattering in real time and compare to many-body perturbation theory. Modern improvements of the description of exchange and correlation are reviewed. In this work, we specifically focus on the Qb@ll code, which we have mainly used for these types of simulations over the last years, and we conclude by pointing to further progress needed going forward.
2D materials↗
Stability Analysis of Coupled Advection-Diffusion Models with Bulk Interface Condition
Numerical stability is of critical importance in general circulation models because it affects the design of algorithms, time to solution, and computational costs associated with the simulations, which are very expensive in practice. In this paper we extend the stability analysis for ocean-atmosphere coupling proposed in [Zhang et al., J. Sci. Comput. 84, 44(2020)] to a more realistic model that includes horizontal advection. We analyze various time-stepping strategies. We find that advection has a stabilizing effect in scenarios common to climate models when bulk interface condition and explicit flux coupling are used. We also show that our method can be used to study the stability impact of advection for other interface conditions such as Dirichlet-Neumann conditions.
97 MATHEMATICS AND COMPUTING↗
Optimal Experimental Design for Inverse Problems in the Presence of Observation Correlations
Optimal experimental design (OED) is the general formalism of sensor placement and decisions on the data collection strategy for engineered or natural experiments. This problem is prevalent in many critical fields such as battery design, numerical weather prediction, geosciences, environmental and urban studies. State-of-the-art computational methods for experimental design do not accommodate correlation structure in observational errors produced by many expensive-to-operate devices such as X-ray machines, radars, and satellites. Discarding evident data correlations leads to biased results, higher expenses, and waste of valuable resources. We present a general formulation of the OED formalism for model-constrained large-scale Bayesian linear inverse problems, where measurement errors are generally correlated. The proposed approach utilizes the Hadamard product of matrices to formulate the weighted-likelihood, and is valid for both finite as well as infinite-dimensional Bayesian inverse problems. Extensive numerical experiments are carried out for empirical verification of the proposed approach using an advection-diffusion model, where the objective is to optimally place a small set of sensors, under a limited budget, to predict the concentration of a contaminant in a closed and bounded domain.
Correlated observations↗
Efficient high-dimensional variational data assimilation with machine-learned reduced-order models
Abstract. Data assimilation (DA) in geophysical sciences remains the cornerstone of robust forecasts from numerical models. Indeed, DA plays a crucial role in the quality of numerical weather prediction and is a crucial building block that has allowed dramatic improvements in weather forecasting over the past few decades. DA is commonly framed in a variational setting, where one solves an optimization problem within a Bayesian formulation using raw model forecasts as a prior and observations as likelihood. This leads to a DA objective function that needs to be minimized, where the decision variables are the initial conditions specified to the model. In traditional DA, the forward model is numerically and computationally expensive. Here we replace the forward model with a low-dimensional, data-driven, and differentiable emulator. Consequently, gradients of our DA objective function with respect to the decision variables are obtained rapidly via automatic differentiation. We demonstrate our approach by performing an emulator-assisted DA forecast of geopotential height. Our results indicate that emulator-assisted DA is faster than traditional equation-based DA forecasts by 4 orders of magnitude, allowing computations to be performed on a workstation rather than a dedicated high-performance computer. In addition, we describe accuracy benefits of emulator-assisted DA when compared to simply using the emulator for forecasting (i.e., without DA). Our overall formulation is denoted AIEADA (Artificial Intelligence Emulator-Assisted Data Assimilation).
58 GEOSCIENCES↗
A Scalable Space-Time Domain Decomposition Approach for Solving Large Scale Nonlinear Regularized Inverse Ill Posed Problems in 4D Variational Data Assimilation
We address the development of innovative algorithms designed to solve the strong-constraint Four Dimensional Variational Data Assimilation (4DVar DA) problems in large scale applications. We present a space-time decomposition approach which employs the whole domain decomposition, i.e. both along the spacial and temporal direction in the overlapping case, and the partitioning of both the solution and the operator. Starting from the global functional defined on the entire domain, we get to a sort of regularized local functionals on the set of sub domains providing the order reduction of both the predictive and the Data Assimilation models. The algorithm convergence is developed. Performance in terms of reduction of time complexity and algorithmic scalability is discussed on the Shallow Water Equations on the sphere. The number of state variables in the model, the number of observations in an assimilation cycle, as well as numerical parameters as the discretization step in time and in space domain are defined on the basis of discretization grid used by data available at repository Ocean Synthesis/Reanalysis Directory of Hamburg University.
97 MATHEMATICS AND COMPUTING↗
Rethink hydrologic modeling framework with AI integrating multi-processes across scales
The proposed work is to develop a new hydrologic modeling framework that leverages vast amount earth and human system observational data, AI technologies, and data-driven information flows to improve predictability of hydrologic system that involves hydrologic, terrestrial, and biogeochemical processes and their interactions with the human and atmosphere systems.
54 ENVIRONMENTAL SCIENCES↗
A scalable matrix-free spectral element approach for unsteady PDE constrained optimization using PETSc/TAO
In this work, we provide a new approach for the efficient matrix-free application of the transpose of the Jacobian for the spectral element method for the adjoint-based solution of partial differential equation (PDE) constrained optimization. This results in optimizations of nonlinear PDEs using explicit integrators where the integration of the adjoint problem is not more expensive than the forward simulation. Solving PDE constrained optimization problems entails combining expertise from multiple areas, including simulation, computation of derivatives, and optimization. The Portable, Extensible Toolkit for Scientific computation (PETSc) together with its companion package, the Toolkit for Advanced Optimization (TAO), is an integrated numerical software library that contains an algorithmic/software stack for solving linear systems, nonlinear systems, ordinary differential equations, differential algebraic equations, and large-scale optimization problems and, as such, is an ideal tool for performing PDE-constrained optimization. This paper describes an efficient approach in which the software stack provided by PETSc/TAO can be used for large-scale nonlinear time-dependent problems. Time integration can involve a range of high-order methods, both implicit and explicit. The PDE-constrained optimization algorithm used is gradient-based and seamlessly integrated with the simulation of the physical problem.
97 MATHEMATICS AND COMPUTING↗
Stability Analysis of Interface Conditions for Ocean-Atmosphere Coupling
In this paper, we analyze the stability of different coupling strategies for multidomain PDEs that arise in general circulation models used in climate simulations. We focus on fully coupled ocean–atmosphere models that are needed to represent and understand the complicated interactions of these two systems, becoming increasingly important in climate change assessment in recent years. Numerical stability issues typically arise because of different time-stepping strategies applied to the coupled PDE system. In particular, the contributing factors include using large time steps, lack of accurate interface flux, and single-iteration coupling. We investigate the stability of the coupled ocean–atmosphere models for various interface conditions such as the Dirichlet–Neumann condition and the bulk interface condition, which is unique to climate modeling. By analyzing a simplified model, we demonstrate here how the parameterization of the bulk condition and other numerical and physical parameters affect the coupling stability and establish stability conditions for different coupling strategies.
97 MATHEMATICS AND COMPUTING↗
A PETSc Parallel-in-Time Solver based on MGRIT algorithm
We address the development of a modular implementation of the MGRIT (MultiGrid-In-Time) algorithm to solve linear and nonlinear systems that arise from the discretization of evolutionary models with a parallel-in-time approach in the context of the PETSc (the Portable, Extensible Toolkit for Scientific computing) library. Our aim is to give the opportunity of predicting the performance gain achievable when using the MGRIT approach instead of the Time Stepping integrator (TS). To this end, we analyze the performance parameters of the algorithm that provide a-priori the best number of processing elements and grid levels to use to address the scaling of MGRIT, regarded as a parallel iterative algorithm proceeding along the time dimension.
Mele, Valeria↗
Stochastic simulation of predictive space–time scenarios of wind speed using observations and physical model outputs
We propose a statistical space-time model for predicting atmospheric wind speed based on deterministic numerical weather predictions and historical measurements. We consider a Gaussian multivariate space-time framework that combines multiple sources of past physical model outputs and measurements in order to produce a probabilistic wind speed forecast within the prediction window. We illustrate this strategy on wind speed forecasts during several months in 2012 for a region near the Great Lakes in the United States. The results show that the prediction is improved in the mean-squared sense relative to the numerical forecasts as well as in probabilistic scores. Moreover, the samples are shown to produce realistic wind scenarios based on sample spectra and space-time correlation structure.
54 ENVIRONMENTAL SCIENCES↗
Internal variability of a dynamically downscaled climate over North America
This study investigates the internal variability (IV) of a regional climate model, and considers the impacts of horizontal resolution and spectral nudging on the IV. A 16-member simulation ensemble was conducted using the Weather Research Forecasting model for three model configurations. Ensemble members included simulations at spatial resolutions of 50 km and 12 km without spectral nudging and simulations at a spatial resolution of 12 km with spectral nudging. All the simulations were generated over the same domain, which covered much of North America. The degree of IV was measured as the spread between the individual members of the ensemble during the integration period. The IV of the 12 km simulation with spectral nudging was also compared with a future climate change simulation projected by the same model configuration. The variables investigated focus on precipitation and near-surface air temperature. While the IVs show a clear annual cycle with larger values in summer and smaller values in winter, the seasonal IV is smaller for a 50-km spatial resolution than for a 12-km resolution when nudging is not applied. Applying a nudging technique to the 12-km simulation reduces the IV by a factor of two, and produces smaller IV than the simulation at 50 km without nudging. Applying a nudging technique also changes the geographic distributions of IV in all examined variables. The IV is much smaller than the inter-annual variability at seasonal scales for regionally averaged temperature and precipitation. The IV is also smaller than the projected changes in air-temperature for the mid- and late 21st century. However, the IV is larger than the projected changes in precipitation for the mid- and late 21st century.
54 ENVIRONMENTAL SCIENCES↗
Discrete Adjoint Sensitivity Analysis of Hybrid Dynamical Systems With Switching [Discrete Adjoint Sensitivity Analysis of Hybrid Dynamical Systems]
Sensitivity analysis is an important tool for describing power system dynamic behavior in response to parameter variations. It is a central component in preventive and corrective control applications. The existing approaches for sensitivity calculations, namely, finite-difference and forward sensitivity analysis, require a computational effort that increases linearly with the number of sensitivity parameters. In this paper, we investigate, implement, and test a discrete adjoint sensitivity approach whose computational effort is effectively independent of the number of sensitivity parameters. The proposed approach is highly efficient for calculating sensitivities of larger systems and is consistent, within machine precision, with the function whose sensitivity we are seeking. This is an essential feature for use in optimization applications. Moreover, our approach includes a consistent treatment of systems with switching, such as dc exciters, by deriving and implementing the adjoint jump conditions that arise from state-dependent and time-dependent switchings. The accuracy and the computational efficiency of the proposed approach are demonstrated in comparison with the forward sensitivity analysis approach. In conclusion, this paper focuses primarily on the power system dynamics, but the approach is general and can be applied to hybrid dynamical systems in a broader range of fields.
42 ENGINEERING↗
Efficient Adjoint Computation of Hybrid Systems of Differential Algebraic Equations with Applications in Power Systems
Sensitivity analysis is an important tool to describe power system dynamic behavior in response to parameter variations. It is a central component in preventive and corrective control applications. The existing approaches for sensitivity calculations, namely, finite-difference and forward sensitivity analysis, require a computational effort that increases linearly with the number of sensitivity parameters. In this work, we investigate, implement, and test a discrete adjoint sensitivity approach whose computational effort is effectively independent of the number of sensitivity parameters. The proposed approach is highly efficient for calculating trajectory sensitivities of larger systems and is consistent, within machine precision, with the function whose sensitivity we are seeking. This is an essential feature for use in optimization applications. Moreover, our approach includes a consistent treatment of systems with switching, such as DC exciters, by deriving and implementing the adjoint jump conditions that arise from state and time-dependent discontinuities. The accuracy and the computational efficiency of the proposed approach are demonstrated in comparison with the forward sensitivity analysis approach.
24 POWER TRANSMISSION AND DISTRIBUTION↗
Lightweight and Accurate Silent Data Corruption Detection in Ordinary Differential Equation Solvers
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fault tolerance↗
Probabilistic Density Function Method for Stochastic ODEs of Power Systems with Uncertain Power Input
Wind and solar power generators are commonly described by a system of stochastic ordinary differential equations (SODEs) where random input parameters represent uncertainty in wind and solar energy. The existing methods for SODEs are mostly limited to delta-correlated random parameters (white noise). Here we use the Probability Density Function (PDF) method for deriving a closed-form deterministic partial differential equation (PDE) for the joint probability density function of the SODEs describing a power generator with time-correlated power input. The resulting PDE is solved numerically. A good agreement with Monte Carlo Simulations shows accuracy of the PDF method.
PDF method, stochastic differential equations, pow↗
Improving the trust in results of numerical simulations and scientific data analytics
This white paper investigates several key aspects of the trust that a user can give to the results of numerical simulations and scientific data analytics. In this document, the notion of trust is related to the integrity of numerical simulations and data analytics applications. This white paper complements the DOE ASCR report on Cybersecurity for Scientific Computing Integrity by (1) exploring the sources of trust loss; (2) reviewing the definitions of trust in several areas; (3) providing numerous cases of result alteration, some of them leading to catastrophic failures; (4) examining the current notion of trust in numerical simulation and scientific data analytics; (5) providing a gap analysis; and (6) suggesting two important research directions and their respective research topics. To simplify the presentation without loss of generality, we consider that trust in results can be lost (or the results’ integrity impaired) because of any form of corruption happening during the execution of the numerical simulation or the data analytics application. In general, the sources of such corruption are threefold: errors, bugs, and attacks. Current applications are already using techniques to deal with different types of corruption. However, not all potential corruptions are covered by these techniques. We firmly believe that the current level of trust that a user has in the results is at least partially founded on ignorance of this issue or the hope that no undetected corruptions will occur during the execution. This white paper explores the notion of trust and suggests recommendations for developing a more scientifically grounded notion of trust in numerical simulation and scientific data analytics. We first formulate the problem and show that it goes beyond previous questions regarding the quality of results such as V&V, uncertainly quantification, and data assimilation. We then explore the complexity of this difficult problem, and we sketch complementary general approaches to address it. This paper does not focus on the trust that the execution will actually complete. The product of simulation or of data analytic executions is the final element of a potentially long chain of transformations, where each stage has the potential to introduce harmful corruptions. These corruptions may produce results that deviate from the user-expected accuracy without notifying the user of this deviation. There are many potential sources of corruption before and during the execution; consequently, in this white paper we do not focus on the protection of the end result after the execution.
97 MATHEMATICS AND COMPUTING↗