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Results for “Inverse Optimization”

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 379 records · Page 21
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Inverse design for waveguide dispersion with a differentiable mode solver

Inverse design of optical components based on adjoint sensitivity analysis has the potential to address the most challenging photonic engineering problems. However, existing inverse design tools based on finite-difference-time-domain (FDTD) models are poorly suited for optimizing waveguide modes for adiabatic transformation or perturbative coupling, which lies at the heart of many important photonic devices. Among these, dispersion engineering of optical waveguides is especially challenging in ultrafast and nonlinear optical applications involving broad optical bandwidths and frequency-dependent anisotropic dielectric material response. In this work, we develop gradient back-propagation through a general-purpose electromagnetic eigenmode solver and use it to demonstrate waveguide dispersion optimization for second harmonic generation with maximized phase-matching bandwidth. This optimization of three design parameters converges in eight steps, reducing the computational cost of optimization by ∼100x compared to exhaustive search and identifying new designs for broadband optical frequency doubling of laser sources in the 1.3–1.4 µm wavelength range. Furthermore, we demonstrate that the computational cost of gradient back-propagation is independent of the number of parameters, as required for optimization of complex geometries. This technique enables practical inverse design for a broad range of previously intractable photonic devices.

Gray, Dodd (ORCID:000000030469599X)↗
DOE OSTI2025

Estimating QSVT angles for matrix inversion with large condition numbers

Quantum Singular Value Transformation (QSVT) is a state-of-the-art, near-optimal quantum algorithm that can be used for matrix inversion. The QSVT circuit is parameterized by a sequence of angles that must be pre-calculated classically, with the number of angles increasing as the matrix condition number grows. Computing QSVT angles for ill-conditioned problems is a numerically challenging task. Here, we propose a numerical technique for estimating QSVT angles for large condition numbers. This technique allows one to avoid expensive numerical computations of QSVT angles and to emulate QSVT circuits for solving ill-conditioned problems.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1982

Optimal two-impulse transfer between specified terminal states of Keplerian orbits

The integrals of motion for an inverse-square force field and a necessary condition for optimality are used in a transfer orbit co-ordinate system to formulate the solution of the optimal two-impulse transfer between fixed position and velocity vectors on Keplerian orbits. In this co-ordinate system, the equations reveal two asymptotes that are useful in analysing the solution. It is shown that there are only two real extremals (both minimums) which are separated by an asymptote. An approximate analytic solution is also obtained by ignoring a quadratic term whose coefficient is approximately zero for a large class of orbit transfer problems.

Jezewski, D. J.↗
DOE OSTI2023

Bayesian inversion and the Tomita–Takesaki modular group

We show that conditional expectations, optimal hypotheses, disintegrations and adjoints of unital completely positive maps are all instances of Bayesian inverses. We study the existence of the latter by means of the Tomita–Takesaki modular group and we provide extensions of a theorem of Takesaki as well as a theorem of Accardi and Cecchini to the setting of not necessarily faithful states on finite-dimensional C* -algebras.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Revisiting matrix-based inversion of scanning mobility particle sizer (SMPS) and humidified tandem differential mobility analyzer (HTDMA) data

Abstract. Tikhonov regularization is a tool for reducing noise amplification during data inversion. This work introduces RegularizationTools.jl, a general-purpose software package for applying Tikhonov regularization to data. The package implements well-established numerical algorithms and is suitable for systems of up to ∼ 1000 equations. Included is an abstraction to systematically categorize specific inversion configurations and their associated hyperparameters. A generic interface translates arbitrary linear forward models defined by a computer function into the corresponding design matrix. This obviates the need to explicitly write out and discretize the Fredholm integral equation, thus facilitating fast prototyping of new regularization schemes associated with measurement techniques. Example applications include the inversion involving data from scanning mobility particle sizers (SMPSs) and humidified tandem differential mobility analyzers (HTDMAs). Inversion of SMPS size distributions reported in this work builds upon the freely available software DifferentialMobilityAnalyzers.jl. The speed of inversion is improved by a factor of ∼ 200, now requiring between 2 and 5 ms per SMPS scan when using 120 size bins. Previously reported occasional failure to converge to a valid solution is reduced by switching from the L-curve method to generalized cross-validation as the metric to search for the optimal regularization parameter. Higher-order inversions resulting in smooth, denoised reconstructions of size distributions are now included in DifferentialMobilityAnalyzers.jl. This work also demonstrates that an SMPS-style matrix-based inversion can be applied to find the growth factor frequency distribution from raw HTDMA data while also accounting for multiply charged particles. The outcome of the aerosol-related inversion methods is showcased by inverting multi-week SMPS and HTDMA datasets from ground-based observations, including SMPS data obtained at Bodega Marine Laboratory during the CalWater 2/ACAPEX campaign and co-located SMPS and HTDMA data collected at the US Department of Energy observatory located at the Southern Great Plains site in Oklahoma, USA. Results show that the proposed approaches are suitable for unsupervised, nonparametric inversion of large-scale datasets as well as inversion in real time during data acquisition on low-cost reduced-instruction-set architectures used in single-board computers. The included software implementation of Tikhonov regularization is freely available, general, and domain-independent and thus can be applied to many other inverse problems arising in atmospheric measurement techniques and beyond.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Comparison of Shape Optimization Methods for Heat Exchanger Fins Using Computational Fluid Dynamics

Inverse design techniques are one way to leverage advances in 3D printing, artificial intelligence, and computational resources to achieve increased performance of heat exchangers. Two optimization techniques (genetic algorithm and particle swarm) and three geometry representations (binary level set, composite Bézier, and free form deformation) are used to increase the heat transfer and reduce the pressure drop of a heat exchanger fin. After running 210,810 OpenFOAM simulations, results indicate that a significant performance increase of the fin can be realized in less than 48 hrs, allowing for such a process to be integrated in traditional design processes. The best design increased the performance of the objective function, compared to the baseline rectangular geometry by 75%. A custom distributed infrastructure was built, allowing for all methods to reach 95% of the final objective values in a little over 4 hrs, handling 1674 OpenFoam simulations per hour.

42 ENGINEERING↗
NASA NTRS1983

Inversion of vegetation canopy reflectance models for estimating agronomic variables. I - Problem definition and initial results using the Suits model

An important but relatively uninvestigated problem in remote sensing is the inversion of vegetative canopy reflectance models to obtain agrophysical parameters, given measured reflectances. The problem is here formally defined and its solution outlined. Numerical nonlinear optimization techniques are used to implement this inversion to obtain the leaf area index using Suits' canopy reflectance model. The results for a variety of cases indicate that this can be done successfully using infrared reflectances at different views or azimuth angles or a combination thereof. The other parameters of the model must be known, although reasonable measurement errors can be tolerated without seriously degrading the accuracy of the inversion. The application of the technique to ground based remote-sensing experiments is potentially useful, but is limited to the degree to which the canopy reflectance model can accurately predict observed reflectances.

Goel, N.↗
DOE OSTI2015

Optimizing Interacting Potentials to Form Targeted Materials Structures

Conventional applications of the principles of statistical mechanics (the "forward" problems), start with particle interaction potentials, and proceed to deduce local structure and macroscopic properties. Other applications (that may be classified as "inverse" problems), begin with targeted configurational information, such as low-order correlation functions that characterize local particle order, and attempt to back out full-system configurations and/or interaction potentials. To supplement these successful experimental and numerical "forward" approaches, we have focused on inverse approaches that make use of analytical and computational tools to optimize interactions for targeted self-assembly of nanosystems. The most original aspect of our work is its inherently inverse approach: instead of predicting structures that result from given interaction potentials among particles, we determine the optimal potential that most robustly stabilizes a given target structure subject to certain constraints. Our inverse approach could revolutionize the manner in which materials are designed and fabricated. There are a number of very tangible properties (e.g. zero thermal expansion behavior), elastic constants, optical properties for photonic applications, and transport properties.

36 MATERIALS SCIENCE↗
DOE OSTI2016

Optimal-Order Preconditioners for Linear Systems Arising in the Semismooth Newton Solution of a Class of Control-Constrained Problems

We present a new multigrid preconditioner for the linear systems arising in the semismooth Newton method solution of certain control-constrained, quadratic distributed optimal control problems. Using a piecewise constant discretization of the control space, each semismooth Newton iteration essentially requires inverting a principal submatrix of the matrix entering the normal equations of the associated unconstrained optimal control problem, the rows (and columns) of the submatrix representing the constraints deemed inactive at the current iteration. Previously developed multigrid preconditioners for the aforementioned submatrices were based on constructing a sequence of conforming coarser spaces and proved to be of suboptimal quality for the class of problems considered. Instead, the multigrid preconditioner introduced in this work uses nonconforming coarse spaces, and it is shown that, under reasonable geometric assumptions on the constraints that are deemed inactive, the preconditioner approximates the inverse of the desired submatrix to optimal order. The preconditioner is tested numerically on a classical elliptic-constrained optimal control problem and further on a constrained image-deblurring problem.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Impact of K-Optimization on Trap Concentration in (Ag,Cu)(In,Ga)Se 2 Solar Cells

Recent progress has been made in improving efficiency in Cu(In,Ga)Se 2 (CIGS) absorbers with steady increases in peak efficiency. One way this has been achieved is by adding Ag to CIGS (ACIGS) to achieve higher V OC . However, these efficiencies are still well below the Shockley-Queisser efficiency limit, and traps acting as recombination centers and compensating centers are one thing limiting the solar efficiency. Past research in CIGS has shown that alkali treatment can improve the efficiency and metastability problems in CIGS, but less is understood about the role of alkali treatments in ACIGS. Here, we investigate the impact of potassium in ACIGS through its impact on trap incorporation and minority carrier lifetime. The samples in this study were grown in a roll-to-roll coater with Mo, ACIGS, CdS, and ZnO structure. Both cells were grown identically except the second (K-optimized) cell was grown with increased K-doping of the Mo contact and was more Cu-poor near the surface to optimize the K profile. This resulted in an efficiency increase from 16.8% to 18.7% for the K-optimized cell, which was mostly due to a 65 mV V OC increase. The doping profile showed a 2X increase in acceptor concentration of the K-optimized cell (2.5×10 15 cm -3 ) which suggests that the K was better incorporated into the ACIGS after these optimizations. To characterize the traps in these cells, deep level transient and optical spectroscopy were used. The DLOS measurements showed an EV+0.98 eV trap whose concentration was reduced 10X in the K-optimized cell (4×10 14 cm -3 ). This is consistent with previous results from the alkali treatment in CIGS, which also showed a decrease in near-conduction band trap concentration [1], but the reduction was larger than previous studies possibly indicating the combination of K and Cu-poor surface may both have aided in reducing the EV+0.98 eV trap concentration. The other primary trap is the mid-gap trap (EV+0.58 eV), which was quantified using DLTS. Its concentration decreased from 9×10 13 cm -3 to 4×10 13 cm -3 in the K-optimized sample, which is a 2X reduction. Previous studies have shown this trap is likely an efficient recombination center [2], which makes sense because it is near mid-gap. This trap has also been associated with V OC instability and reduction, so reducing this trap concentration is essential to achieve high V OC and cell efficiency. To help confirm this association, time-resolved photoluminescence measurements have shown in this sample set and a previous study that the minority carrier lifetime (19 ns baseline to 56 ns K-optimized) and this EV+0.56 eV trap concentration are inversely proportional, which would be expected for a recombination-limited carrier lifetime. The K optimization of ACIGS results in significantly improved cell efficiency and reduced trap concentrations that correlate with the improved material and electrical properties. We will report on this and the impact of the K optimization on the cell metastability.

14 SOLAR ENERGY↗
DOE OSTI2015

Subspace-based Inverse Uncertainty Quantification for Nuclear Data Assessment

Safety analysis and design optimization depend on the accurate prediction of various reactor attributes. Predictions can be enhanced by reducing the uncertainty associated with the attributes of interest. An inverse problem can be defined and solved to assess the sources of uncertainty, and experimental effort can be subsequently directed to further improve the uncertainty associated with these sources. In this work a subspace-based algorithm for inverse sensitivity/uncertainty quantification (IS/UQ) has been developed to enable analysts account for all sources of nuclear data uncertainties in support of target accuracy assessment-type analysis. An approximate analytical solution of the optimization problem is used to guide the search for the dominant uncertainty subspace. By limiting the search to a subspace, the degrees of freedom available for the optimization search are significantly reduced. A quarter PWR fuel assembly is modeled and the accuracy of the multiplication factor and the fission reaction rate are used as reactor attributes whose uncertainties are to be reduced. Numerical experiments are used to demonstrate the computational efficiency of the proposed algorithm. Our ongoing work is focusing on extending the proposed algorithm to account for various forms of feedback, e.g., thermal-hydraulics and depletion effects.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2017

On domain symmetry and its use in homogenization

The present study focuses on solving partial differential equations in domains exhibiting symmetries and periodic boundary conditions for the purpose of homogenization. We show in a systematic manner how the symmetry can be exploited to significantly reduce the complexity of the problem and the computational burden. This is especially relevant in inverse problems, when one needs to solve the partial differential equation (the primal problem) many times in an optimization algorithm. The main motivation of our study is inverse homogenization used to design architected composite materials with novel properties which are being fabricated at ever increasing rates thanks to recent advances in additive manufacturing. For example, one may optimize the morphology of a two-phase composite unit cell to achieve isotropic homogenized properties with maximal bulk modulus and minimal Poisson ratio. Typically, the isotropy is enforced by applying constraints to the optimization problem. However, in two dimensions, one can alternatively optimize the morphology of an equilateral triangle and then rotate and reflect the triangle to form a space filling D 3 symmetric hexagonal unit cell that necessarily exhibits isotropic homogenized properties. One can further use this D 3 symmetry to reduce the computational expense by performing the “unit strain” periodic boundary condition simulations on the single triangle symmetry sector rather than the six fold larger hexagon. In this paper we use group representation theory to derive the necessary periodic boundary conditions on the symmetry sectors of unit cells. The developments are done in a general setting, and specialized to the two-dimensional dihedral symmetries of the abelian D 2 , i.e. orthotropic, square unit cell and nonabelian D 3 , i.e. trigonal, hexagon unit cell. We then demonstrate how this theory can be applied by evaluating the homogenized properties of a two-phase planar composite over the triangle symmetry sector of a D 3 symmetric hexagonal unit cell.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Multigrid Optimization for Large-Scale Ptychographic Phase Retrieval

Ptychography is a popular imaging technique that combines diffractive imaging with scanning microscopy. The technique consists of a coherent beam that is scanned across an object in a series of overlapping positions, leading to reliable and improved reconstructions. Ptychographic microscopes allow for large fields to be imaged at high resolution at the cost of additional computational expense. Herein, we propose a multigrid-based optimization framework to reduce the computational burdens of large-scale ptychographic phase retrieval. Our proposed method exploits the inherent hierarchical structures in ptychography through tailored restriction and prolongation operators for the object and data domains. Our numerical results show that our proposed scheme accelerates the convergence of its underlying solver and outperforms the ptychographical iterative engine, a workhorse in the optics community.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Transient and Steady-State Inverse Problems in Sierra/Aria

Inverse problems arise in a wide range of applications, whenever unknown model parameters cannot be measured directly. Instead, the unknown parameters are estimated using experimental data and forward simulations. Thermal inverse problems, such as material characterization problems, are often large-scale and transient. Therefore, they require intrusive adjoint-based gradient implementations in order to be solved efficiently. The capability to solve large-scale transient thermal inverse problems using an adjoint-based approach was recently implemented in SNL Sierra Mechanics, a massively parallel capable multiphysics code suite. This report outlines the theory, optimization formulation, and path taken to implement thermal inverse capabilities in Sierra within a unit test framework. The capability utilizes Sierra/Aria and Sierra/Fuego data structures, the Rapid Optimization Library, and an interface to the Sierra/InverseOpt library. The existing Sierra/Aria time integrator is leveraged to implement a time-dependent adjoint solver.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Assessing the design of integrated methane sensing networks

Abstract While methane is the second largest contributor to global warming after carbon dioxide, it has a larger warming effect over a much shorter lifetime. Despite accelerated technological efforts to radically reduce global carbon dioxide emissions, rapid reductions in methane emissions are needed to limit near-term warming. Being primarily emitted as a byproduct from agricultural activities and energy extraction, methane is currently monitored via bottom–up (i.e. activity level) or top–down (via airborne or satellite retrievals) approaches. However, significant methane leaks remain undetected and emission rates are challenging to characterize with current monitoring frameworks. In this paper, we study the design of a layered monitoring approach that combines bottom–up and top–down approaches as an integrated sensing network. By recognizing that varying meteorological conditions and emission rates impact the efficacy of bottom–up monitoring, we develop a probabilistic approach to optimal sensor placement in its bottom–up network. Subsequently, we derive an inverse Bayesian framework to quantify the improvement that a design-optimized integrated framework has on emission-rate quantifications and their uncertainties. We find that under realistic meteorological conditions, the overall error in estimating the true emission rates is approximately 1.3 times higher, with their uncertainties being approximately 2.4 times higher, when using a randomized network over an optimized network, highlighting the importance of optimizing the design of integrated methane sensing networks. Further, we find that optimized networks can improve scenario coverage fractions by more than a factor of 2 over experimentally-studied networks, and identify a budget threshold beyond which the rate of optimized-network coverage improvement exhibits diminishing returns, suggesting that strategic sensor placement is also crucial for maximizing network efficiency.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2015

Variational Dirichlet Blur Kernel Estimation

Blind image deconvolution involves two key objectives: 1) latent image and 2) blur estimation. For latent image estimation, we propose a fast deconvolution algorithm, which uses an image prior of nondimensional Gaussianity measure to enforce sparsity and an undetermined boundary condition methodology to reduce boundary artifacts. For blur estimation, a linear inverse problem with normalization and nonnegative constraints must be solved. However, the normalization constraint is ignored in many blind image deblurring methods, mainly because it makes the problem less tractable. In this paper, we show that the normalization constraint can be very naturally incorporated into the estimation process by using a Dirichlet distribution to approximate the posterior distribution of the blur. Making use of variational Dirichlet approximation, we provide a blur posterior approximation that considers the uncertainty of the estimate and removes noise in the estimated kernel. Furthermore, experiments with synthetic and real data demonstrate that the proposed method is very competitive to the state-of-the-art blind image restoration methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Computational design of metamaterials with self contact

Inverse homogenization in combination with contact modeling, topology optimization and shape optimization is used to design metamaterials with optimized macroscopic response. The homogenization assumes length scale separation which allows the non-linear macroscopic behavior to be obtained by analyzing a single unit cell in a lattice structure. Self contact in the unit cell, which is modeled using a third medium contact method, is leveraged to obtain a complex homogenized response. The inverse homogenization problem is initially formulated as a topology optimization problem, where the macroscopic stress–strain behavior is tuned to our liking. However, it is well known that boundary phenomena are difficult to model in topology optimization and that interface modeling is crucial to accurately analyze contact. For that reason, the boundary representation of the topology optimized design is extracted and used as initial design in a subsequent shape optimization. The behaviors of our designs are verified by performing rigorous post-processing analyzes using conforming meshes and conventional contact formulations.

42 ENGINEERING↗
DOE OSTI2025

Optimal Power Management for Large-Scale Battery Energy Storage Systems via Bayesian Inference

Large-scale battery energy storage systems (BESS) have found ever-increasing use across industry and society to accelerate clean energy transition and improve energy supply reliability and resilience. However, their optimal power management poses significant challenges: the underlying high-dimensional nonlinear nonconvex optimization lacks computational tractability in real-world implementation, and the uncertainty of the exogenous power demand makes exact optimization difficult. This paper presents a new solution framework to address these bottlenecks. The solution pivots on introducing power-sharing ratios to specify each cell’s power quota from the output power demand. To find the optimal power-sharing ratios, we formulate a nonlinear model predictive control (NMPC) problem to achieve power-loss-minimizing BESS operation while complying with safety, cell balancing, and power supply-demand constraints. We then propose a parameterized control policy for the power-sharing ratios, which utilizes only three parameters, to reduce the computational demand in solving the NMPC problem. This policy parameterization allows us to translate the NMPC problem into a Bayesian inference problem for the sake of 1) computational tractability, and 2) overcoming the nonconvexity of the optimization problem. We leverage the ensemble Kalman inversion technique to solve the parameter estimation problem. Concurrently, a low-level control loop is developed to seamlessly integrate our proposed approach with the BESS to ensure practical implementation. This low-level controller receives the optimal power-sharing ratios, generates output power references for the cells, and maintains a balance between power supply and demand despite uncertainty in output power. We conduct extensive simulations and experiments on a 20-cell prototype to validate the proposed approach.

Battery energy storage systems (BESSs)↗