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At least 1,369 records · Page 76

Discretized energy minimization in a wave guide with point sources

An anti-noise problem on a finite time interval is solved by minimization of a quadratic functional on the Hilbert space of square integrable controls. To this end, the one-dimensional wave equation with point sources and pointwise reflecting boundary conditions is decomposed into a system for the two propagating components of waves. Wellposedness of this system is proved for a class of data that includes piecewise linear initial conditions and piecewise constant forcing functions. It is shown that for such data the optimal piecewise constant control is the solution of a sparse linear system. Methods for its computational treatment are presented as well as examples of their applicability. The convergence of discrete approximations to the general optimization problem is demonstrated by finite element methods.

Propst, G.↗

Constraining the Varied Response of Northern Hemisphere Winter Circulation Waviness to Climate Change

Abstract While a large latitudinal displacement of the westerly jet brings about disproportionate socioeconomic impacts over Northern Hemisphere midlatitude continents, it is not well understood as to whether the winter circulation will become wavier or less in response to climate change. Here, using observations and large ensembles of climate models, we show that changes in atmospheric waviness can be estimated from the optimal structures of the westerly jet for wavier circulation, which are obtained from an advection‐diffusion model. Thus, the changes in westerly jet structure in climate models under climate change provide a physical constraint on changes in atmospheric waviness, indicating that the North Atlantic wave activity will experience a robust decline in a warmer climate, while future North Pacific wave activity is obscured by model uncertainty rather than internal variability. These findings highlight the changes to jet stream structure as a constraint for regional circulation waviness in a changing climate.

54 ENVIRONMENTAL SCIENCES↗

Landsat D Thematic Mapper image dimensionality reduction and geometric correction accuracy

To characterize and quantify the performance of the Landsat thematic mapper (TM), techniques for dimensionality reduction by linear transformation have been studied and evaluated and the accuracy of the correction of geometric errors in TM images analyzed. Theoretical evaluations and comparisons for existing methods for the design of linear transformation for dimensionality reduction are presented. These methods include the discrete Karhunen Loeve (KL) expansion, Multiple Discriminant Analysis (MDA), Thematic Mapper (TM)-Tasseled Cap Linear Transformation and Singular Value Decomposition (SVD). A unified approach to these design problems is presented in which each method involves optimizing an objective function with respect to the linear transformation matrix. From these studies, four modified methods are proposed. They are referred to as the Space Variant Linear Transformation, the KL Transform-MDA hybrid method, and the First and Second Version of the Weighted MDA method. The modifications involve the assignment of weights to classes to achieve improvements in the class conditional probability of error for classes with high weights. Experimental evaluations of the existing and proposed methods have been performed using the six reflective bands of the TM data. It is shown that in terms of probability of classification error and the percentage of the cumulative eigenvalues, the six reflective bands of the TM data require only a three dimensional feature space. It is shown experimentally as well that for the proposed methods, the classes with high weights have improvements in class conditional probability of error estimates as expected.

Ford, G. E.↗

Piecewise linear approximation with minimum number of linear segments and minimum error: A fast approach to tighten and warm start the hierarchical mixed integer formulation

In several areas of economics and engineering, it is often necessary to fit discrete data points or approximate nonlinear functions with continuous functions. Piecewise linear (PWL) functions are a convenient way to achieve this. PWL functions can be modeled in mathematical problems using only linear and integer variables. Moreover, there is a computational benefit in using PWL functions that have the least possible number of segments. This work proposes a novel hierarchical mixed integer linear programming (MILP) formulation that identifies a continuous PWL approximation with minimum number of linear segments for a given target maximum error. The proposed MILP formulation also identifies the solution with the least maximum error among the solutions with minimum number of segments. Then, this work proposes a fast iterative algorithm that identifies non necessarily continuous PWL approximations by solving O(S log N) linear programming (LP) problems, where N is the number of data points and S is the minimum number of segments in the non necessarily continuous case. This work demonstrates that tight bounds for the MILP problem can be derived from these approximations. Next, a fast algorithm is introduced to transform a non necessarily continuous PWL approximation into a continuous one. Finally, the tight bounds and the continuous PWL approximations are used to tighten and warm start the MILP problem. The tightened formulation is shown in experimental results to be more efficient, especially for large data sets, with a solution time that is up to two orders of magnitude less than the existing literature.

97 MATHEMATICS AND COMPUTING↗

WE-EF-207-01: FEATURED PRESENTATION and BEST IN PHYSICS (IMAGING): Task-Driven Imaging for Cone-Beam CT in Interventional Guidance

Purpose: This work introduces a task-driven imaging framework that utilizes a patient-specific anatomical model, mathematical definition of the imaging task, and a model of the imaging system to prospectively design acquisition and reconstruction techniques that maximize task-based imaging performance. Utility of the framework is demonstrated in the joint optimization of tube current modulation and view-dependent reconstruction kernel in filtered-backprojection reconstruction and non-circular orbit design in model-based reconstruction. Methods: The system model is based on a cascaded systems analysis of cone-beam CT capable of predicting the spatially varying noise and resolution characteristics as a function of the anatomical model and a wide range of imaging parameters. Detectability index for a non-prewhitening observer model is used as the objective function in a task-driven optimization. The combination of tube current and reconstruction kernel modulation profiles were identified through an alternating optimization algorithm where tube current was updated analytically followed by a gradient-based optimization of reconstruction kernel. The non-circular orbit is first parameterized as a linear combination of bases functions and the coefficients were then optimized using an evolutionary algorithm. The task-driven strategy was compared with conventional acquisitions without modulation, using automatic exposure control, and in a circular orbit. Results: The task-driven strategy outperformed conventional techniques in all tasks investigated, improving the detectability of a spherical lesion detection task by an average of 50% in the interior of a pelvis phantom. The non-circular orbit design successfully mitigated photon starvation effects arising from a dense embolization coil in a head phantom, improving the conspicuity of an intracranial hemorrhage proximal to the coil. Conclusion: The task-driven imaging framework leverages a knowledge of the imaging task within a patient-specific anatomical model to optimize image acquisition and reconstruction techniques, thereby improving imaging performance beyond that achievable with conventional approaches. 2R01-CA-112163; R01-EB-017226; U01-EB-018758; Siemens Healthcare (Forcheim, Germany)

60 APPLIED LIFE SCIENCES↗

PROFILE user's guide

User information for program PROFILE, an aerodynamics design utility for refining, plotting, and tabulating airfoil profiles is provided. The theory and implementation details for two of the more complex options are also presented. These are the REFINE option, for smoothing curvature in selected regions while retaining or seeking some specified thickness ratio, and the OPTIMIZE option, which seeks a specified curvature distribution. REFINE uses linear techniques to manipulate ordinates via the central difference approximation to second derivatives, while OPTIMIZE works directly with curvature using nonlinear least squares techniques. Use of programs QPLOT and BPLOT is also described, since all of the plots provided by PROFILE (airfoil coordinates, curvature distributions) are achieved via the general purpose QPLOT utility. BPLOT illustrates (again, via QPLOT) the shape functions used by two of PROFILE's options. The programs were designed and implemented for the Applied Aerodynamics Branch at NASA Ames Research Center, Moffett Field, California, and written in FORTRAN and run on a VAX-11/780 under VMS.

Collins, L.↗

MO-F-CAMPUS-T-02: Optimizing Orientations of Hundreds of Intensity-Modulated Beams to Treat Multiple Brain Targets

Purpose: To investigate a new modulated beam orientation optimization (MBOO) approach maximizing treatment planning quality for the state-of-the-art flattening filter free (FFF) beam that has enabled rapid treatments of multiple brain targets. Methods: MBOO selects and optimizes a large number of intensity-modulated beams (400 or more) from all accessible beam angles surrounding a patient’s skull. The optimization algorithm was implemented on a standalone system that interfaced with the 3D Dicom images and structure sets. A standard published data set that consisted of 1 to 12 metastatic brain tumor combinations was selected for MBOO planning. The planning results from various coplanar and non-coplanar configurations via MBOO were then compared with the results obtained from a clinical volume modulated arc therapy (VMAT) delivery system (Truebeam RapidArc, Varian Oncology). Results: When planning a few number of targets (n<4), MBOO produced results equivalent to non-coplanar multi-arc VMAT planning in terms of target volume coverage and normal tissue sparing. For example, the 12-Gy and 4-Gy normal brain volumes for the 3-target plans differed by less than 1 mL ( 3.0 mLvs 3.8 mL; and 35.2 mL vs 36.3 mL, respectively) for MBOO versus VMAT. However, when planning a larger number of targets (n≥4), MBOO significantly reduced the dose to the normal brain as compared to VMAT, though the target volume coverage was equivalent. For example, the 12-Gy and 4-Gy normal brain volumes for the 12-target plans were 10.8 mL vs. 18.0 mL and 217.9 mL vs. 390.0 mL, respectively for the non-coplanar MBOO versus the non-coplanar VMAT treatment plans, yielding a reduction in volume of more than 60% for the case. Conclusion: MBOO is a unique approach for maximizing normal tissue sparing when treating a large number (n≥4) of brain tumors with FFF linear accelerators. Dr Ma and Dr Sahgal are currently on the board of international society of stereotactic radiosurgery. Dr Sahgal has received support for educational presentations from Elekta company.

60 APPLIED LIFE SCIENCES↗

Enhancing Distribution Grid Resilience Through Model Predictive Controller Enabled Prioritized Load Restoration Strategy

Effective resilience improvement strategies enable the power grid to cope with disruptive extreme events. Most power grid outages are caused by disruptions in distribution grids. Motivated by the urgent need for power system resilience research, this paper proposes a priority-weighted optimal load restoration technique to enhance the resilience of distribution grids against extreme events. The proposed technique is based on smart distribution technology and framed as sequential multi-step decision process (MDP) and mixed integer linear program (MILP). It is formulated as optimal control problem with a model predictive control (MPC) approach. We applied the devised MILP-MPC-based load restoration technique to a simplified single-bus version of the IEEE 13-bus distribution system with integrated distributed energy resources (DERs) such as wind turbine, photovoitaic array, microturbine, and energy storage device. The technique executes a reducing and rolling horizon optimization in each control step in real-time using the forecasted information of the renewables, the fuel status of the microturbine and the state of charge of the energy storage device. We consider an extreme event which triggered outage of the upstream utility grid and caused islanded operation of the distribution grid. We demonstrated the effectiveness of the proposed MPC approach in restoring the distribution grid loads based on their priority during the main grid outage-caused islanded operation.

61 RADIATION PROTECTION AND DOSIMETRY↗

Multifidelity Ensemble Kalman Filtering Using Surrogate Models Defined by Theory-Guided Autoencoders

Data assimilation is a Bayesian inference process that obtains an enhanced understanding of a physical system of interest by fusing information from an inexact physics-based model, and from noisy sparse observations of reality. The multifidelity ensemble Kalman filter (MFEnKF) recently developed by the authors combines a full-order physical model and a hierarchy of reduced order surrogate models in order to increase the computational efficiency of data assimilation. The standard MFEnKF uses linear couplings between models, and is statistically optimal in case of Gaussian probability densities. This work extends the MFEnKF into to make use of a broader class of surrogate model such as those based on machine learning methods such as autoencoders non-linear couplings in between the model hierarchies. We identify the right-invertibility property for autoencoders as being a key predictor of success in the forecasting power of autoencoder-based reduced order models. We propose a methodology that allows us to construct reduced order surrogate models that are more accurate than the ones obtained via conventional linear methods. Numerical experiments with the canonical Lorenz'96 model illustrate that nonlinear surrogates perform better than linear projection-based ones in the context of multifidelity ensemble Kalman filtering. We additionality show a large-scale proof-of-concept result with the quasi-geostrophic equations, showing the competitiveness of the method with a traditional reduced order model-based MFEnKF.

97 MATHEMATICS AND COMPUTING↗

Enhancing Distribution Grid Resilience Through Model Predictive Controller Enabled Prioritized Load Restoration Strategy: Preprint

Effective resilience improvement strategies enable the power grid to cope with disruptive extreme events. Most power grid outages are caused by disruptions in distribution grids. Motivated by the urgent need for power system resilience research, this paper proposes a priority-weighted optimal load restoration technique to enhance the resilience of distribution grids against extreme events. The proposed technique is based on smart distribution technology and framed as sequential multi-step decision process (MDP) and mixed integer linear program (MILP). It is formulated as optimal control problem with a model predictive control (MPC) approach. We applied the devised MILP-MPC-based load restoration technique to a simplified single-bus version of the IEEE 13-bus distribution system with integrated distributed energy resources (DERs) such as wind turbine, photovoltaic array, microturbine, and energy storage device. The technique executes a reducing and rolling horizon optimization in each control step in real-time using the forecasted information of the renewables, the fuel status of the microturbine and the state of charge of the energy storage device. We consider an extreme event which triggered outage of the upstream utility grid and caused islanded operation of the distribution grid. We demonstrated the effectiveness of the proposed MPC approach in restoring the distribution grid loads based on their priority during the main grid outage-caused islanded operation.

61 RADIATION PROTECTION AND DOSIMETRY↗

Enhancing Distribution Grid Resilience Through Model Predictive Controller Enabled Prioritized Load Restoration Strategy

Effective resilience improvement strategies enable the power grid to cope with disruptive extreme events. Most power grid outages are caused by disruptions in distribution grids. Motivated by the urgent need for power system resilience research, this paper proposes a priority-weighted optimal load restoration technique to enhance the resilience of distribution grids against extreme events. The proposed technique is based on smart distribution technology and framed as sequential multi-step decision process (MDP) and mixed integer linear program (MILP). It is formulated as optimal control problem with a model predictive control (MPC) approach. We applied the devised MILP-MPC-based load restoration technique to a simplified single-bus version of the IEEE 13-bus distribution system with integrated distributed energy resources (DERs) such as wind turbine, photovoltaic array, microturbine, and energy storage device. The technique executes a reducing and rolling horizon optimization in each control step in real-time using the forecasted information of the renewables, the fuel status of the microturbine and the state of charge of the energy storage device. We consider an extreme event which triggered outage of the upstream utility grid and caused islanded operation of the distribution grid. We demonstrated the effectiveness of the proposed MPC approach in restoring the distribution grid loads based on their priority during the main grid outage-caused islanded operation.

61 RADIATION PROTECTION AND DOSIMETRY↗

An analysis of physics limited dispatch of nuclear renewable integrated energy systems using deep reinforcement learning and dynamic modeling

Previous approaches to dispatching nuclear integrated energy systems (NIES) have focused on the profitability and flexibility of these systems to operate on energy grids with highly variable pricing. However, due to the complexity involved in modeling and designing these systems, there has been less emphasis on ensuring that these dispatch strategies are physically achievable. It is imperative to develop methods that allow the system to remain within the desired NIES operating conditions and perform this based on realistic limited forecasted information. This research employs next generation artificial intelligence, namely deep reinforcement learning (DRL), and a dynamic system model written in Modelica to find a safe and profitable dispatch strategy for a solar nuclear hybrid design. The DRL agent is shown to find a novel dispatch strategy that manages both power ramping and power levels while respecting operational limits. This DRL-based dispatch is compared to other dispatching strategies including an optimal design solution from mixed integer linear programming (MILP). It is found that incorporating the physics of such a tightly coupled NIES limits the profitability of the MILP-based dispatch strategy. As a result, the MILP solution overestimates the design’s generated revenue. In contrast, DRL significantly reduces the number of breaches of safe operational conditions during energy arbitrage while maintaining profitability. Furthermore, this work paves the way for a more detailed assessment of NIES profitability and could be used to aid operator decisions on future NIES projects.

14 - SOLAR ENERGY↗

CAMELOT: A machine learning approach for coarse-grained simulations of aggregation of block-copolymeric protein sequences

We report the development and deployment of a coarse-graining method that is well suited for computer simulations of aggregation and phase separation of protein sequences with block-copolymeric architectures. Our algorithm, named CAMELOT for Coarse-grained simulations Aided by MachinE Learning Optimization and Training, leverages information from converged all atom simulations that is used to determine a suitable resolution and parameterize the coarse-grained model. To parameterize a system-specific coarse-grained model, we use a combination of Boltzmann inversion, non-linear regression, and a Gaussian process Bayesian optimization approach. The accuracy of the coarse-grained model is demonstrated through direct comparisons to results from all atom simulations. We demonstrate the utility of our coarse-graining approach using the block-copolymeric sequence from the exon 1 encoded sequence of the huntingtin protein. This sequence comprises of 17 residues from the N-terminal end of huntingtin (N17) followed by a polyglutamine (polyQ) tract. Simulations based on the CAMELOT approach are used to show that the adsorption and unfolding of the wild type N17 and its sequence variants on the surface of polyQ tracts engender a patchy colloid like architecture that promotes the formation of linear aggregates. These results provide a plausible explanation for experimental observations, which show that N17 accelerates the formation of linear aggregates in block-copolymeric N17-polyQ sequences. The CAMELOT approach is versatile and is generalizable for simulating the aggregation and phase behavior of a range of block-copolymeric protein sequences.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Invertible Neural Networks for Aerodynamic Design of Wind Turbine Blades

The state-of-the-practice methods for aerodynamic design of wind turbine blads use linearized blade element momentum theory (BEM) to optimize the twist and chord profiles from a pre-selected set of 2D airfoil shapes. In this work, we apply invertible neural network (INN) tools to enable the rapid inverse aerodynamic design of wind turbine blades including component airfoils. The INN is trained on data obtained through the use of robust automated mesh generation and the HAMSTR computational fluid dynamics solver with advanced turbulence and transition models validated for turbine applications. Our design technique is a significant improvement over the state-of-the-practice linearized blade element momentum (BEM) techniques in capturing 3D nonlinear aerodynamic effects that are critical for optimal design of the rotors. This is made possible by developing sparse, invertible neural networks (INNs) for inverse design and optimization that realize a 100x cost reduction compared to adjoint-based computational fluid dynamics (CFD) approaches, while enabling increased robustness of the final design. We demonstrate the INN tool for design of a section of the NREL 5-MW blade. All generated shapes satisfy the desired aerodynamic characteristics, demonstrating the success of the INN approach for inverse design of wind turbine blades.

aerodynamic design↗

Systematic quark/gluon identification with ratios of likelihoods

Discriminating between quark- and gluon-initiated jets has long been a central focus of jet substructure, leading to the introduction of numerous observables and calculations to high perturbative accuracy. At the same time, there have been many attempts to fully exploit the jet radiation pattern using tools from statistics and machine learning. We propose a new approach that combines a deep analytic understanding of jet substructure with the optimality promised by machine learning and statistics. After specifying an approximation to the full emission phase space, we show how to construct the optimal observable for a given classification task. This procedure is demonstrated for the case of quark and gluons jets, where we show how to systematically capture sub-eikonal corrections in the splitting functions, and prove that linear combinations of weighted multiplicity is the optimal observable. In addition to providing a new and powerful framework for systematically improving jet substructure observables, we demonstrate the performance of several quark versus gluon jet tagging observables in parton-level Monte Carlo simulations, and find that they perform at or near the level of a deep neural network classifier. Combined with the rapid recent progress in the development of higher order parton showers, we believe that our approach provides a basis for systematically exploiting subleading effects in jet substructure analyses at the Large Hadron Collider (LHC) and beyond.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Proactive Operations and Investment Planning via Stochastic Optimization to Enhance Power Systems’ Extreme Weather Resilience

We present scalable stochastic optimization approaches for improving power systems’ resilience to extreme weather events. We consider both proactive redispatch and transmission line hardening as alternatives for mitigating expected load shed due to extreme weather, resulting in large-scale stochastic linear programs (LPs) and mixed-integer linear programs (MILPs). We solve these stochastic optimization problems with progressive hedging (PH), a parallel, scenario-based decomposition algorithm. Our computational experiments indicate that our proposed method for enhancing power system resilience can provide high-quality solutions efficiently. With up to 128 scenarios on a 2,000-bus network, the operations (redispatch) and investment (hardening) resilience problems can be solved in approximately 6 min and 2 h of wall-clock time, respectively. Additionally, we solve the investment problems with up to 512 scenarios, demonstrating that the approach scales very well with the number of scenarios. Moreover, the method produces high quality solutions that result in statistically significant reductions in expected load shed. Our proposed approach can be augmented to incorporate a variety of other operational and investment resilience strategies, or a combination of such strategies.

24 POWER TRANSMISSION AND DISTRIBUTION↗