Demonstration of a Scaling Advantage for a Quantum Annealer over Simulated Annealing
Not Available
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
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Calculation of large-aspect-ratio tokamak and toroidally-averaged stellarator equilibria of high-beta reduced magnetohydrodynamics via simulated annealing
A simulated annealing (SA) relaxation method is used for the calculation of high-beta reduced magnetohydrodynamics (MHD) equilibria in toroidal geometry. The SA method, based on artificial dynamics derived from the MHD Hamiltonian structure, is used to calculate equilibria of large-aspect-ratio and circular-cross-section tokamaks as well as toroidally averaged stellarators. Tokamak equilibria including incompressible poloidal rotations are obtained and the Shafranov shift is seen to increase nearly quadratically in the rotation speed. A mapping procedure between non-rotating and poloidally rotating equilibria is shown to explain the quadratic dependence of equilibria shift on rotation. Calculated stellarator equilibria are seen to agree reasonably with previous results. The numerical results demonstrate the first successful application of the SA method to obtain toroidal equilibria.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Parallel simulated annealing with embedded machine learning and multifidelity models for reactor core design
This paper presents extensions to a penalty-free, parallel simulated annealing (SA) algorithm for multi-constrained combinatorial optimization with the aim of embedding multi-fidelity physics models into the annealing procedure. The method uses a low-fidelity, quickly executing model for rapid design space exploration and a high-fidelity model for detailed constraint resolution and on-the-fly bias correction. Machine learning models updated within the annealing procedure were used to bridge the gap between the multi-fidelity models, which led to accurate rapid exploration and efficient detailed constraint resolution. A software implementation of the new multi-fidelity optimization methods, called ML-PSA, was demonstrated on a continuous multi-fidelity optimization problem and a constrained combinatorial PWR lattice design problem. These problems demonstrate some of the features, parallel performance characteristics, and extensible nature of the multi-fidelity SA methods. This paper shows that the developed software and procedure are a general optimization tool that can be applied to a wide variety of scientific and engineering design optimization applications. (authors)
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
Linear stability analysis via simulated annealing and accelerated relaxation
Simulated annealing (SA) is a kind of relaxation method for finding equilibria of Hamiltonian systems. A set of evolution equations is solved with SA, which is derived from the original Hamiltonian system so that the energy of the system changes monotonically while preserving Casimir invariants inherent to noncanonical Hamiltonian systems. The energy extremum reached by SA is an equilibrium. Since SA searches for an energy extremum, it can also be used for stability analysis when initiated from a state where a perturbation is added to an equilibrium. The procedure of the stability analysis is explained, and some examples are shown. Because the time evolution is computationally time consuming, efficient relaxation is necessary for SA to be practically useful. An acceleration method is developed by introducing time dependence in the symmetric kernel used in the double bracket, which is part of the SA formulation described here. An explicit formulation for low-beta reduced magnetohydrodynamics (MHD) in cylindrical geometry is presented. In conclusion, since SA for low-beta reduced MHD has two advection fields that relax, it is important to balance the orders of magnitude of these advection fields.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Simulated annealing of reduced magnetohydrodynamic systems
Theory of simulated annealing (SA), a method for equilibrium and stability analyses for Hamiltonian systems, is reviewed. The SA explained in this review is based on a double bracket formulation that derives from Hamiltonian structure. In addition to general theoretical aspects, the explicit formulation as well as numerical applications are presented. Both finite and infinite degree-of-freedom systems are treated, in particular, the heavy top, a toy model mimicking low-beta reduced magnetohydrodynamics (MHD) and low- and high-beta reduced MHD. Furthermore, the numerical results successfully demonstrate the usefulness of SA for equilibrium and stability analyses. At the same time, the results raise some future issues that are discussed in the paper.
Poisson Bracket↗
Transient Storage Model Parameter Optimization Using the Simulated Annealing Method
Hyporheic exchange in streams is critical to ecosystem functions such as nutrient cycling along river corridors, especially for slowly moving or small stream systems. The transient storage model (TSM) has been widely used for modeling of hyporheic exchange. TSM calibration, for hyporheic exchange, is typically used to estimate four parameters, including the mass exchange rate coefficient, the dispersion coefficient, stream cross-sectional area, and hyporheic zone cross-sectional area. Prior studies have raised concerns regarding the non-uniqueness of the inverse problem for the TSM, that is, the occurrence of different parameter vectors resulting in TSM solution that reproduces the observed in-stream tracer break through curve (BTC) with the same error. This leads to practical non-identifiability in determining the unknown parameter vector values even when global-optimal values exist, and the parameter optimization becomes practically non-unique. To address this problem, we applied the simulated annealing method to calibrate the TSM to BTCs, because it is less susceptible to local minima-induced non-identifiability. A hypothetical (or synthetic) tracer test data set with known parameters was developed to demonstrate the capability of the simulated annealing method to find the global minimum parameter vector, and it identified the “hypothetically-true” global minimum parameter vector even with input data that were modified with up to 10% noise without increasing the number of iterations required for convergence. The simulated annealing TSM was then calibrated using two in-stream tracer tests conducted in East Fork Poplar Creek, Tennessee. In conclusion, simulated annealing was determined to be appropriate for quantifying the TSM parameter vector because of its search capability for the global minimum parameter vector.
54 ENVIRONMENTAL SCIENCES↗
Optimization of Type 4 composite pressure vessels using genetic algorithms and simulated annealing
We propose and demonstrate two methodologies for weight minimization of Type 4 (plastic lined, fiber wrapped) compressed hydrogen pressure vessels: genetic algorithms and simulated annealing. We consider 70 MPa vessels with a safety factor of 2.25, and analyze the vessels with classical laminate theory. We propose an objective function based on Tsai-Wu criterion, composite thickness, a safety factor, and a penalization factor. Here, the optimum results are analyzed and compared by a high resolution finite element model. Computer simulations show that the proposed methodology produces more efficient designs by reducing the weight by up to 9.8% and 11.2% when compared to previously published vessel optimization research.
08 HYDROGEN↗
Confining Liquids inside Carbon Nanotubes: Accelerated Molecular Dynamics with Spliced, Soft-Core Potentials and Simulated Annealing
Understanding emergent phenomena of fluids under physical confinement requires the development of advanced tools for rapid and accurate simulation of their physiochemical properties. Simulating liquid molecules commensurate in size with the nanoscale enclosures that confine them is a key challenge. In this work, we demonstrate an accelerated molecular dynamics simulation technique that combines soft-core potentials (SCP) and simulated annealing (SA) to analyze confined liquids. This integrated SCP/SA method relies on a new spliced soft-core potential (SSCP), which enables tunable accuracy with respect to the target hard-core potential (HCP). SCP/SA enables the packing of enclosures with bulk material in a controlled, thermodynamically consistent manner. The enhanced SSCP accuracy is a critical feature of SCP/SA, enabling a smooth transition between the SCP and the HCP at a desired SCP hardness. We applied SCP/SA to the problem of filling a carbon nanotube (CNT) in periodic boundary conditions with a popular ionic liquid (IL), 1- butyl-3-methylimidazolium hexafluorophosphate $[\text{BMIM}^+][\text{PF}^–_6]$. We performed a series of triplicate simulations on systems with varying CNT diameter and charge to demonstrate SCP/SA’s versatility. Beyond this IL/CNT system, the SCP/SA simulation framework has a broad range of potential applications, not limited to nanoscale enclosures and interfaces, including both solid-state and biological systems.
36 MATERIALS SCIENCE↗
Accelerating Convergence of Free Energy Computations with Hamiltonian Simulated Annealing of Solvent (HSAS)
Coupling between binding of a ligand to a receptor and the displacement of a number of bound water molecules is a common event in molecular recognition processes. When the binding site is deeply buried and the exchange of water molecules with the bulk region is difficult to sample, the convergence and accuracy in free energy calculations can be severely compromised. Traditionally, Grand Canonical Monte Carlo (GCMC) based methods have been used to accelerate equilibration of water-at the expense, however, of lengthy trials before a molecular dynamics (MD) simulation. In this paper, a user-friendly and cost-efficient method, Hamiltonian simulated annealing of solvent in combination with lambda-exchange of free energy perturbation (FEP) is proposed to accelerate the sampling of water molecules in free energy calculations. As an illustrative example with reliable data from previous GCMC simulations, absolute binding affinity of camphor to cytochrome P450 was calculated. The simulated hydration state change in the buried binding pocket quantitatively agrees with GCMC simulations. Finally, it is shown that the new protocol significantly accelerates sampling of water in a buried binding pocket and the convergence of free energy, with negligible setup and computing costs compared to GCMC methods.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Inversion of downhole electrical measurements for proppant mapping using very fast simulated annealing
Proppant mapping is critical for optimizing fracture treatment design and improving wells’ productivity. An electrode-based resistivity tool concept was developed earlier for proppant mapping in cased-hole wells. An array of insulating gaps is installed and cemented in place as a permanent part of the casing string. The electrical measurements are performed by imposing a voltage across each insulating gap, one at a time, before and after hydraulic fracture operations. The voltages across other insulating gaps near the transmitter gap are recorded. The method relies on direct excitation of the casing, which is expected to overcome the severe limitations of induction tools in cased-hole wells. A forward model based on a finite volume method has been developed to simulate the tool’s response to one or multiple fractures. To enable the implementation of such a practical system in multistage fractured horizontal wells, a fast and robust inversion approach is required. To that end, we have developed a divide-and-conquer approach based on a global optimization algorithm very fast simulated annealing (VFSA). Specifically, the original inverse problem is divided into subproblems and each subproblem can be solved separately using VFSA. The results indicate that our approach can invert the data and output widths and radii of multiple fractures without requiring a large number of forward simulations. The robustness of the inverse solver is also tested by adding Gaussian noise to the synthetic data. We tested example cases that demonstrate that when up to 5% noise is introduced, VFSA still provides very accurate inversion results with moderate uncertainties. Inversion results with some more realistic conditions, e.g., tilted fractures, complex fractures, and so on, are also presented.
Geochemistry & Geophysics↗
Optimization of type III pressure vessels using genetic algorithm and simulated annealing
Not Available
Alcántar, V.↗
Angular filter refractometry analysis using simulated annealing [An improved method for characterizing plasma density profiles using angular filter refractometry]
Here, a new method of analysis for angular filter refractometry images was developed to characterize laser-produced, long-scale-length plasmas using an annealing algorithm to iterative converge upon a solution. Angular filter refractometry (AFR) is a novel technique used to characterize the density pro files of laser-produced, long-scale-length plasmas. A synthetic AFR image is constructed by a user-defined density profile described by eight parameters, and the algorithm systematically alters the parameters until the comparison is optimized. The optimization and statistical uncertainty calculation is based on a minimization of the $\chi$2 test statistic. The algorithm was successfully applied to experimental data of plasma expanding from a flat, laser-irradiated target, resulting in average uncertainty in the density profile of 5-10% in the region of interest.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Dependence on Dielectric Model and pH in a Synthetic Helical Peptide Studied by Monte Carlo Simulated Annealing
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Okamoto, Y.↗
Deterministic direct aperture optimization using multiphase piecewise constant segmentation
Purpose Direct aperture optimization (DAO) attempts to incorporate machine constraints in the inverse optimization to eliminate the post‐processing steps in fluence map optimization (FMO) that degrade plan quality. Current commercial DAO methods utilize a stochastic or greedy approach to search a small aperture solution space. In this study, we propose a novel deterministic direct aperture optimization that integrates the segmentation of fluence map in the optimization problem using the multiphase piecewise constant Mumford‐Shah formulation. Methods The Mumford‐Shah based direct aperture optimization problem was formulated to include an L2‐norm dose fidelity term to penalize differences between the projected dose and the prescribed dose, an anisotropic total variation term to promote piecewise continuity in the fluence maps, and the multiphase piecewise constant Mumford‐Shah function to partition the fluence into pairwise discrete segments. A proximal‐class, first‐order primal‐dual solver was implemented to solve the large scale optimization problem, and an alternating module strategy was implemented to update fluence and delivery segments. Three patients of varying complexity—one glioblastoma multiforme (GBM) patient, one lung (LNG) patient, and one bilateral head and neck (H&N) patient with 3 PTVs—were selected to test the new DAO method. For each patient, 20 non‐coplanar beams were first selected using column generation, followed by the Mumford‐Shah based DAO (DAO MS ). For comparison, a popular and successful approach to DAO known as simulated annealing—a stochastic approach—was replicated. The simulated annealing DAO (DAO SA ) plans were then created using the same beam angles and maximum number of segments per beam. PTV coverage, PTV homogeneity , and OAR sparing were assessed for each plan. In addition, high dose spillage, defined as the 50% isodose volume divided by the tumor volume, as well as conformity, defined as the van't Riet conformation number, were evaluated. Results DAO MS achieved essentially the same OAR doses compared with the DAO SA plans for the GBM case. The average difference of OAR D max and D mean between the two plans were within 0.05% of the plan prescription dose. The lung case showed slightly improved critical structure sparing using the DAO MS approach, where the average OAR D max and D mean were reduced by 3.67% and 1.08%, respectively, of the prescription dose. The DAO MS plan substantially improved OAR dose sparing for the H&N patient, where the average OAR D max and D mean were reduced by over 10% of the prescription dose. The DAO MS and DAO SA plans were comparable for the GBM and LNG PTV coverage, while the DAO MS plan substantially improved the H&N PTV coverage, increasing D99 by 6.98% of the prescription dose. For the GBM and LNG patients, the DAO MS and DAO SA plans had comparable high dose spillage but slightly worse conformity with the DAO MS approach. For the H&N plan, DAO MS was considerably superior in high dose spillage and conformity to the DAO SA . The deterministic approach is able to solve the DAO problem substantially faster than the simulated annealing approach, with a 9.5‐ to 40‐fold decrease in total solve time, depending on the patient case. Conclusions A novel deterministic direct aperture optimization formulation was developed and evaluated. It combines fluence map optimization and the multiphase piecewise constant Mumford‐Shah segmentation into a unified framework, and the resulting optimization problem can be solved efficiently. Compared to the widely and commercially used simulated annealing DAO approach, it showed comparable dosimetry behavior for simple plans, and substantially improved OAR sparing, PTV coverage, PTV homogeneity, high dose spillage, and conformity for the more complex head and neck plan.
Nguyen, Dan↗
Qubit Assignment Using Time Reversal
As quantum computers with large numbers of qubits become increasingly available, experiments executed on a given device may not utilize all available qubits. In this case, the outcome of executing a quantum program will depend on the ability to efficiently select a subset of high-performing physical qubits. For any given quantum program and device there are many ways to assign physical qubits for execution of the program, and assignments will differ in performance due to the variability in quality across qubits and entangling operations on a single device. Evaluating the performance of each assignment using fidelity estimation introduces significant experimental overhead and will be infeasible for many applications, while relying on standard device benchmarks provides incomplete information about the performance of any specific program. Furthermore, the number of possible assignments grows combinatorially in the number of qubits on the device and in the program, motivating the use of heuristic optimization techniques. We demonstrate a practical solution to the problem of qubit assignment by using simulated annealing with a cost function based on the Loschmidt echo, a diagnostic that measures the reversibility of a quantum process. We provide theoretical justification for this choice of cost function by demonstrating that the optimal qubit assignment coincides with the optimal qubit assignment based on state fidelity in the weak error limit, and we provide experimental justification using diagnostics performed on Google’s superconducting qubit devices. We then establish the performance of simulated annealing for qubit assignment using classical simulations of noisy devices as well as optimization experiments performed on a quantum processor. Our results demonstrate that the use of Loschmidt echoes and simulated annealing provides a scalable and flexible approach to optimizing qubit assignment on near-term hardware.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Generalized spin σ -SCF method
We introduce a generalization of the σ-SCF method to approximate noncollinear spin ground and excited single-reference electronic states by minimizing the Hamiltonian variance. The new method is based on the σ-SCF method, originally proposed by Ye et al. [J. Chem. Phys. 147, 214104 (2017)], and provides a prescription to determine ground and excited noncollinear spin states on an equal footing. Our implementation was carried out utilizing an initial simulated annealing stage followed by a mean-field iterative self-consistent approach to simplify the cumbersome search introduced by generalizing the spin degrees of freedom. The simulated annealing stage ensures a broad exploration of the Hilbert space spanned by the generalized spin single-reference states with random complex element-wise rotations of the generalized density matrix elements in the simulated annealing stage. The mean-field iterative self-consistent stage employs an effective Fockian derived from the variance, which is utilized to converge tightly to the solutions. This process helps us to easily find complex spin structures, avoiding manipulating the initial guess. As proof-of-concept tests, we present results for Hn (n = 3–7) planar rings and polyhedral clusters with geometrical spin frustration. We show that most of these systems have noncollinear spin excited states that can be interpreted in terms of geometric spin frustration. These states are not directly targeted by energy minimization methods, which are meant to converge to the ground state. This stresses the capability of the σ-SCF methodology to find approximate noncollinear spin structures as mean-field excited states.
Chemistry↗
On the Computational Viability of Quantum Optimization for PMU Placement
Using optimal phasor measurement unit placement as a prototypical problem, we assess the computational viability of the current generation D-Wave Systems 2000Q quantum annealer for power systems design problems. We reformulate minimum dominating set for the annealer hardware, solve the reformulation for a standard set of IEEE test systems, and benchmark solution quality and time to solution against the CPLEX optimizer and simulated annealing. For some problem instances the 2000Q outpaces CPLEX. For instances where the 2000Q underperforms with respect to CPLEX and simulated annealing, we suggest hardware improvements for the next generation of quantum annealers.
hardware↗