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Constrained minimization of smooth functions using a genetic algorithm
The use of genetic algorithms for minimization of differentiable functions that are subject to differentiable constraints is considered. A technique is demonstrated for converting the solution of the necessary conditions for a constrained minimum into an unconstrained function minimization. This technique is extended as a global constrained optimization algorithm. The theory is applied to calculating minimum-fuel ascent control settings for an energy state model of an aerospace plane.
Robust online monitoring for calibration assessment of transmitters and instrumentation - 260
Robust online monitoring (OLM) technologies are expected to enable the extension or elimination of periodic sensor calibration intervals in operating and new reactors. Advances in OLM technologies will improve the safety and reliability of current and planned nuclear power systems through improved accuracy and increased reliability of sensors used to monitor key parameters. In this paper, we discuss an overview of research being performed within the Nuclear Energy Enabling Technologies (NEET)/Advanced Sensors and Instrumentation (ASI) program, for the development of OLM algorithms to use sensor outputs and, in combination with other available information, 1) determine whether one or more sensors are out of calibration or failing and 2) replace a failing sensor with reliable, accurate sensor outputs. A Gaussian Process (GP)-based uncertainty quantification (UQ) method previously developed for UQ in OLM, was adapted for this purpose. The resulting models are being evaluated for use in high-confidence signal validation for the purpose of detecting and diagnosing sensor faults, and for computing virtual sensor outputs that may be used as a temporary replacement for failing sensors. In addition to assessing sensor drift, approaches for extracting sensor response time in an automated fashion were developed, for monitoring changes in sensor response time in pressure transmitters. Such changes are also indicative of various fault modes. These algorithms were evaluated with existing measurement data from several laboratory-scale flow loops. Ongoing research in this project is focused on further evaluation of the algorithms, optimization for accuracy and computational efficiency, and integration into a suite of tools for robust OLM that are applicable to monitoring sensor calibration state in nuclear power plants. (authors)
A scalable matrix-free spectral element approach for unsteady PDE constrained optimization using PETSc/TAO
In this work, we provide a new approach for the efficient matrix-free application of the transpose of the Jacobian for the spectral element method for the adjoint-based solution of partial differential equation (PDE) constrained optimization. This results in optimizations of nonlinear PDEs using explicit integrators where the integration of the adjoint problem is not more expensive than the forward simulation. Solving PDE constrained optimization problems entails combining expertise from multiple areas, including simulation, computation of derivatives, and optimization. The Portable, Extensible Toolkit for Scientific computation (PETSc) together with its companion package, the Toolkit for Advanced Optimization (TAO), is an integrated numerical software library that contains an algorithmic/software stack for solving linear systems, nonlinear systems, ordinary differential equations, differential algebraic equations, and large-scale optimization problems and, as such, is an ideal tool for performing PDE-constrained optimization. This paper describes an efficient approach in which the software stack provided by PETSc/TAO can be used for large-scale nonlinear time-dependent problems. Time integration can involve a range of high-order methods, both implicit and explicit. The PDE-constrained optimization algorithm used is gradient-based and seamlessly integrated with the simulation of the physical problem.
SU-E-T-10: A Clinical Implementation and the Dosimetric Evidence in High Dose Rate Vaginal Multichannel Applicator Brachytherapy
Purpose: The multichannel cylindrical applicator has a distinctive modification of the traditional single channel cylindrical applicator. The novel multichannel applicator has additional peripheral channels that provide more flexibility both in treatment planning process and outcomes. To protect by reducing doses to adjacent organ at risk (OAR) while maintaining target coverage with inverse plan optimization are the goals for such novel Brachytherapy device. Through a series of comparison and analysis of reults in more than forty patients who received HDR Brachytherapy using multichannel vaginal applicator, this procedure has been implemented in our institution. Methods: Multichannel planning was CT image based. The CTV of 5mm vaginal cuff rind with prescribed length was well reconstructed as well as bladder and rectum. At least D95 of CTV coverage is 95% of prescribed dose. Multichannel inverse plan optimization algorithm not only shapes target dose cloud but set dose avoids to OAR’s exclusively. The doses of D2cc, D5cc and D5; volume of V2Gy in OAR’s were selected to compare with single channel results when sole central channel is only possibility. Results: Study demonstrates plan superiorly in OAR’s doe reduction in multi-channel plan. The D2cc of the rectum and bladder were showing a little lower for multichannel vs. single channel. The V2Gy of the rectum was 93.72% vs. 83.79% (p=0.007) for single channel vs. multichannel respectively. Absolute reduced mean dose of D5 by multichannel was 17 cGy (s.d.=6.4) and 44 cGy (s.d.=15.2) in bladder and rectum respectively. Conclusion: The optimization solution in multichannel was to maintain D95 CTV coverage while reducing the dose to OAR’s. Dosimetric advantage in sparing critical organs by using a multichannel applicator in HDR Brachytherapy treatment of the vaginal cuff is so promising and has been implemented clinically.
Alchemy: A Model-Based Approach for 2D to 3D Autonomous Nuclear System Design
Engineering design of nuclear power plant (NPP) piping and equipment systems frequently bypasses crucial 2D system planning, instead moving straight to 3D modeling. This often leads to designs that exceed building envelope constraints, forcing expensive and time-consuming redesigns. When 2D modeling is employed, it typically involves labor-intensive manual workflows that convert 2D drawings into 3D models, resulting in inefficiencies and errors across design iterations. These workflows further suffer from poor software interoperability and dependence on proprietary software ecosystems, thereby contributing to schedule delays and cost overruns. This paper presents Alchemy, an autonomous framework that transforms 2D system definitions into Industry Foundation Classes (IFC)-compliant 3D building information models (BIMs) for expediting nuclear facility design at the conceptual preliminary phase. Using a model-based approach, the framework treats the 2D system diagram as the central reference model employed to automatically generate all subsequent outputs, ensuring consistency between the system definition and the resulting physical design. A web-based interface enables engineers to define hierarchical system topologies including associated equipment, geometric properties, and connectivity requirements. A two-phase equipment layout optimization algorithm automatically computes collision-free spatial configurations within predefined building envelopes. An artificial intelligence (AI)-assisted pipe routing module then generates orthogonal, collision-free routing paths, allowing the user to select either an A* search-based method or an Ant Colony Optimization (ACO)-based method. All outputs are authored natively in IFC format, relying on open-source technologies and standardized formats in order to ensure extensibility and eliminate proprietary software dependencies. The proposed framework is validated on two representative pressurized-water reactor (PWR)-based case studies, for which it autonomously generates IFC-compliant 3D models in minutes, drastically reducing workflows that typically require hours of manual effort. The generated model demonstrates topologically correct equipment placement, physically plausible spatial relationships, and collision-free pipe routing consistent with known PWR loop configurations. This work represents a foundational step toward digital engineering for nuclear facility preliminary design, with future ongoing development targeting design code compliance and expanded system complexity.
An asynchronous parallel high-throughput model calibration framework for crystal plasticity finite element constitutive models
Crystal plasticity finite element model (CPFEM) is a powerful numerical simulation in the integrated computational materials engineering toolboxes that relates microstructures to homogenized materials properties and establishes the structure–property linkages in computational materials science. However, to establish the predictive capability, one needs to calibrate the underlying constitutive model, verify the solution and validate the model prediction against experimental data. Bayesian optimization (BO) has stood out as a gradient-free efficient global optimization algorithm that is capable of calibrating constitutive models for CPFEM. Here in this paper, we apply a recently developed asynchronous parallel constrained BO algorithm to calibrate phenomenological constitutive models for stainless steel 304 L, Tantalum, and Cantor high-entropy alloy.
Sensitivity-based Similarity Metrics for New Experiment Design Optimization
The nuclear data used in advanced reactor simulations requires validation. Data from nuclear criticality experiments can provide this validation. New nuclear criticality experiment design requires extensive knowledge and expert judgement such that the experimental design parameters are selected in such a way to keep the experiment subcritical. To aide in this experimental design process, professionals can utilize sensitivity and uncertainty analysis. Sensitivity and uncertainty analysis relies on matching new application experiments with currently existing benchmark experiments. Currently, there is functionality in the Whisper 1.1 software package to calculate a similarity metric based on neutron multiplication factor sensitivity coefficients between a new application designed by the user and existing International Criticality Safety Benchmark Experiment Project (ICSBEP) benchmarks. The Whisper 1.1 software package is included in Monte Carlo N-Particle ® Code Version 6.21 (MCNP ® 6.2). This work is geared toward expanding this capability to new similarity metrics based on beta-effective sensitivity coefficients and reactivity coefficient sensitivity coefficients. While the investigation of these sensitivity coefficients is presented in detail in separate works at this same conference, this work will be primarily focused on studying the similarity metrics in more detail. These similarity metrics will then be incorporated into the optimization algorithms used for experiment design in EUCLID (Experiments Underpinned by Computational Learning for Improvements in nuclear Data), which is a Los Alamos National Laboratory (LANL) project designed to constrain nuclear data of interest, such that adjustments can be made to possible inaccuracies. A more detailed optimization can be subsequently performed by breaking down these similarity metrics by isotope, reaction, and energy.
Flexible silicon photonic architecture for accelerating distributed deep learning
The increasing size and complexity of deep learning (DL) models have led to the wide adoption of distributed training methods in datacenters (DCs) and high-performance computing (HPC) systems. However, communication among distributed computing units (CUs) has emerged as a major bottleneck in the training process. In this study, we propose Flex-SiPAC, a flexible silicon photonic accelerated compute cluster designed to accelerate multi-tenant distributed DL training workloads. Flex-SiPAC takes a co-design approach that combines a silicon photonic hardware platform with a tailored collective algorithm, optimized to leverage the unique physical properties of the architecture. The hardware platform integrates a novel wavelength-reconfigurable transceiver design and a micro-resonator-based wavelength-reconfigurable switch, enabling the system to achieve flexible bandwidth steering in the wavelength domain. The collective algorithm is designed to support reconfigurable topologies, enabling efficient all-reduce communications that are commonly used in DL training. The feasibility of the Flex-SiPAC architecture is demonstrated through two testbed experiments. First, an optical testbed experiment demonstrates the flexible routing of wavelengths by shuffling an array of input wavelengths using a custom-designed spatial-wavelength selective switch. Second, a four-GPU testbed running two DL workloads shows a 23% improvement in job completion time compared to a similarly sized leaf-spine topology. We further evaluate Flex-SiPAC using large-scale simulations, which show that Flex-SiPAC is able to reduce the communication time by 26% to 29% compared to state-of-the-art compute clusters under representative collective operations.
mystic - a brief introduction
The mystic framework enables the solving of difficult optimization problems through three major innovations: (1) plug-and-play component-based optimization algorithms, (2) the ability to dynamically construct and apply generalzed trnasforms, K , where x' = K(x) , and (3) workflows providing asynchronous execution and statefulness. These features, in conjunction with supporting packages pathos , pyina , and klepto , can provide massively-parallel scalable workflows for quickly solving optimization problems in complex nonlinear spaces. mystic can be used to simplify non-convex optimization problems by transforming away nonlinearities through user-built kernel transforms. This tutorial demonstrates using mystic for machine learning with automated dimensional-reduction, using embarrasingly parallel solver ensembles to find an accurate interpolated surrogate for a nonlinear surface, and the determination of worst-case bounds on expectation value of an objective function under uncertainty.
Computational mechanics analysis tools for parallel-vector supercomputers
Computational algorithms for structural analysis on parallel-vector supercomputers are reviewed. These parallel algorithms, developed by the authors, are for the assembly of structural equations, 'out-of-core' strategies for linear equation solution, massively distributed-memory equation solution, unsymmetric equation solution, general eigen-solution, geometrically nonlinear finite element analysis, design sensitivity analysis for structural dynamics, optimization algorithm and domain decomposition. The source code for many of these algorithms is available from NASA Langley.
Combined Retrievals of Boreal Forest Fire Aerosol Properties with a Polarimeter and Lidar
Absorbing aerosols play an important, but uncertain, role in the global climate. Much of this uncertainty is due to a lack of adequate aerosol measurements. While great strides have been made in observational capability in the previous years and decades, it has become increasingly apparent that this development must continue. Scanning polarimeters have been designed to help resolve this issue by making accurate, multi-spectral, multi-angle polarized observations. This work involves the use of the Research Scanning Polarimeter (RSP). The RSP was designed as the airborne prototype for the Aerosol Polarimetery Sensor (APS), which was due to be launched as part of the (ultimately failed) NASA Glory mission. Field observations with the RSP, however, have established that simultaneous retrievals of aerosol absorption and vertical distribution over bright land surfaces are quite uncertain. We test a merger of RSP and High Spectral Resolution Lidar (HSRL) data with observations of boreal forest fire smoke, collected during the Arctic Research of the Composition of the Troposphere from Aircraft and Satellites (ARCTAS). During ARCTAS, the RSP and HSRL instruments were mounted on the same aircraft, and validation data were provided by instruments on an aircraft flying a coordinated flight pattern. We found that the lidar data did indeed improve aerosol retrievals using an optimal estimation method, although not primarily because of the constraints imposed on the aerosol vertical distribution. The more useful piece of information from the HSRL was the total column aerosol optical depth, which was used to select the initial value (optimization starting point) of the aerosol number concentration. When ground based sun photometer network climatologies of number concentration were used as an initial value, we found that roughly half of the retrievals had unrealistic sizes and imaginary indices, even though the retrieved spectral optical depths agreed within uncertainties to independent observations. The convergence to an unrealistic local minimum by the optimal estimator is related to the relatively low sensitivity to particles smaller than 0.1 ( m) at large optical thicknesses. Thus, optimization algorithms used for operational aerosol retrievals of the fine mode size distribution, when the total optical depth is large, will require initial values generated from table look-ups that exclude unrealistic size/complex index mixtures. External constraints from lidar on initial values used in the optimal estimation methods will also be valuable in reducing the likelihood of obtaining spurious retrievals.
Exploring Network-Related Optimization Problems Using Quantum Heuristics
Network-related connectivity optimization problems are underlying a wide range of applications and are also of high computational complexity. We consider studying network optimization problems using two types of quantum heuristics.One is quantum annealing, and the other Quantum Alternating Operator Ansatz, an extension of the Quantum Approximate Optimization Algorithms for gate-model quantum computation, in which a cost-function based unitary and a non-commuting mixing unitary are applied alternately. We present problem mappings for problems of finding the spanning-tree or spanning-graph of a graph that optimizes certain costs, and a variant that further requires the spanning-tree be degree-bounded. With quantum annealing, all constraints are cast into penalty terms in the cost Hamiltonian, and the solution is encoded as the ground state of the Hamiltonian. We provide three mappings to the quadratic unconstrained binary optimization (QUBO) form, compare the resource requirements, and analyze the tradeoffs. For QAOA, we give special focus on the design of mixers based on the constraints presented in the problem, such that the system evolution remains in a subspace of the full Hilbert space where all constraints are satisfied. In the spanning-tree problem, one such hard constraint is that a mixer applied to a spanning-tree needs also be a spanning tree. This involves checking the connectivity of a subgraph, which is a global condition common for most network-related problems. We show how this feature can be efficiently represented in the mixer in a quantum coherent way, based on manipulation of a descendant-matrix and an adjacent matrix. We further develop a mixer for the spanning-graphs based on the spanning-tree mixer.
Study network-related optimization problems using quantum alternating optimization ansatz
Network-related connectivity optimization problems are underlying a wide range of applications and are also of high computational complexity. We consider studying network optimization problems using two types of quantum heuristics. One is quantum annealing, and the other Quantum Alternating Operator Ansatz, an extension of the Quantum Approximate Optimization Algorithms for gate-model quantum computation, in which a cost-function based unitary and a non-commuting mixing unitary are applied alternately. We present problem mappings for problems of finding the spanning-tree or spanning-graph of a graph that optimizes certain costs, and a variant that further requires the spanning-tree be degree-bounded. With quantum annealing, all constraints are cast into penalty terms in the cost Hamiltonian, and the solution is encoded as the ground state of the Hamiltonian. We provide three mappings to the quadratic unconstrained binary optimization (QUBO) form, compare the resource requirements, and analyze the tradeoffs. For QAOA, we give special focus on the design of mixers based on the constraints presented in the problem, such that the system evolution remains in a subspace of the full Hilbert space where all constraints are satisfied. In the spanning-tree problem, one such hard constraint is that a mixer applied to a spanning-tree needs also be a spanning tree. This involves checking the connectivity of a subgraph, which is a global condition common for most network-related problems. We show how this feature can be efficiently represented in the mixer in a quantum coherent way, based on manipulation of a descendant-matrix and an adjacent matrix. We further develop a mixer for the spanning-graphs based on the spanning-tree mixer.
Computer Simulation For Multilevel Optimization Of Design
New simulator for multilevel optimization of complex hierarchical systems reduces cost of analysis in experimentation with multilevel design-optimization algorithms. Computer program mimics qualitative behavior and data couplings that occur among subsystems of complex engineering system, such as car, aircraft, or building. Eliminates engineering analyses in subsystems by replacing them with judiciously-chosen analytical functions. Serves as tool for development of strategy for multilevel optimization of design.
MO-D-213-04: The Proximity to the Skin of PTV Affects PTV Coverage and Skin Dose for TomoTherapy
Purpose: The proximity to the skin surface of the PTV for the patients with skin disease could be a concern in terms of the PTV coverage and actual surface dose (SD). IMRT optimization algorithms increase the beam intensity close to the skin in order to compensate for lack of scattering material, leading to enhanced SD but potential hot spots. This study aims to investigate the effect of PTV proximity to the skin on planning and measured SD Methods: All measurements were done for 6 MV X-ray beam of Helical TomoTherapy. An anthropomorphic phantom was scanned in a CT simulator in a routine manner with thermoplastic mask immobilization. PTVs were created with varying distances to the skin of 0 mm -(PTV1), 1 mm- (PTV2), 2 mm-(PTV3) and 3 mm-(PTV4). Also, a 5 mm bolus was used with PTV1 (PTV5). All planning constraints were kept the same in all studies (hard constraint: 95% of the prescription dose covered 95% of the PTV). Gafchromic film (EBT3) was placed under the mask on the phantom surface, and the resulting dose was estimated using RIT software. Results: Optimizing the dose using different PTVs lead to average planned target doses of 10.8, 10.3, 10.2, 10.3 and 10.0 Gy, with maximum doses 12.2, 11.2, 11.1, 11.1 and 10.0 Gy for PTV1, PTV2, PTV3, PTV4 and PTV5, respectively. EBT3 measurements indicated a significant decrease of SD with skin distance by 12.7% (PTV1), 21.9% (PTV2), 24.8% (PTV3) and 28.4% (PTV4) comparing to prescription dose. Placement of a 5 mm bolus on the phantom surface resulted in a SD close to prescribed (+0.5%). Conclusion: This work provides a clear demonstration of the relationship between the skin dose and the PTV to the skin distance. The results indicate the necessity of a bolus even for TomoTherapy when high skin dose is required.
Development and application of marginal likelihood optimization for integral parameter adjustment
When adjusting nuclear data with integral experiments, care must be taken that spurious adjustments are not made by assimilating poorly characterized integral parameters. If there are unaccounted for biases or poorly estimated uncertainties in the calculated and experimental values for an integral parameter, the Bayesian data assimilation may adjust the nuclear data in a manner that does not reflect the physics of the integral parameter. To identify and lessen the impact of these inconsistent integral parameters, in this study we present a Marginal Likelihood Optimization algorithm. In a data-driven way, the marginalized likelihood is used to modulate hyperparameter terms that decrease the influence of inconsistent integral parameters on the adjustment. The advantage of this approach over other methods in the literature is that it incorporates correlation information and does not remove an integral parameter from the adjustment. Herein, we present and motivate the algorithm, and apply it to an integral data assimilation case study.
Evaluation of a commercial automatic treatment planning system for prostate cancers
Recent developments in Radiation Oncology treatment planning have led to the development of software packages that facilitate automated intensity-modulated radiation therapy (IMRT) and volumetric-modulated arc therapy (VMAT) planning. Such solutions include site-specific modules, plan library methods, and algorithm-based methods. In this study, the plan quality for prostate cancer generated by the Auto-Planning module of the Pinnacle{sup 3} radiation therapy treatment planning system (v9.10, Fitchburg, WI) is retrospectively evaluated. The Auto-Planning module of Pinnacle{sup 3} uses a progressive optimization algorithm. Twenty-three prostate cancer cases, which had previously been planned and treated without lymph node irradiation, were replanned using the Auto-Planning module. Dose distributions were statistically compared with those of manual planning by the paired t-test at 5% significance level. Auto-Planning was performed without any manual intervention. Planning target volume (PTV) dose and dose to rectum were comparable between Auto-Planning and manual planning. The former, however, significantly reduced the dose to the bladder and femurs. Regression analysis was performed to examine the correlation between volume overlap between bladder and PTV divided by the total bladder volume and resultant V70. The findings showed that manual planning typically exhibits a logistic way for dose constraint, whereas Auto-Planning shows a more linear tendency. By calculating the Akaike information criterion (AIC) to validate the statistical model, a reduction of interoperator variation in Auto-Planning was shown. We showed that, for prostate cancer, the Auto-Planning module provided plans that are better than or comparable with those of manual planning. By comparing our results with those previously reported for head and neck cancer treatment, we recommend the homogeneous plan quality generated by the Auto-Planning module, which exhibits less dependence on anatomic complexity.