22 Search Results

We consider the design and operation of water networks simultaneously. Water network problems can be divided into two categories: the design problem and the operation problem. The design problem involves determining the appropriate pipe sizing and placements of pump stations, while the operation problem involves scheduling pump stations over multiple time periods to account for changes in supply and demand. Our focus is on networks that involve water co-produced with oil and gas. While solving the optimization formulation for such networks, we found that obtaining a primal (feasible) solution is more challenging than obtaining dual bounds using off-the-shelf mixed-integer nonlinearmore » programming solvers. Therefore, we propose two methods to obtain good primal solutions. One method involves a decomposition framework that utilizes a convex reformulation, while the other is based on time decomposition. To test our proposed methods, we conduct computational experiments on a network derived from the PARETO case study.« less

We present a data-driven reduced-order modeling of the space-charge dynamics for electromagnetic particle-in-cell (EMPIC) plasma simulations based on dynamic mode decomposition (DMD). The dynamics of the charged particles in kinetic plasma simulations such as EMPIC is manifested through the plasma current density defined along the edges of the spatial mesh. We showcase the efficacy of DMD in modeling the time evolution of current density through a low-dimensional feature space. Not only do such DMD based predictive reduced-order models help accelerate EMPIC simulations, they also have the potential to facilitate investigative analysis and control applications. Here, we demonstrate the proposed DMD-EMPICmore » scheme for reduced-order modeling of current density and speedup in EMPIC simulations involving electron beam under the influence of magnetic field, virtual cathode oscillations, and backward wave oscillator.« less

There is a growing interest in developing a parametric representation of liquid sloshing inside a container stemming from its practical applications in modern engineering systems. The resonant excitation due to sloshing, on the other hand, can cause unstable and nonlinear water waves, resulting in chaotic motions and non-Gaussian wave profiles. This paper presents a novel machine learning-based framework for nonlinear liquid sloshing representation learning. The proposed method is a parametric modeling technique that is based on sequential learning and sparse regularization. The dynamics are categorized into two parts: linear evolution and nonlinear forcing. The former advances the dynamical system inmore » time on an embedded manifold, while the latter causes divergent behaviors in temporal evolution, such as bursting and switching. The effectiveness of the proposed framework is demonstrated using an experimental dataset of liquid sloshing in a tank under horizontal excitation with a wide range of frequencies and vertical slat screen settings immersed in the tank perpendicular to the excitation.« less

Computing the numerical solution of the Kadanoff–Baym equations, a set of nonlinear integral differential equations satisfied by the two-time Green's functions derived from many-body perturbation theory for a quantum many-body system away from equilibrium, is a challenging task. Recently, we have successfully applied dynamic mode decomposition (DMD) to construct a data driven reduced order model that can be used to extrapolate the time-diagonal of a two-time Green's function from numerical solutions of the KBE within a small time window. In this paper, we extend the previous work and use DMD to predict off-diagonal elements of the two-time Green's function. Wemore » partition the two-time Green's function into a number of one-time functions along the diagonal and subdiagonals of the two-time window as well as in horizontal and vertical directions. We use DMD to construct separate reduced order models to predict the dynamics of these one-time functions in a two-step procedure. We extrapolate along diagonal and several subdiagonals within a subdiagonal band of a two-time window in the first step. In the second step, we use DMD to extrapolate the Green's function outside of the sub-diagonal band. In conclusion, we demonstrate the efficiency and accuracy of this approach by applying it to a two-band Hubbard model problem.« less

This paper develops a robust dynamic mode decomposition (RDMD) method endowed with statistical and numerical robustness. Statistical robustness ensures estimation efficiency at the Gaussian and non-Gaussian probability distributions, including heavy-tailed distributions. The proposed RDMD is statistically robust because the outliers in the data set are flagged via projection statistics and suppressed using a Schweppe-type Huber generalized maximum-likelihood estimator that minimizes a convex Huber cost function. The latter is solved using the iteratively reweighted least-squares algorithm that is known to exhibit an excellent convergence property and numerical stability than the Newton algorithms. Several numerical simulations using canonical models of dynamical systemsmore » demonstrate the excellent performance of the proposed RDMD method. The results reveal that it outperforms several other methods proposed in the literature.« less

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 ismore » 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.« less

A classical reduced order model (ROM) for dynamical problems typically involves only the spatial reduction of a given problem. Recently, a novel space–time ROM for linear dynamical problems has been developed [Choi et al., Space–tume reduced order model for large-scale linear dynamical systems with application to Boltzmann transport problems, Journal of Computational Physics, 2020], which further reduces the problem size by introducing a temporal reduction in addition to a spatial reduction without much loss in accuracy. The authors show an order of a thousand speed-up with a relative error of less than ${10}^{–5}$more » for a large-scale Boltzmann transport problem. In this work, we present for the first time the derivation of the space–time least-squares Petrov–Galerkin (LSPG) projection for linear dynamical systems and its corresponding block structures. Utilizing these block structures, we demonstrate the ease of construction of the space–time ROM method with two model problems: 2D diffusion and 2D convection diffusion, with and without a linear source term. For each problem, we demonstrate the entire process of generating the full order model (FOM) data, constructing the space–time ROM, and predicting the reduced-order solutions, all in less than 120 lines of Python code. We compare our LSPG method with the traditional Galerkin method and show that the space–time ROMs can achieve $\mathcal{O}\left({10}^{–3}\right)$ to $\mathcal{O}\left({10}^{–4}\right)$ relative errors for these problems. Depending on parameter–separability, online speed-ups may or may not be achieved. For the FOMs with parameter–separability, the space–time ROMs can achieve $\mathcal{O}\left(10\right)$ online speed-ups. Finally, we present an error analysis for the space–time LSPG projection and derive an error bound, which shows an improvement compared to traditional spatial Galerkin ROM methods.« less

Detection and timely identification of power system disturbances are essential for situation awareness and reliable electricity grid operation. Because records of actual events in the system are limited, ensemble simulation-based events are needed to provide adequate data for building event-detection models through deep learning; e.g., a convolutional neural network (CNN). An ensemble numerical simulation-based training data set have been generated through dynamic simulations performed on the Polish system with various types of faults in different locations. Such data augmentation is proven to be able to provide adequate data for deep learning. The synchronous generators’ frequency signals are used and encodedmore » into images for developing and evaluating CNN models for classification of fault types and locations. With a time-domain stacked image set as the benchmark, two different time-series encoding approaches, i.e., wavelet decomposition-based frequency-domain stacking and polar coordinate system-based Gramian Angular Field (GAF) stacking, are also adopted to evaluate and compare the CNN model performance and applicability. The various encoding approaches are suitable for different fault types and spatial zonation. With optimized settings of the developed CNN models, the classification and localization accuracies can go beyond 84 and 91%, respectively.« less

Time-frequency analysis that disaggregates a signal in both time and frequency domain is an important supporting technique for building energy analysis such as noise cancellation in data-driven building load forecasting. There is a gap in the literature related to comparing various time–frequency-analysis techniques, especially discrete wavelet transform (DWT) and empirical mode decomposition (EMD), to guide the selection and tuning of time–frequency-analysis techniques in data-driven building load forecasting. This article provides a framework to conduct a comprehensive comparison among thirteen DWT/EMD techniques with various parameters in a load forecasting modeling task. A real campus building is used as a case studymore » for illustration. The DWT and EMD techniques are also compared under various data-driven modeling algorithms for building load forecasting. The results in the case study show that the load forecasting models trained with noise-cancelled energy data have increased their accuracy to 9.6% on average tested under unseen data. This study also shows that the effectiveness of DWT/EMD techniques depends on the data-driven algorithms used for load forecasting modeling and the training data. Hence, DWT/EMD-based noise cancellation needs customized selection and tuning to optimize their performance for data-driven building load forecasting modeling.« less

Soil microbial carbon use efficiency (CUE) is a combination of growth and respiration, which may respond differently to climate change depending on physical protection of soil carbon (C) and its availability to microbes. In a mid-latitude hardwood forest in central Massachusetts, 27 years of soil warming (+5 °C) has resulted in C loss and altered soil organic matter (SOM) quality, yet the underlying mechanisms remain unclear. In this work, we hypothesized that long-term warming reduces physical aggregate protection of SOM, microbial CUE, and its temperature sensitivity. Soil was separated into macroaggregate (250–2000 μm) and microaggregate (<250 μm) fractions, and CUEmore » was measured with ¹⁸O enriched water (H₂¹⁸O) in samples incubated at 15 and 25 °C for 24 h. We found that long-term warming reduced soil C and nitrogen concentrations and extracellular enzyme activity in macroaggregates, but did not affect physical protection of SOM. Long-term warming showed little effect on CUE or microbial biomass turnover time because it reduced both growth and respiration. However, CUE was less temperature sensitive in macroaggregates from the warmed compared to the control plots. Our findings suggest that microbial thermal responses to long-term warming occur mostly in soil compartments where SOM is less physically protected and thus more vulnerable to microbial degradation.« less