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At least 307 records · Page 17

Multifidelity validation of digital surrogates using variable-density turbulent mixing models

In this study, ensembles of experimental data are presented and utilized to compare and validate two models used in the simulation of variable-density (Atwood = 0.22), compressible turbulent mixing. Though models of this kind (Reynolds averaged NavierStokes and large-eddy simulations) have been validated extensively with more canonical flows in previous studies, here the present approach offers novelty in the complexity of the geometry, the ensemble-based validation, and the uniformity of the computational framework on which the models are tested. Moreover, all experimental and computational tasks were completed by the authors which has led to a tightly coupled experimental configuration with its “digital twin.” The experimental divergent-shock-tube facility and its data acquisition methods are described and replicated in simulation space. A 2D Euler model which neglects the turbulent mixing at the interface is optimized to experimental data using a Gaussian process. This model then serves as the basis for both the 2D RANS and 3D LES studies that make comparisons to the mixing-layer data from the experiment. A relatively simple RANS model is shown to produce good agreement with experimental data only at late flow development times. The LES ensembles generally show good agreement with experimental data but display sensitivity to the characterization of initial conditions. Resolution-dependent behavior is also observed for certain higher-order statistics of interest. Overall, the LES model successfully captures the effects of divergent geometry, compressibility, and combined nonlinear instabilities inherent to the problem. The successful prediction of mixing width and its growth rate highlight the existence of three distinct regimes in the development of the instability, each with similarities to previously studied instabilities.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Optimal Power Management for Large-Scale Battery Energy Storage Systems via Bayesian Inference

Large-scale battery energy storage systems (BESS) have found ever-increasing use across industry and society to accelerate clean energy transition and improve energy supply reliability and resilience. However, their optimal power management poses significant challenges: the underlying high-dimensional nonlinear nonconvex optimization lacks computational tractability in real-world implementation, and the uncertainty of the exogenous power demand makes exact optimization difficult. This paper presents a new solution framework to address these bottlenecks. The solution pivots on introducing power-sharing ratios to specify each cell’s power quota from the output power demand. To find the optimal power-sharing ratios, we formulate a nonlinear model predictive control (NMPC) problem to achieve power-loss-minimizing BESS operation while complying with safety, cell balancing, and power supply-demand constraints. We then propose a parameterized control policy for the power-sharing ratios, which utilizes only three parameters, to reduce the computational demand in solving the NMPC problem. This policy parameterization allows us to translate the NMPC problem into a Bayesian inference problem for the sake of 1) computational tractability, and 2) overcoming the nonconvexity of the optimization problem. We leverage the ensemble Kalman inversion technique to solve the parameter estimation problem. Concurrently, a low-level control loop is developed to seamlessly integrate our proposed approach with the BESS to ensure practical implementation. This low-level controller receives the optimal power-sharing ratios, generates output power references for the cells, and maintains a balance between power supply and demand despite uncertainty in output power. We conduct extensive simulations and experiments on a 20-cell prototype to validate the proposed approach.

Battery energy storage systems (BESSs)↗

Bias-Variance Trade-Off in Physics-Informed Neural Networks with Randomized Smoothing for High-Dimensional PDEs

Physics-Informed Neural Networks (PINNs) have triggered a paradigm shift in scientific computing, leveraging mesh-free properties and robust approximation capabilities. While proving effective for low-dimensional partial differential equations (PDEs), the computational cost of PINNs remains a hurdle in high-dimensional scenarios. This is particularly pronounced when computing high-order and high-dimensional derivatives in the physics-informed loss. Randomized Smoothing PINN (RS-PINN) introduces Gaussian noise for stochastic smoothing of the original neural net model, enabling the use of Monte Carlo methods for derivative approximation, which eliminates the need for costly automatic differentiation. Despite its computational efficiency, especially in the approximation of high-dimensional derivatives, RS-PINN introduces biases in both loss and gradients, negatively impacting convergence, especially when coupled with stochastic gradient descent (SGD) algorithms. We present a comprehensive analysis of biases in RS-PINN, attributing them to the nonlinearity of the Mean Squared Error (MSE) loss as well as the intrinsic nonlinearity of the PDE itself. We propose tailored bias correction techniques, delineating their application based on the order of PDE nonlinearity. The derivation of an unbiased RS-PINN allows for a detailed examination of its advantages and disadvantages compared to the biased version. Specifically, the biased version has a lower variance and runs faster than the unbiased version, but it is less accurate due to the bias. To optimize the bias-variance trade-off, we combine the two approaches in a hybrid method that balances the rapid convergence of the biased version with the high accuracy of the unbiased version. In addition to methodological contributions, we present an enhanced implementation of RS-PINN. Extensive experiments on diverse high-dimensional PDEs, including Fokker-Planck, Hamilton-Jacobi-Bellman (HJB), viscous Burgers’, Allen-Cahn, and Sine-Gordon equations, illustrate the bias-variance trade-off and highlight the effectiveness of the hybrid RS-PINN. Empirical guidelines are provided for selecting biased, unbiased, or hybrid versions, depending on the dimensionality and nonlinearity of the specific PDE problem.

97 MATHEMATICS AND COMPUTING↗

Intelligent Partitioning based Fully Parallel AC Security-Constrained Optimal Power Flow

Today’s power grid is becoming more diverse and integrated with high-level distributed energy resources and smart control technologies that is creating a new set of grid management challenges in terms of large-scale, nonlinear, and non-convex problem modeling, complex and time-consuming computation, as well as difficult uncertainty handling. This project focused on solving a challenging multi-period security-constrained generation scheduling problem, which is of great importance for maximizing the social welfare of real-time dispatch, day-ahead market, as well as weekly planning of power systems. Our developed software explored parallel optimization algorithms for complex and realistic power system models, and develop fast, efficient, and robust grid optimization solutions on the high-performance computing platform that will enable increased grid economics, flexibility, resilience, as well as energy security in the United States.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Predicting Critical Transitions in Multiscale Data

Predicting the dynamics of complex nonlinear systems remains a challenging problem both in dynamical systems theory as well as real world science and engineering applications. Data-driven methods utilizing the latest advances in machine learning (ML) provide a promising new paradigm for this task. Our work centered on Reservoir Computing (RC), which has shown itself to be capable of skillfully predicting chaotic dynamics in multiscale systems. In the first part of the work, the focus is on how to improve predictions of critical transitions in a class of slow-fast metastable systems in which the equations are known. An additional goal was to determine whether a relationship exists between RC and Koopman operator theory, to improve the efficiency and broaden the applicability of the approach. In the second part of this work, a variation on the RC model known as Reconstructive Reservoir Computing (RRC) is applied to real-world data to identify anomalies.

97 MATHEMATICS AND COMPUTING↗

Optimal Operation of PV Sources in DC Grids for Improving Technical, Economical, and Environmental Conditions by Using Vortex Search Algorithm and a Matrix Hourly Power Flow

This document presents a master–slave methodology for solving the problem of optimal operation of photovoltaic (PV) distributed generators (DGs) in direct current (DC) networks. This problem was modeled using a nonlinear programming model (NLP) that considers the minimization of three different objective functions in a daily operation of the system. The first one corresponds to the minimization of the total operational cost of the system, including the energy purchasing cost to the conventional generators and maintenance costs of the PV sources; the second objective function corresponds to the reduction of the energy losses associated with the transport of energy in the network, and the third objective function is related to the minimization of the total emissions of CO2 by the conventional generators installed on the DC grid. The minimization of these objective functions is achieved by using a master–slave optimization approach through the application of the Vortex Search algorithm combined with a matrix hourly power flow. To evaluate the effectiveness and robustness of the proposed approach, two test scenarios were used, which correspond to a grid-connected and a standalone network located in two different regions of Colombia. The grid-connected system emulates the behavior of the solar resource and power demand of the city of Medellín-Antioquia, and the standalone network corresponds to an adaptation of the generation and demand curves for the municipality of Capurganá-Choco. A numerical comparison was performed with four optimization methodologies reported in the literature: particle swarm optimization, multiverse optimizer, crow search algorithm, and salp swarm algorithm. The results obtained demonstrate that the proposed optimization approach achieved excellent solutions in terms of response quality, repeatability, and processing times.

14 SOLAR ENERGY↗

Customizable wave tailoring nonlinear materials enabled by bilevel inverse design

Abstract Passive wave transformation via nonlinearity is ubiquitous in settings from acoustics to optics and electromagnetics. It is well known that different nonlinearities yield different effects on propagating signals, which raises the question of “what precise nonlinearity is the best for a given wave tailoring application?” In this work, considering a one-dimensional spring-mass chain connected by polynomial springs (a variant of the Fermi-Pasta-Ulam-Tsingou system), we introduce a bilevel inverse design method which couples the shape optimization of structures for tailored constitutive responses with reduced-order nonlinear dynamical inverse design. We apply it to two qualitatively distinct problems—minimization of peak transmitted kinetic energy from impact, and pulse shape transformation—demonstrating our method’s breadth of applicability. For the impact problem, we obtain two fundamental insights. First, small differences in nonlinearity can drastically change the dynamic response of the system, from severely under- to outperforming a comparative linear system. Second, the oft-used strategy of impact mitigation via “energy locking” bistability can be significantly outperformed by our optimal nonlinearity. We validate this case with impact experiments and find excellent agreement. This study establishes a framework for broader passive nonlinear mechanical wave tailoring material design, with applications to computing, signal processing, shock mitigation, and autonomous materials.

Science & Technology - Other Topics↗

Optimal charging scheduling and management for a fast-charging battery electric bus system

Herein we discuss how battery electric buses (BEBs) are rapidly being embraced by public transit agencies because of their environmental and economic benefits. To address the problems of limited driving range and time-consuming charging for BEBs, manufacturers have developed rapid on-route charging technology that utilizes typical layovers at terminals to charge buses in operation using high power. With on-route fast-charging, BEBs are as capable as their diesel counterparts in terms of range and operating time. However, on-route fast-charging makes it more challenging to schedule and manage charging events for a BEB system. First, on-route fast-charging may lead to high electricity power demand charges. Second, it may increase electricity energy charges because of charging that occurs during on-peak hours. Without careful charging scheduling and management, on-route fast-charging may significantly increase fuel costs and reduce the economic attractiveness of BEBs. The present study proposes a network modeling framework to optimize the charging scheduling and management for a fast-charging BEB system, effectively minimizing total charging costs. The charging schedule determines when to charge a BEB, while the charging management strategically controls the actual charging power. Charging costs include both electricity demand charges and energy charges. The charging scheduling and management problem is first formulated as a nonlinear nonconvex program with time-continuous variables. A discretizing method and a linear reformulation technique are then adopted to reformulate the model as a linear program, which can be easily solved using off-the-shelf solvers, even for large-scale problems. Finally, the model is demonstrated with extensive numerical studies based on two real-world bus networks. The results demonstrate that the proposed model can effectively determine the optimal charging scheduling and management for a fast-charging BEB system, which carries the potential for use in large-scale real-world bus networks.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Joint Topology Identification and State Estimation in Unobservable Distribution Grids

Many distribution system operations (e.g., state estimation, control, fault detection/localization) rely on the assumption that the underlying topology is accurately defined. In general, topology identification is a challenging problem in distribution systems as these systems are unobservable with a very limited number of available measurements. In this paper, we tackle this problem by designing a compressive sensing framework that jointly estimates the systems states and network topology via an integrated mixed integer nonlinear program (MINLP) formulation. Here, two reformulations of the original MINLP problems are investigated. Firstly, in order to remove the nonlinearity in the MINLP formulation, a mixed integer linear programming (MILP) problem that employs auxiliary variables is derived. Furthermore, to achieve a faster solution, convex relaxation of the original formulation is derived. Finally, using a Markovian model for topology changes, prior information about system topology is used to improve topology identification particularly when a limited amount of measurements is available. Simulation results on IEEE 37-bus test feeder and IEEE 123-bus test feeder illustrate the efficiency and scalability of the proposed approaches from both state estimation and topology identification point of view (even with 30% of available data).

42 ENGINEERING↗

Curriculum-based Reinforcement Learning for Distribution System Critical Load Restoration

This paper focuses on the critical load restoration problem in distribution systems following major outages. To provide fast online response and optimal sequential decision-making support, a reinforcement learning (RL) based approach is proposed to optimize the restoration. Due to the complexities stemming from the large policy search space, renewable uncertainty, and nonlinearity in a complex grid control problem, directly applying RL algorithms to train a satisfactory policy requires extensive tuning to be successful. To address this challenge, this paper leverages the curriculum learning (CL) technique to design a training curriculum involving a simpler steppingstone problem that guides the RL agent to learn to solve the original hard problem in a progressive and more effective manner. We demonstrate that compared with direct learning, CL facilitates controller training to achieve better performance. To study realistic scenarios where renewable forecasts used for decision-making are in general imperfect, the experiments compare the trained RL controllers against two model predictive controllers (MPCs) using renewable forecasts with different error levels and observe how these controllers can hedge against the uncertainty. Results show that RL controllers are less susceptible to forecast errors than the baseline MPCs and can provide a more reliable restoration process.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Sparse regression for plasma physics

Many scientific problems can be formulated as sparse regression, i.e., regression onto a set of parameters when there is a desire or expectation that some of the parameters are exactly zero or do not substantially contribute. This includes many problems in signal and image processing, system identification, optimization, and parameter estimation methods such as Gaussian process regression. Sparsity facilitates exploring high-dimensional spaces while finding parsimonious and interpretable solutions. In the present work, we illustrate some of the important ways in which sparse regression appears in plasma physics and point out recent contributions and remaining challenges to solving these problems in this field. Further, a brief review is provided for the optimization problem and the state-of-the-art solvers, especially for constrained and high-dimensional sparse regression.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Multilevel-in-width training for deep neural network regression

A common challenge in regression is that for many problems, the degrees of freedom required for a high-quality solution also allows for overfitting. Regularization is a class of strategies that seek to restrict the range of possible solutions so as to discourage overfitting while still enabling good solutions, and different regularization strategies impose different types of restrictions. In this paper, we present a multilevel regularization strategy that constructs and trains a hierarchy of neural networks, each of which has layers that are wider versions of the previous network's layers. Here, we draw intuition and techniques from the field of Algebraic Multigrid (AMG), traditionally used for solving linear and nonlinear systems of equations, and specifically adapt the Full Approximation Scheme (FAS) for nonlinear systems of equations to the problem of deep learning. Training through V-cycles then encourage the neural networks to build a hierarchical understanding of the problem. We refer to this approach as multilevel-in-width to distinguish from prior multilevel works which hierarchically alter the depth of neural networks. The resulting approach is a highly flexible framework that can be applied to a variety of layer types, which we demonstrate with both fully connected and convolutional layers. We experimentally show with PDE regression problems that our multilevel training approach is an effective regularizer, improving the generalize performance of the neural networks studied.

97 MATHEMATICS AND COMPUTING↗

High‐order cubature rules for tetrahedra

Summary In this paper, we construct new high‐order numerical integration schemes for tetrahedra, with positive weights and integration points that are in the interior of the domain. The construction of cubature rules is a challenging problem, which requires the solution of strongly nonlinear algebraic (moment) equations with side conditions given by affine inequality constraints. We present a robust algorithm based on a sequence of three modified Newton procedures to solve the constrained minimization problem. In the literature, numerical integration rules for the tetrahedron are available up to order p =15. We obtain integration rules for the tetrahedron from p =2 to p =20, which are computed using multiprecision arithmetic. For p ≤15, our approach provides integration rules that have the same or fewer number of integration points than existing rules; for p =16 to p =20, our rules are new. Numerical tests are presented that verify the polynomial‐precision of the cubature rules. Convergence studies are performed for the integration of exponential, rational, weakly singular and trigonometric test functions over tetrahedra with flat and curved faces. In all tests, improvements in accuracy is realized as p is increased, though in some cases nonmonotonic convergence is observed.

Jaśkowiec, Jan↗

Assessment of Survey Results from Advanced Reactor Industry Domain Experts on Nonlinear Soil-Structure Interaction Analysis Software Verification and Validation

The seismic load case has a significant impact on the design and cost of nuclear power plants. Given the need to substantially reduce cost, advanced reactor designers are looking to leverage numerical tools that enable seismic analysis of an integrated vessel/support/structure/soil system. Modern nonlinear analysis tools provide a solution, capturing dynamic coupling between components (including soil-structure interaction (SSI)) concurrent with nonlinear behavior in one or more parts of the system. Although these methods have a rich history of technical development and implementation, software quality assurance (SQA) following nuclear industry standards remains a significant burden for those wishing to adopt such methods for advanced reactor design and licensing. To reduce the SQA burden, this project will develop the guidance for SQA verification and validation (V&V) of coupled nonlinear SSI analysis tools, to include a test matrix of software features and test problems to support commercial grade dedication (CGD). The guidance is intended to be technology-neutral: supporting designers of all advanced reactors. To maximize the value of the project to reactor designers, the project team performed focused surveys of and interviews with advanced reactor designers. Additionally, the project surveyed members of the broader industry involved in reactor design and licensing. The aggregated industry feedback consists of written survey responses, live polling responses, focused interviews, and informal feedback provided after outreach presentations, collectively referred to as “survey results”. Herein, the survey results are reported, reviewed, and assessed to inform follow-on project activities. The survey results confirmed the familiarity of the industry with the coupled nonlinear SSI analysis. They also affirm the project need based upon the expressed intent to (1) incorporate nonlinear features and (2) pursue the coupled nonlinear SSI analysis to reduce seismic demands and construction costs. All reactor designers indicated their intent to incorporate two or more nonlinear features, and all reactor designer respondents opined that the coupled nonlinear SSI analysis would allow for the optimization of the reactor design and construction. However, the programmatic challenges, whether real or perceived, present a significant barrier to reactor designers. The barrier most commonly identified by the reactor designer population was regulatory risk, with 70% citing this as a reason not to pursue the approach. The perceived regulatory risk identified by the reactor designers underscores the importance of regulator engagement and dialogue in this project. Additionally, half of the reactor designers identified cost and lack of guidance as a deterrent. The survey results also provide insights to tailor specific aspects of the guidance document and test matrix. The project plans to prepare both a formal referenceable guidance document and a collaborative, web-based test matrix and problem set. The project will focus on more complete test problem definitions for the prioritized nonlinear features over shallower problem descriptions for a larger set of features. The nonlinearities prioritized as high based upon survey feedback include fluid-structure interaction and seismic isolation and energy dissipation devices. The nonlinearities prioritized as intermediate include nonlinear geomaterials, nonlinear concrete, nonlinear steel, and interface/contact nonlinearity. Deep embedment and the associated nonlinear phenomena are assigned the lowest priority based upon survey feedback.

42 ENGINEERING↗

A new process-based and scale-aware desert dust emission scheme for global climate models – Part I: Description and evaluation against inverse modeling emissions

Desert dust accounts for most of the atmosphere's aerosol burden by mass and produces numerous important impacts on the Earth system. However, current global climate models (GCMs) and land-surface models (LSMs) struggle to accurately represent key dust emission processes, in part because of inadequate representations of soil particle sizes that affect the dust emission threshold, surface roughness elements that absorb wind momentum, and boundary-layer characteristics that control wind fluctuations. Furthermore, because dust emission is driven by small-scale (~ 1 km or smaller) processes, simulating the global cycle of desert dust in GCMs with coarse horizontal resolutions (~ 100 km) presents a fundamental challenge. This representation problem is exacerbated by dust emission fluxes scaling nonlinearly with wind speed above a threshold wind speed that is sensitive to land-surface characteristics. Here, we address these fundamental problems underlying the simulation of dust emissions in GCMs and LSMs by developing improved descriptions of (1) the effect of soil texture on the dust emission threshold, (2) the effects of nonerodible roughness elements (both rocks and green vegetation) on the surface wind stress, and (3) the effects of boundary-layer turbulence on driving intermittent dust emissions. We then use the resulting revised dust emission parameterization to simulate global dust emissions in a standalone model forced by reanalysis meteorology and land-surface fields. We further propose (4) a simple methodology to rescale lower-resolution dust emission simulations to match the spatial variability of higher-resolution emission simulations in GCMs. The resulting dust emission simulation shows substantially improved agreement against regional dust emissions observationally constrained by inverse modeling. We thus find that our revised dust emission parameterization can substantially improve dust emission simulations in GCMs and LSMs.

54 ENVIRONMENTAL SCIENCES↗

A taxonomy of constraints in black-box simulation-based optimization

The types of constraints encountered in black-box simulation-based optimization problems differ significantly from those addressed in nonlinear programming. Here, we introduce a characterization of constraints to address this situation. We provide formal definitions for several constraint classes and present illustrative examples in the context of the resulting taxonomy. This taxonomy, denoted KARQ, is useful for modeling and problem formulation, as well as optimization software development and deployment. It can also be used as the basis for a dialog with practitioners in moving problems to increasingly solvable branches of optimization.

42 ENGINEERING↗

Accelerated Sparse Recovery via Gradient Descent with Nonlinear Conjugate Gradient Momentum

This paper applies an idea of adaptive momentum for the nonlinear conjugate gradient to accelerate optimization problems in sparse recovery. Specifically, we consider two types of minimization problems: a (single) differentiable function and the sum of a non-smooth function and a differentiable function. In the first case, we adopt a fixed step size to avoid the traditional line search and establish the convergence analysis of the proposed algorithm for a quadratic problem. This acceleration is further incorporated with an operator splitting technique to deal with the non-smooth function in the second case. As a result, we use the convex ι 1 and the nonconvex ι 1 – ι 2 functionals as two case studies to demonstrate the efficiency of the proposed approaches over traditional methods.

97 MATHEMATICS AND COMPUTING↗

Chapter 4 - Recent Advances in Identification of Differential Equations from Noisy Data: IDENT Review

Differential equations and numerical methods are extensively used to model various real-world phenomena in science and engineering. With modern developments, we aim to find the underlying differential equation from a single observation of time-dependent data. If we assume that the differential equation is a linear combination of various linear and nonlinear differential terms, then the identification problem can be formulated as solving a linear system. The goal then reduces to finding the optimal coefficient vector that best represents the time derivative of the given data. We review some recent works on the identification of differential equations. We find some common themes for the improved accuracy: (i) The formulation of linear system with proper denoising is important, (ii) how to utilize sparsity and model selection to find the correct coefficient support needs careful attention, and (iii) there are ways to improve the coefficient recovery. We present an overview and analysis of recent developments on the topic.

97 MATHEMATICS AND COMPUTING↗