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At least 1,423 records · Page 79

Bilevel optimization, deep learning and fractional Laplacian regularization with applications in tomography

Here we consider a generalized bilevel optimization framework for solving inverse problems. We introduce fractional Laplacian as a regularizer to improve the reconstruction quality, and compare it with the total variation regularization. We emphasize that the key advantage of using fractional Laplacian as a regularizer is that it leads to a linear operator, as opposed to the total variation regularization which results in a nonlinear degenerate operator. Inspired by residual neural networks, to learn the optimal strength of regularization and the exponent of fractional Laplacian, we develop a dedicated bilevel optimization neural network with a variable depth for a general regularized inverse problem. We illustrate how to incorporate various regularizer choices into our proposed network. As an example, we consider tomographic reconstruction as a model problem and show an improvement in reconstruction quality, especially for limited data, via fractional Laplacian regularization. We successfully learn the regularization strength and the fractional exponent via our proposed bilevel optimization neural network. We observe that the fractional Laplacian regularization outperforms total variation regularization. This is specially encouraging, and important, in the case of limited and noisy data.

97 MATHEMATICS AND COMPUTING↗

Optimization of Ca14MgSb11 through Chemical Substitutions on Sb Sites: Optimizing Seebeck Coefficient and Resistivity Simultaneously

In thermoelectric materials, chemical substitutions are widely used to optimize thermoelectric properties. The Zintl phase compound, Yb14MgSb11, has been demonstrated as a promising thermoelectric material at high temperatures. It is iso-structural with Ca14AlSb11 with space group I41/acd. Its iso-structural analog, Ca14MgSb11, was discovered to be a semiconductor and have vacancies on the Sb(3) sites, although in its nominal composition it can be described as consisting of fourteen Ca2+ cations with one [MgSb4]9− tetrahedron, one Sb37− linear anion and four isolated Sb3− anions (Sb(3) site) in one formula unit. When Sn substitutes Sb in Ca14MgSb11, optimized Seebeck coefficient and resistivity were achieved simultaneously although the Sn amount is small (<2%). This is difficult to achieve in thermoelectric materials as the Seebeck coefficient and resistivity are inversely related with respect to carrier concentration. Thermal conductivity of Ca14MgSb11-xSnx remains almost the same as Ca14MgSb11. The calculated zT value of Ca14MgSb10.80Sn0.20 reaches 0.49 at 1075 K, which is 53% higher than that of Ca14MgSb11 at the same temperature. The band structure of Ca14MgSb7Sn4 is calculated to simulate the effect of Sn substitutions. Compared to the band structure of Ca14MgSb11, the band gap of Ca14MgSb7Sn4 is smaller (0.2 eV) and the Fermi-level shifts into the valence band. The absolute values for density of states (DOS) of Ca14MgSb7Sn4 are smaller near the Fermi-level at the top of valence band and 5p-orbitals of Sn contribute most to the valence bands near the Fermi-level.

Hu, Yufei (ORCID:0000000308898786)↗

A two-stage service restoration method for electric power distribution systems

Improving the reliability of power distribution systems is critically important for both utilities and customers. This calls for an efficient service restoration module within a distribution management system to support the implementation of self-healing smart grid networks. Although the emerging smart grid technologies, including distributed generators (DGs) and remote-controlled switches, enhance the self-healing capability and allow faster recovery, they still pose additional complexity to the service restoration problem, especially under cold load pickup (CLPU) conditions. Herein, a novel two-stage restoration framework is proposed to generate a restoration solutions with a sequence of control actions. The first stage generates a restoration plan that supports both the traditional service restoration using feeder reconfiguration and the grid-forming DG-assisted intentional islanding methods. The second stage generates an optimal sequence of switching operations to bring the outaged system quickly to the final restored configuration. The problem is formulated as a mixed-integer linear program that incorporates system connectivity, operating constraints, and the CLPU models. It is demonstrated that on using a multi-feeder test case, the proposed framework is effective in utilizing all available resources to quickly restore the service and generate an optimal sequence of switching actions to be used by the operator to reach the desired optimal configuration.

24 POWER TRANSMISSION AND DISTRIBUTION↗

NEW DEVELOPMENTS ON INVERSE POLYGON MAPPING TO CALCULATE GRAVITATIONAL LENSING MAGNIFICATION MAPS: OPTIMIZED COMPUTATIONS

We derive an exact solution (in the form of a series expansion) to compute gravitational lensing magnification maps. It is based on the backward gravitational lens mapping of a partition of the image plane in polygonal cells (inverse polygon mapping, IPM), not including critical points (except perhaps at the cell boundaries). The zeroth-order term of the series expansion leads to the method described by Mediavilla et al. The first-order term is used to study the error induced by the truncation of the series at zeroth order, explaining the high accuracy of the IPM even at this low order of approximation. Interpreting the Inverse Ray Shooting (IRS) method in terms of IPM, we explain the previously reported N {sup -3/4} dependence of the IRS error with the number of collected rays per pixel. Cells intersected by critical curves (critical cells) transform to non-simply connected regions with topological pathologies like auto-overlapping or non-preservation of the boundary under the transformation. To define a non-critical partition, we use a linear approximation of the critical curve to divide each critical cell into two non-critical subcells. The optimal choice of the cell size depends basically on the curvature of the critical curves. For typical applications in which the pixel of the magnification map is a small fraction of the Einstein radius, a one-to-one relationship between the cell and pixel sizes in the absence of lensing guarantees both the consistence of the method and a very high accuracy. This prescription is simple but very conservative. We show that substantially larger cells can be used to obtain magnification maps with huge savings in computation time.

97 MATHEMATICS AND COMPUTING↗

Self-consistent implementation of meta-GGA functionals for the ONETEP linear-scaling electronic structure package

Accurate and computationally efficient exchange-correlation functionals are critical to the successful application of linear-scaling density functional theory (DFT). Local and semi-local functionals of the density are naturally compatible with linear-scaling approaches, having a general form which assumes the locality of electronic interactions and which can be efficiently evaluated by numerical quadrature. Presently, the most sophisticated and flexible semi-local functionals are members of the meta-generalized-gradient approximation (meta-GGA) family, and depend upon the kinetic energy density, τ, in addition to the charge density and its gradient. In order to extend the theoretical and computational advantages of τ-dependent meta-GGA functionals to large-scale DFT calculations on thousands of atoms, we have implemented support for τ-dependent meta-GGA functionals in the ONETEP program. In this paper we lay out the theoretical innovations necessary to implement τ-dependent meta-GGA functionals within ONETEP's linear-scaling formalism. We present expressions for the gradient of the τ-dependent exchange-correlation energy, necessary for direct energy minimization. We also derive the forms of the τ-dependent exchange-correlation potential and kinetic energy density in terms of the strictly localized, self-consistently optimized orbitals used by ONETEP. To validate the numerical accuracy of our self-consistent meta-GGA implementation, we performed calculations using the B97M-V and PKZB meta-GGAs on a variety of small molecules. Using only a minimal basis set of self-consistently optimized local orbitals, we obtain energies in excellent agreement with large basis set calculations performed using other codes. Lastly, to establish the linear-scaling computational cost and applicability of our approach to large-scale calculations, we present the outcome of self-consistent meta-GGA calculations on amyloid fibrils of increasing size, up to tens of thousands of atoms.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Threaded Multi-Core GEMM with MoA and Cache-Blocking: Preprint

A threaded multi-core implementation of the high performance dense linear algebra matrix-matrix multiply GEMM kernel is described. This kernel is widely implemented by vendors in the basic linear algebra subroutine BLAS library. The mathematics of arrays (MoA) paradigm due to Mullin (1988) results in contiguous memory accesses by employing outer-product forms. Our performance studies demonstrate that the MoA implementation of double precision DGEMM combined with optimal cache-blocking strategies results in at least a 25% performance gain on the Intel Xeon Skylake processor over the vendor supplied Intel MKL basic linear algebra libraries. Results are presented for the NREL Eagle supercomputer. The multi-core DGEMM achieves over 100 GigaFlops/sec with eight openMP threads.

cache-blocking↗

Muon Muon Collider: Feasibility Study

A feasibility study is presented of a 2 + 2 TeV muon collider with a luminosity of L = 10{sup 35} cm{sup -2}s{sup -1}. The resulting design is not optimized for performance, and certainly not for cost; however, it does suffice - we believe - to allow us to make a credible case, that a muon collider is a serious possibility for particle physics and, therefore, worthy of R and D support so that the reality of, and interest in, a muon collider can be better assayed. The goal of this support would be to completely assess the physics potential and to evaluate the cost and development of the necessary technology. The muon collider complex consists of components which first produce copious pions, then capture the pions and the resulting muons from their decay; this is followed by an ionization cooling channel to reduce the longitudinal and transverse emittance of the muon beam. The next stage is to accelerate the muons and, finally, inject them into a collider ring wich has a small beta function at the colliding point. This is the first attempt at a point design and it will require further study and optimization. Experimental work will be needed to verify the validity of diverse crucial elements in the design. Muons because of their large mass compared to an electron, do not produce significant synchrotron radiation. As a result there is negligible beamstrahlung and high energy collisions are not limited by this phenomena. In addition, muons can be accelerated in circular devices which will be considerably smaller than two full-energy linacs as required in an e{sup +} - e{sup -} collider. A hadron collider would require a CM energy 5 to 10 times higher than 4 TeV to have an equivalent energy reach. Since the accelerator size is limited by the strength of bending magnets, the hadron collider for the same physics reach would have to be much larger than the muon collider. In addition, muon collisions should be cleaner than hadron collisions. There are many detailed particle reactions which are open to a muon collider and the physics of such reactions - what one learns and the necessary luminosity to see interesting events - are described in detail. Most of the physics accesible to an e{sup +} - e{sup -} collider could be studied in a muon collider. In addition the production of Higgs bosons in the s-channel will allow the measurement of Higgs masses and total widths to high precision; likewise, t{bar t} and W{sup +}W{sup -} threshold studies would yield m{sub t} and m{sub w} to great accuracy. These reactions are at low center of mass energy (if the MSSM is correct) and the luminosity and {Delta}p/p of the beams required for these measurements is detailed in the Physics Chapter. On the other hand, at 2 + 2 TeV, a luminosity of L {approx} 10{sup 35} cm{sup -2}s{sup -1} is desirable for studies such as, the scattering of longitudinal W bosons or the production of heavy scalar particles. Not explored in this work, but worth noting, are the opportunities for muon-proton and muon-heavy ion collisions as well as the enormous richness of such a facility for fixed target physics provided by the intense beams of neutrinos, muons, pions, kaons, antiprotons and spallation neutrons. To see all the interesting physics described herein requires a careful study of the operation of a detector in the very large background. Three sources of background have been identified. The first is from any halo accompanying the muon beams in the collider ring. Very carefully prepared beams will have to be injected and maintained. The second is due to the fact that on average 35% of the muon energy appears in its decay electron. The energy of the electron subsequently is converted into EM showers either from the synchrotron radiation they emit in the collider magnetic field or from direct collision with the surrounding material. The decays that occur as the beams traverse the low beta insert are of particular concern for detector backgrounds. A third source of background is e{sup +} - e{sup -} pair creation from {mu}{sup +} - {mu}{sup -} interaction. Studies of how to shield the detector and reduce the background are addressed in the Detector Chapter. Polarization of the muons allows many very interesting measurements which are discussed in the Physics Chapter. Unlike the electron collider in which the electron beam is highly polarized and the positron beam unpolarized, both muon beams may be partially polarized. It is necessary to select forward moving muons from the pion's decay and thus reduce the available number of muons and hence the luminosity. The necessary machine technology needed to achieve such a collider is discussed in the Option Chapter; at the moment it is not part of our point design, although such capability would almost certainly be incorporated into an actual device.

43 PARTICLE ACCELERATORS↗

Nonlinear optimization for a tumor invasion PDE model

In this work, we introduce a methodology to approximate unknown parameters that appear on a non-linear reaction–diffusion model of tumor invasion. These equations consider that tumor-induced alteration of micro-environmental pH furnishes a mechanism for cancer invasion. A coupled system reaction–diffusion explaining this model is given by three partial differential equations for the non-dimensional spatial distribution and temporal evolution of the density of normal tissue, the neoplastic tissue growth and the excess concentration of H{sup +} ions. The tumor model parameters have a corresponding biological meaning: the reabsorption rate, the destructive influence of H{sup +} ions in the healthy tissue, the growth rate of tumor tissue and the diffusion coefficient. We propose to solve the direct problem using the Finite Element Method (FEM) and minimize an appropriate functional including both the real data (obtained via in-vitro experiments and fluorescence ratio imaging microscopy) and the numerical solution. The gradient of the functional is computed by the adjoint method.

60 APPLIED LIFE SCIENCES↗

Design of a 6 TeV muon collider

Here, a preliminary design of a muon collider ring with the center of mass (CM) energy of 6 TeV is presented. The ring circumference is 6.3 km, and the $\beta$ functions at collision point are 1 cm in each plane. The ring linear optics, the non-linear chromaticity compensation in the Interaction Region (IR), and the additional non-linear orthogonal correcting knobs are described. Magnet specifications are based on the maximum pole-tip field of 20T in dipoles and 15T in quadrupoles. Careful compensation of the non-linear chromatic and amplitude dependent effects provide a sufficiently large dynamic aperture for the momentum range of up to $\pm$0.5% without considering magnet errors.

43 PARTICLE ACCELERATORS↗

Gyrokinetic simulation of driftwave instability in field-reversed configuration

Following the recent remarkable progress in magnetohydrodynamic (MHD) stability control in the C-2U advanced beam driven field-reversed configuration (FRC), turbulent transport has become one of the foremost obstacles on the path towards an FRC-based fusion reactor. Significant effort has been made to expand kinetic simulation capabilities in FRC magnetic geometry. The recently upgraded Gyrokinetic Toroidal Code (GTC) now accommodates realistic magnetic geometry from the C-2U experiment at Tri Alpha Energy, Inc. and is optimized to efficiently handle the FRC's magnetic field line orientation. Initial electrostatic GTC simulations find that ion-scale instabilities are linearly stable in the FRC core for realistic pressure gradient drives. Estimated instability thresholds from linear GTC simulations are qualitatively consistent with critical gradients determined from experimental Doppler backscattering fluctuation data, which also find ion scale modes to be depressed in the FRC core. Beyond GTC, A New Code (ANC) has been developed to accurately resolve the magnetic field separatrix and address the interaction between the core and scrape-off layer regions, which ultimately determines global plasma confinement in the FRC. The current status of ANC and future development targets are discussed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Learning Optimal Solutions for Extremely Fast AC Optimal Power Flow

We develop, in this paper, a machine learning approach to optimize the real-time operation of electric power grids. In particular, we learn feasible solutions to the AC optimal power flow (OPF) problem with negligible optimality gaps. The AC OPF problem aims at identifying optimal operational conditions of the power grids that minimize power losses and/or generation costs. Due to the computational challenges with solving this nonconvex problem, many efforts have focused on linearizing or approximating the problem in order to solve the AC OPF on faster timescales. However, many of these approximations can be fairly poor representations of the actual system state and still require solving an optimization problem, which can be time consuming for large networks. In this work, we learn a mapping between the system loading and optimal generation values, enabling us to find near-optimal and feasible AC OPF solutions. This allows us to bypass solving the traditionally nonconvex AC OPF problem, resulting in a significant decrease in computational burden for grid operators.

machine learning↗

Fuzzified PaCcET for Economic-Emission Scheduling of Microgrids

In this paper, a new approach is proposed to solve a multi-objective economic-emission scheduling problem in microgrids (MGs) by simultaneously minimizing the energy and emission costs of the MG with various distributed energy resources (DERs). The proposed approach is an extension of a computationally effective multiobjective optimization technique, Pareto concavity elimination transformation (PaCcET). The proposed approach, referred to as Fuzzified-PaCcET, employs a fuzzy logic controller to dynamically revise crossover and mutation rates in the original PaCcET leading to the faster convergence of the solution. The proposed approach finds the best Pareto front, also referred to as a Non-dominated set (NDS) of solutions, instead of finding a single optimal solution. In order to find the solutions on concave areas of the Pareto front, an iterative objective space transformation is performed in the PaCcET algorithm to allow a linear combination of objective functions (in the transformed objective space). The proposed Fuzzified-PaCcET-based scheduling is implemented on a MG with various dispatchable and non-dispatchable DERs to find the set of optimal solutions according to the total fuel cost of DERs, as well as the most optimum environmental cost. In order to extract the best compromise solution (BCS) among NDS of solutions, a fuzzy-based method is implemented. The comparison of the simulation results of the Fuzzified-PaCcET with that of PaCcET shows that Fuzzified-PaCcET can generate better solution with less computational burden.

Gautam, Mukesh↗

Learning Optimal Solutions for Extremely Fast AC Optimal Power Flow: Preprint

We develop, in this paper, a machine learning approach to optimize the real-time operation of electric power grids. In particular, we learn feasible solutions to the AC optimal power flow (OPF) problem with negligible optimality gaps. The AC OPF problem aims at identifying optimal operational conditions of the power grids that minimize power losses and/or generation costs. Due to the computational challenges with solving this nonconvex problem, many efforts have focused on linearizing or approximating the problem in order to solve the AC OPF on faster timescales. However, many of these approximations can be fairly poor representations of the actual system state and still require solving an optimization problem, which can be time consuming for large networks. In this work, we learn a mapping between the system loading and optimal generation values, enabling us to find near-optimal and feasible AC OPF solutions. This allows us to bypass solving the traditionally nonconvex AC OPF problem, resulting in a significant decrease in computational burden for grid operators.

machine learning↗

Fuzzified PaCcET for Economic-Emission Scheduling of Microgrids

In this paper, a new approach is proposed to solve a multi-objective economic-emission scheduling problem in microgrids (MGs) by simultaneously minimizing the energy and emission costs of the MG with various distributed energy resources (DERs). The proposed approach is an extension of a computationally effective multiobjective optimization technique, Pareto concavity elimination transformation (PaCcET). The proposed approach, referred to as Fuzzified-PaCcET, employs a fuzzy logic controller to dynamically revise crossover and mutation rates in the original PaCcET leading to the faster convergence of the solution. The proposed approach finds the best Pareto front, also referred to as a Non-dominated set (NDS) of solutions, instead of finding a single optimal solution. In order to find the solutions on concave areas of the Pareto front, an iterative objective space transformation is performed in the PaCcET algorithm to allow a linear combination of objective functions (in the transformed objective space). The proposed Fuzzified-PaCcET-based scheduling is implemented on a MG with various dispatchable and non-dispatchable DERs to find the set of optimal solutions according to the total fuel cost of DERs, as well as the most optimum environmental cost. In order to extract the best compromise solution (BCS) among NDS of solutions, a fuzzy-based method is implemented. The comparison of the simulation results of the Fuzzified-PaCcET with that of PaCcET shows that Fuzzified-PaCcET can generate better solution with less computational burden.

42 ENGINEERING↗

Analysis and Optimization of a Novel Hexagonal Waveguide Concentrator for Solar Thermal Applications

This paper analyzes a novel, cost-effective planar waveguide solar concentrator design that is inspired by cellular hexagonal structures in nature with the benefits of facile installation and low operation and maintenance cost. A coupled thermal and optical analysis of solar irradiation through an ideal hexagonal waveguide concentrator integrated with a linear receiver is presented, along with a cost analysis methodology, to establish the upper limit of performance. The techno-economic model, coupled with numerical optimization, is used to determine designs that maximized power density and minimized the cost of heat in the temperature range of 100–250 °C, which constitutes more than half of the industrial process heat demand. Depending on the incident solar irradiation and the application temperature, the cost of heat for the optimal design configuration ranged between 0.1–0.27 $/W and 0.075–0.18 $/W for waveguide made of ZK7 glass and polycarbonate, respectively. A techno-economic analysis showed the potential of the technology to achieve cost as low as 80 $/m2 and 61 $/m2 for waveguide made of ZK7 glass and polycarbonate material, respectively, which is less than half the cost of state-of-the-art parabolic trough concentrators. Overall, the hexagonal waveguide solar concentrator technology shows immense potential for decarbonizing the industrial process heat and thermal desalination sectors.

14 SOLAR ENERGY↗

Minimum GHG emissions and energy consumption of U.S. PET and polyolefin packaging supply chains in a circular economy

There is a wide agreement on the urgency of transforming linear management of plastics towards a circular economy model. However, no clear pathways exist as to required recycling technologies involved and system-wide environmental impacts. This study explores such pathways in the U.S. for the most commonly used packaging plastics through a combination of mechanical and emerging advanced recycling technologies. A system optimization model aimed at minimizing environmental impacts was developed to determine optimal end-of-life (EOL) management and locations of existing and emerging U.S. recycling infrastructures. Our study includes material flows from virgin resin production through semi-manufacturing processes to existing EOL disposal and recycling processes. An optimized circular plastics packaging system achieved greenhouse gas (GHG) emission savings of up to 28% and cumulative energy demand (CED) savings of up to 46%, compared to the linear economy. Moreover, these savings of GHG emissions and CED impacts represent a reduction of 0.16% and 0.49% compared to annual U.S. GHG emissions and energy consumption in 2022, respectively. The optimal recycling rates and systems-level circularity ranged from 78–99% and 57–75%, respectively. Increased energy savings led to increased GHG emissions showing a potential trade-off between GHG emissions and energy. Analysis of 40 scenarios showed the importance of material collection distances, blend limit of mechanically recycled resins, process yields, and mandated recycling rates for achieving a sustainable circular economy of plastics.

09 - BIOMASS FUELS↗

A Mixed integer linear programming‐based distributed energy management for networked microgrids considering network operational objectives and constraints

Abstract Mixed integer linear programming (MILP)–based distributed energy management for networked microgrids embedded modern distribution systems is proposed. Considering the diverse ownership of microgrids, distributed energy resources (DERs) that interface directly with utilities and responsive loads, an alternating direction method of multipliers–based distributed framework was formulated for the scheduling of networked microgrids embedded modern distribution systems by adjusting nodal price signals iteratively. In addition, to make the formulated optimization problems resolvable through more accessible and popular MILP solvers, different linearisation techniques were employed to transform the nonlinear terms into linear or mixed integer linear formats. The proposed MILP‐based distributed method preserves all participants' autonomy (e.g., microgrids, DERs that interface directly with utilities and responsive loads), while incentivising them to actively participate in the distribution system operation with price signals. The proposed method is validated with results of numerical simulation using a modern distribution system consisting of multiple networked microgrids, DERs that interface directly with utilities, as well as responsive loads.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Parallel performance of algebraic multigrid domain decomposition

Algebraic multigrid (AMG) is a widely used scalable solver and preconditioner for large-scale linear systems resulting from the discretization of a wide class of elliptic PDEs. While AMG has optimal computational complexity, the cost of communication has become a significant bottleneck that limits its scalability as processor counts continue to grow on modern machines. This article examines the design, implementation, and parallel performance of a novel algorithm, algebraic multigrid domain decomposition (AMG-DD), designed specifically to limit communication. The goal of AMG-DD is to provide a low-communication alternative to standard AMG V-cycles by trading some additional computational overhead for a significant reduction in communication cost. Numerical results show that AMG-DD achieves superior accuracy per communication cost compared with AMG, and speedup over AMG is demonstrated on a large GPU cluster.

97 MATHEMATICS AND COMPUTING↗