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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 847 records · Page 47
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

Development and application of a machine learning based multi-objective optimization workflow for CO 2 -EOR projects

Carbon dioxide-Enhanced Oil Recovery (CO 2 -EOR) is known as one of techniques for hydrocarbon production improvement as wells as an important candidate to reduce greenhouse gas emissions. Thus, an ideal development strategy for a CO 2 -EOR project would consider multiple objectives including to maximize oil recovery, CO 2 storage volume and project economic outcomes. This work proposes a robust computational framework that couples artificial neural network (ANN) and multi-objective optimizers to optimize the aforementioned objectives in CO 2 -EOR processes simultaneously. Expert ANN systems are trained and employed as surrogate models of the high-fidelity compositional simulator in the optimization workflow. The robustness of the development optimization protocol is confirmed via a synthetic injection-pattern-base case study. Afterward a field implementation to Morrow-B formation to optimize the tertiary recovery stage of the field development is discussed. This work compares the optimum solution found using an aggregate objective function and the solution repository (Pareto front) generated by the multi-objective optimization process. The comparison indicates the existence of potential multi-solutions satisfying certain criteria in a CO 2 -EOR project designing, which cannot be found using traditional weighted sum method. The optimization results provide significant insight into the decision-making process of CO 2 -EOR project when multiple objective functions are considered.

02 PETROLEUM↗
DOE OSTI2013

Distance-to-Agreement Investigation of Tomotherapy's Bony Anatomy-Based Autoregistration and Planning Target Volume Contour-Based Optimization

Purpose: To compare Tomotherapy's megavoltage computed tomography bony anatomy autoregistration with the best achievable registration, assuming no deformation and perfect knowledge of planning target volume (PTV) location. Methods and Materials: Distance-to-agreement (DTA) of the PTV was determined by applying a rigid-body shift to the PTV region of interest of the prostate from its reference position, assuming no deformations. Planning target volume region of interest of the prostate was extracted from the patient archives. The reference position was set by the 6 degrees of freedom (dof)—x, y, z, roll, pitch, and yaw—optimization results from the previous study at this institution. The DTA and the compensating parameters were calculated by the shift of the PTV from the reference 6-dof to the 4-dof—x, y, z, and roll—optimization. In this study, the effectiveness of Tomotherapy's 4-dof bony anatomy–based autoregistration was compared with the idealized 4-dof PTV contour-based optimization. Results: The maximum DTA (maxDTA) of the bony anatomy-based autoregistration was 3.2 ± 1.9 mm, with the maximum value of 8.0 mm. The maxDTA of the contour-based optimization was 1.8 ± 1.3 mm, with the maximum value of 5.7 mm. Comparison of Pearson correlation of the compensating parameters between the 2 4-dof optimization algorithms shows that there is a small but statistically significant correlation in y and z (0.236 and 0.300, respectively), whereas there is very weak correlation in x and roll (0.062 and 0.025, respectively). Conclusions: We find that there is an average improvement of approximately 1 mm in terms of maxDTA on the PTV going from 4-dof bony anatomy-based autoregistration to the 4-dof contour-based optimization. Pearson correlation analysis of the 2 4-dof optimizations suggests that uncertainties due to deformation and inadequate resolution account for much of the compensating parameters, but pitch variation also makes a statistically significant contribution.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2013

Linear Energy Transfer-Guided Optimization in Intensity Modulated Proton Therapy: Feasibility Study and Clinical Potential

Purpose: To investigate the feasibility and potential clinical benefit of linear energy transfer (LET) guided plan optimization in intensity modulated proton therapy (IMPT). Methods and Materials: A multicriteria optimization (MCO) module was used to generate a series of Pareto-optimal IMPT base plans (BPs), corresponding to defined objectives, for 5 patients with head-and-neck cancer and 2 with pancreatic cancer. A Monte Carlo platform was used to calculate dose and LET distributions for each BP. A custom-designed MCO navigation module allowed the user to interpolate between BPs to produce deliverable Pareto-optimal solutions. Differences among the BPs were evaluated for each patient, based on dose–volume and LET–volume histograms and 3-dimensional distributions. An LET-based relative biological effectiveness (RBE) model was used to evaluate the potential clinical benefit when navigating the space of Pareto-optimal BPs. Results: The mean LET values for the target varied up to 30% among the BPs for the head-and-neck patients and up to 14% for the pancreatic cancer patients. Variations were more prominent in organs at risk (OARs), where mean LET values differed by a factor of up to 2 among the BPs for the same patient. An inverse relation between dose and LET distributions for the OARs was typically observed. Accounting for LET-dependent variable RBE values, a potential improvement on RBE-weighted dose of up to 40%, averaged over several structures under study, was noticed during MCO navigation. Conclusions: We present a novel strategy for optimizing proton therapy to maximize dose-averaged LET in tumor targets while simultaneously minimizing dose-averaged LET in normal tissue structures. MCO BPs show substantial LET variations, leading to potentially significant differences in RBE-weighted doses. Pareto-surface navigation, using both dose and LET distributions for guidance, provides the means for evaluating a large variety of deliverable plans and aids in identifying the clinically optimal solution.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2016

Calibration of an agricultural-hydrological model (RZWQM2) using surrogate global optimization

Robust calibration of an agricultural-hydrological model is critical for simulating crop yield and water quality and making reasonable agricultural management. However, calibration of the agricultural-hydrological system models is challenging because of model complexity, the existence of strong parameter correlation, and significant computational requirements. Therefore, only a limited number of simulations can be allowed in any attempt to find a near-optimal solution within an affordable time, which greatly restricts the successful application of the model. The goal of this study is to locate the optimal solution of the Root Zone Water Quality Model (RZWQM2) given a limited simulation time, so as to improve the model simulation and help make rational and effective agricultural-hydrological decisions. To this end, we propose a computationally efficient global optimization procedure using sparse-grid based surrogates. We first used advanced sparse grid (SG) interpolation to construct a surrogate system of the actual RZWQM2, and then we calibrate the surrogate model using the global optimization algorithm, Quantum-behaved Particle Swarm Optimization (QPSO). As the surrogate model is a polynomial with fast evaluation, it can be efficiently evaluated with a sufficiently large number of times during the optimization, which facilitates the global search. We calibrate seven model parameters against five years of yield, drain flow, and NO 3 -N loss data from a subsurface-drained corn-soybean field in Iowa. Results indicate that an accurate surrogate model can be created for the RZWQM2 with a relatively small number of SG points (i.e., RZWQM2 runs). Compared to the conventional QPSO algorithm, our surrogate-based optimization method can achieve a smaller objective function value and better calibration performance using a fewer number of expensive RZWQM2 executions, which greatly improves computational efficiency.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2021

A two-dimensional analytical unit cell model for redox flow battery evaluation and optimization

Cell performance optimization is important for improving the overall system efficiency of a redox flow battery. To gain better insights into key controlling factors of system efficiency, this work first proposed a theoretical model for a unit flow battery cell by extending a two-dimensional analytic model to a full battery cell. Such a model is then used for cell performance optimization after validating it with experimental and numerical modeling data. With the model results, the activation, equilibrium, and pump energy losses are identified as the dominant sources of battery energy losses. Further, a guideline for reducing these sources is also proposed. Following the guideline, the mass transport coefficient is shown as a key control factor of the equilibrium energy loss and Coulombic efficiency (CE). Approaches are then proposed to improve CE and the overall system efficiency. The mass transport is also revealed as the mechanism of pump rate optimization where an optimal pump rate significantly reduces the equilibrium energy loss. With both low equilibrium and pump energy losses, an optimal electrode porosity or specific area design can further improve a battery's system efficiency based on an optimal porosity predicted by the present model. The model also demonstrates distinct behaviors and overestimation in the system efficiency when reduced to a zero-dimensional model with neglected mass transport resistance. With the new model, the guideline, and new insights, this work provides a reliable and efficient tool for the evaluation and optimization of redox flow battery design in practical applications.

25 ENERGY STORAGE↗
DOE OSTI2014

Multicriteria optimization informed VMAT planning

We developed a patient-specific volumetric-modulated arc therapy (VMAT) optimization procedure using dose-volume histogram (DVH) information from multicriteria optimization (MCO) of intensity-modulated radiotherapy (IMRT) plans. The study included 10 patients with prostate cancer undergoing standard fractionation treatment, 10 patients with prostate cancer undergoing hypofractionation treatment, and 5 patients with head/neck cancer. MCO-IMRT plans using 20 and 7 treatment fields were generated for each patient on the RayStation treatment planning system (clinical version 2.5, RaySearch Laboratories, Stockholm, Sweden). The resulting DVH of the 20-field MCO-IMRT plan for each patient was used as the reference DVH, and the extracted point values of the resulting DVH of the MCO-IMRT plan were used as objectives and constraints for VMAT optimization. Weights of objectives or constraints of VMAT optimization or both were further tuned to generate the best match with the reference DVH of the MCO-IMRT plan. The final optimal VMAT plan quality was evaluated by comparison with MCO-IMRT plans based on homogeneity index, conformity number of planning target volume, and organ at risk sparing. The influence of gantry spacing, arc number, and delivery time on VMAT plan quality for different tumor sites was also evaluated. The resulting VMAT plan quality essentially matched the 20-field MCO-IMRT plan but with a shorter delivery time and less monitor units. VMAT plan quality of head/neck cancer cases improved using dual arcs whereas prostate cases did not. VMAT plan quality was improved by fine gantry spacing of 2 for the head/neck cancer cases and the hypofractionation-treated prostate cancer cases but not for the standard fractionation–treated prostate cancer cases. MCO-informed VMAT optimization is a useful and valuable way to generate patient-specific optimal VMAT plans, though modification of the weights of objectives or constraints extracted from resulting DVH of MCO-IMRT or both is necessary.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2022

X-ray FEL linear accelerator design via start-to-end global optimization

An X-ray Free Electron Laser (FEL) prefers using an electron beam with low emittance, small energy spread, and a high core current to generate coherent radiation through an undulator. In order to attain such a high brightness beam, the linear accelerator beam dynamics design generally involves separate photoinjector optimization and linac optimization. In this paper, we propose a new beam dynamics design strategy based on global optimization with fast start-to-end simulations from the photocathode to the end of the accelerator. The new start-to-end model significantly reduces the simulation time and makes the global optimization practical. The global optimization method avoids the need to choose a single solution based on bunch length at the injector exit for the linac optimization and helps find the solution with unfavorable bunch length at the injector exit but better phase space distribution that can result in better final electron beam phase space distribution at the entrance of the undulator. Here, using the start-to-end global optimization, we showed in an application example, with a 100 pC beam that good transverse emittance and over kilo-Ampere final core current can be attained using a photoinjector that consists of a VHF gun and boosting RF cavities.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2022

Topology optimization of an airfoil fin microchannel heat exchanger using artificial intelligence

High-performance microchannel heat exchangers are needed to supply heat for power conversion for nuclear microreactors. An airfoil fin microchannel design, constructed of Alloy 617 with helium as the working fluid, is analyzed and optimized using a design of experiments with artificial intelligence techniques. The use of airfoil fins offers the potential to reduce pressure drop across the heat exchanger, as compared to other types of channel configurations. A framework for topology optimization of airfoil fin printed circuit heat exchangers (PCHEs) has been developed that can be readily extended to different fin sizes and shapes, as well as different inlet and operating conditions, materials of construction, and working fluids. An optimization procedure is developed that employs computational fluid dynamics for a set of design points identified using Latin hypercube sampling. Computational fluid dynamics is used to analyze a simplified two-channel configuration where five design parameters are varied – inlet angle, fin scale, extent of staggering, transverse and longitudinal pitches. Two methods (a 5D polynomial and a regression neural network) are compared for generating surrogate models and the resulting response surface approximation is input to a genetic algorithm that is used to identify a set of optimal parameters. The optimal geometries are found across six channel Reynolds numbers ranging from 1000 to 5000, since inlet conditions affect flow through the heat exchanger. Additionally, a set of optimal designs that maximizes heat transfer and minimizes pressure drop is identified, and a thermal stress analysis is performed on the optimal design. Correlations for the Nusselt number and Darcy friction factor are developed that can be useful for thermal hydraulic analyses using system codes. Thermal stresses are analyzed and a brief discussion of the status of code cases of PCHEs for nuclear applications is given. Testing and thermomechanical modeling is needed to facilitate future code compliance of PCHEs for high pressure and high temperature applications.

42 ENGINEERING↗
DOE OSTI2016

Program optimizations: The interplay between power, performance, and energy

Practical considerations for future supercomputer designs will impose limits on both instantaneous power consumption and total energy consumption. Working within these constraints while providing the maximum possible performance, application developers will need to optimize their code for speed alongside power and energy concerns. This paper analyzes the effectiveness of several code optimizations including loop fusion, data structure transformations, and global allocations. A per component measurement and analysis of different architectures is performed, enabling the examination of code optimizations on different compute subsystems. Using an explicit hydrodynamics proxy application from the U.S. Department of Energy, LULESH, we show how code optimizations impact different computational phases of the simulation. This provides insight for simulation developers into the best optimizations to use during particular simulation compute phases when optimizing code for future supercomputing platforms. Here, we examine and contrast both x86 and Blue Gene architectures with respect to these optimizations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

GBOpt: Grain boundary structure optimization using Monte Carlo and evolutionary algorithms

Polycrystalline materials are made of many small crystals separated by grain boundaries (GBs), whose atomic structure strongly influences material properties. Because the structure of a GB determines its properties, the optimal structure must be known in order to determine those impacts. There are many ways of placing atoms in the GB region, but the optimal structure is defined as the one that gives the lowest value of a target property (typically energy). GB structure optimization has been successfully demonstrated using stochastic and evolutionary methods, but no reusable, community-maintained open-source workflow has been developed. GBOpt (Grain Boundary Optimization) is an open-source Python package that creates that workflow, where we have presently implemented two approaches: Markov Chain Monte Carlo, and genetic algorithm based on elite selection. We demonstrate this capability by successfully reproducing the known optimal structures of a specific GB in two materials, and point interested readers to the GitHub repository for additional examples, including optimization for different properties. Both of the implemented approaches recovered the known structures, with the genetic algorithm approach finding the optimal structure faster on average.

99 - GENERAL AND MISCELLANEOUS↗
DOE OSTI2022

Machine learning-based optimization of air-cooled heat sinks

Machine learning-based models using Artificial Neural Network (ANN) and greedy search algorithm are used to optimize air-cooled parallel plate-finned heat sinks (PPFHSs) subjected to laminar flow over an extensive range of design parameters. Here, the thermal and hydraulic performances of PPFHSs are represented by heat transfer coefficient (h) and pressure drop (ΔP), respectively. Optimization objectives for PPFHS designs can vary from industry to industry depending on their design priorities. The present study proposes a novel and generalized optimization method that defines practical optimization objectives and provides an accurate optimization process to design effective PPFHSs for a wide range of industrial applications with different design requirements. Three optimization objectives are presented in this study: (i) the largest h PΔ, (ii) the largest h within a specified maximum allowed flow rate, and (iii) the lowest weight that maximizes h for operation within the maximum allowed flow rate. While the shortcoming of the first objective is demonstrated, the other two objectives are found to be suitable for designing effective heat sinks (HSs) across different applications. Results suggest a promising trend from the third objective to develop HSs with ~ 37-68% lower weight, 80-85% reduced ΔP, and negligible penalty in h compared with optimized HSs obtained from the second objective. However, since the third objective leads to HSs with thinner fins, structural analysis should be performed to ensure reliable operation of the HSs.

42 ENGINEERING↗
DOE OSTI2025

Net Present Value Optimization of a Natural Gas Combined Cycle Plant with CO 2 Capture using a Water-Lean Solvent Considering Transient Electricity Price for Multiple Regions

Global CO 2 emissions are increasing at about a 1.5% rate per year. Fossil fuel-based plants are one of the main contributors to this rise. In the power generation industry, fossil fuel plants are dominant, and many plants are under development. In this study, a natural gas combined cycle (NGCC) power plant with postcombustion capture using a leading water-lean solvent is considered. For optimal design and operating schedule, large-scale dynamic optimization is undertaken for net present value (NPV) optimization. The first principle dynamic model of NGCC is developed, including a model of the highly efficient H-class gas turbines. For computational tractability of the dynamic optimization problem, a reduced-order model is developed by using the Hankel singular value decomposition. A waterlean solvent, N-(2-ethoxyethyl)-3-morpholinopropan-1-amine, is used for carbon capture. A model of the capture system is developed in Aspen Plus, which is used to develop a reduced-order model by using ALAMO, a machine learning software. In addition, a reduced model of the CO 2 compression system with a dehydration unit is also considered. The integrated system is used for NPV optimization by using the Python-based PYOMO platform. The PCC process is analyzed for three configurations-conventional packed bed, rotating packed bed (RPB), and a combination of RPB and direct contact cooler. The NPV optimization is performed for 14 regional markets by considering year-long clustered and continuous locational marginal price data with a 1 h interval. Optimization results show that the PCC can achieve 90% CO 2 capture with a positive NPV for six regions. Sensitivity studies conducted by using the PCC configurations indicate that the process is economically feasible for 9 regions out of 14 regional electricity markets with NPV values in the range of 33−540 $MM.

cabon capture↗
DOE OSTI2023

Efficient Optimization of Energy Recovery From Geothermal Reservoirs With Recurrent Neural Network Predictive Models

Improving the long-term energy production performance of geothermal reservoirs can be accomplished by optimizing field development and management plans. Reliable prediction models, however, are needed to evaluate and optimize the performance of the underlying reservoirs under various operation and development strategies. In traditional frameworks, physics-based simulation models are used to predict the energy production performance of geothermal reservoirs. However, detailed simulation models are not trivial to construct, require a reliable description of the reservoir conditions and properties, and entail high computational complexity. Data-driven predictive models can offer an efficient alternative for use in optimization workflows. This paper presents an optimization framework for net power generation in geothermal reservoirs using a variant of the recurrent neural network (RNN) as a data-driven predictive model. The RNN architecture is developed and trained to replace the simulation model for computationally efficient prediction of the objective function and its gradients with respect to the well control variables. The net power generation performance of the field is optimized by automatically adjusting the mass flow rate of production and injection wells over 12 years, using a gradient-based local search algorithm. Two field-scale examples are presented to investigate the performance of the developed data-driven prediction and optimization framework. Furthermore, the prediction and optimization results from the RNN model are evaluated through comparison with the results obtained by using a numerical simulation model of a real geothermal reservoir.

15 GEOTHERMAL ENERGY↗
DOE OSTI2014

Laboratory transferability of optimally shaped laser pulses for quantum control

Optimal control experiments can readily identify effective shaped laser pulses, or “photonic reagents,” that achieve a wide variety of objectives. An important additional practical desire is for photonic reagent prescriptions to produce good, if not optimal, objective yields when transferred to a different system or laboratory. Building on general experience in chemistry, the hope is that transferred photonic reagent prescriptions may remain functional even though all features of a shaped pulse profile at the sample typically cannot be reproduced exactly. As a specific example, we assess the potential for transferring optimal photonic reagents for the objective of optimizing a ratio of photoproduct ions from a family of halomethanes through three related experiments. First, applying the same set of photonic reagents with systematically varying second- and third-order chirp on both laser systems generated similar shapes of the associated control landscape (i.e., relation between the objective yield and the variables describing the photonic reagents). Second, optimal photonic reagents obtained from the first laser system were found to still produce near optimal yields on the second laser system. Third, transferring a collection of photonic reagents optimized on the first laser system to the second laser system reproduced systematic trends in photoproduct yields upon interaction with the homologous chemical family. These three transfers of photonic reagents are demonstrated to be successful upon paying reasonable attention to overall laser system characteristics. The ability to transfer photonic reagents from one laser system to another is analogous to well-established utilitarian operating procedures with traditional chemical reagents. The practical implications of the present results for experimental quantum control are discussed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

Optimized aperiodic multilayer structures for use as narrow-angular absorbers

In this paper, we investigate aperiodic multilayer structures for use as narrow-angular absorbers. The layer thicknesses and materials are optimized using a genetic global optimization algorithm coupled to a transfer matrix code to maximize the angular selectivity in the absorptance at a single or multiple wavelengths. We first consider structures composed of alternating layers of tungsten and silicon or silica, and find that it is not possible to achieve angular selectivity in the absorptance with such structures. We next consider structures composed of alternating layers of silicon and silica, and show that when optimized they exhibit high angular selectivity in absorptance. In addition, as the angular selectivity in absorptance increases, the wavelength range of high angular selectivity also decreases. Optimizing the material composition of the multilayer structures, in addition to optimizing the layer thicknesses, leads to marginal improvement in angular selectivity. Finally, we show that by optimizing the absorptance of the multilayer structures at multiple wavelengths, we can obtain structures exhibiting almost perfect absorptance at normal incidence and narrow angular width in absorptance at these wavelengths. Similar to the structures optimized at a single wavelength, the wavelength range of high angularly selective absorptance is narrow.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Cost- and Risk-Based Seismic Design Optimization of Nuclear Power Plant Safety Systems

Seismic analysis, design, and qualification of systems, structures, and components (SSCs) is a significant contributor to the capital cost of a nuclear power plant. To reduce capital costs of advanced nuclear power plants and make commercial nuclear energy more competitive, innovations are needed in their structural design and construction, and not just in the reactor core and associated systems. Seismic isolation has been identified as an important cost-cutting technology that enables standardization of equipment across various sites. This paper develops and demonstrates a cost- and risk-based seismic design optimization of a representative safety system in a nuclear power plant with the dual goals of minimizing overnight capital cost and meeting safety goals. The design optimization can also include component seismic isolation, in which case, the optimized design includes a set of equipment that needs to be seismically isolated to minimize capital cost. The open-source codes MASTODON and Dakota are used for seismic probabilistic risk assessment and design optimization, respectively. A generic nuclear facility with a safety system comprising SSCs that are common to nuclear power plants is considered for the demonstration of the design optimization and is assumed to be located at the Idaho National Laboratory site. Generic costs and seismic design cost functions are assumed for the SSCs of the safety system. The sum of the costs of the SSCs is minimized in the optimization process, while the risk of failure of the safety system is provided as a constraint. Furthermore, results show that the optimization process reduces capital costs significantly while automatically prioritizing the safety of SSCs that contribute most to the risk of the safety system.

42 ENGINEERING↗
DOE OSTI2025

Advancing the STS Neutron Moderator Design with an Automated Optimization Workflow and Unstructured Mesh Modeling

With the Second Target Station approaching its final design phase, a detailed neutronics evaluation of its critical components is necessary. Optimizing the dimensions of the two cold-source moderators that are at the heart of this facility presents a multi-objective optimization problem for which an accurate geometric description is crucial. We have applied a fully automated optimization workflow in which a detailed unstructured mesh geometry is automatically generated with Attila4MC, starting from a parametrized CREO geometry followed by preprocessing with SpaceClaim. With this geometry, a MCNP run is performed to calculate the brightness metrics, which are subsequently provided to the optimization algorithm in DAKOTA that provides new parameters and drives the optimization loop until convergence. In this paper, we show the results of the analysis that are used for the final design of the cylindrical and tube moderator. The optimization simulations provide a refinement to and confirmation of the conclusions of the previous design iteration. Additional to the optimization, a sensitivity study is performed to study the effect of minor geometry changes, which is important for the final engineering design. In conclusion, with these studies, we demonstrate that the automated workflow and high-fidelity unstructured mesh modeling are efficient tools for a thorough design evaluation.

DAKOTA↗
DOE OSTI2012

GLOBAL OPTIMIZATION METHODS FOR GRAVITATIONAL LENS SYSTEMS WITH REGULARIZED SOURCES

Several approaches exist to model gravitational lens systems. In this study, we apply global optimization methods to find the optimal set of lens parameters using a genetic algorithm. We treat the full optimization procedure as a two-step process: an analytical description of the source plane intensity distribution is used to find an initial approximation to the optimal lens parameters; the second stage of the optimization uses a pixelated source plane with the semilinear method to determine an optimal source. Regularization is handled by means of an iterative method and the generalized cross validation (GCV) and unbiased predictive risk estimator (UPRE) functions that are commonly used in standard image deconvolution problems. This approach simultaneously estimates the optimal regularization parameter and the number of degrees of freedom in the source. Using the GCV and UPRE functions, we are able to justify an estimation of the number of source degrees of freedom found in previous work. We test our approach by applying our code to a subset of the lens systems included in the SLACS survey.

79 ASTRONOMY AND ASTROPHYSICS↗