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Results for “Nonlinear 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 OSTI2023

Sparse regression for plasma physics

Many scientific problems can be formulated as sparse regression, i.e., regression onto a set of parameters when there is a desire or expectation that some of the parameters are exactly zero or do not substantially contribute. This includes many problems in signal and image processing, system identification, optimization, and parameter estimation methods such as Gaussian process regression. Sparsity facilitates exploring high-dimensional spaces while finding parsimonious and interpretable solutions. In the present work, we illustrate some of the important ways in which sparse regression appears in plasma physics and point out recent contributions and remaining challenges to solving these problems in this field. Further, a brief review is provided for the optimization problem and the state-of-the-art solvers, especially for constrained and high-dimensional sparse regression.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2013

Role of dc space charge field in the optimization of microwave conversion efficiency from a modulated intense relativistic electron beam

We demonstrate an efficiency of 70% with 5.1 GW microwave power for a diode voltage of 770 kV and a current modulation coefficient of 1.67 in a klystron-like relativistic backward wave oscillator. The device combines the advantages of reducing electron beam radius, adopting dual-cavity extractor, and introducing two pre-modulation cavities. A large dc space charge field is present due to the conversion of considerable potential energy to kinetic energy at the end of beam-wave interaction region. A nonlinear theory is developed to show that the dc space charge field can increase the current modulation coefficient and microwave conversion efficiency significantly.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Optimization of dynamic aperture for hadron lattices in eRHIC

The potential upgrade of the Relativistic Heavy Ion Collider (RHIC) to an electron ion collider (eRHIC) involves numerous extensive changes to the existing collider complex. The expected very high luminosity is planned to be achieved at eRHIC with the help of squeezing the beta function of the hadron ring at the IP to a few cm, causing a large rise of the natural chromaticities and thus bringing with it challenges for the beam long term stability (Dynamic aperture). We present our effort to expand the DA by carefully tuning the nonlinear magnets thus controlling the size of the footprints in tune space and all lower order resonance driving terms. We show a reasonably large DA through particle tracking over millions of turns of beam revolution.

43 PARTICLE ACCELERATORS↗
DOE OSTI2021

Nonlinear Matrix Approximation with Radial Basis Function Components

We introduce and investigate matrix approximation by decomposition into a sum of radial basis function (RBF) components. An RBF component is a generalization of the outer product between a pair of vectors, where an RBF function replaces the scalar multiplication between individual vector elements. Even though the RBF functions are positive definite, the summation across components is not restricted to convex combinations and allows us to compute the decomposition for any real matrix that is not necessarily symmetric or positive definite. We formulate the problem of seeking such a decomposition as an optimization problem with a nonlinear and non-convex loss function. Several modern versions of the gradient descent method, including their scalable stochastic counterparts, are used to solve this problem. We provide extensive empirical evidence of the effectiveness of the RBF decomposition and that of the gradient-based fitting algorithm. While being conceptually motivated by singular value decomposition (SVD), our proposed nonlinear counterpart outperforms SVD by drastically reducing the memory required to approximate a data matrix with the same L2 error for a wide range of matrix types. For example, it leads to 2 to 6 times memory save for Gaussian noise, graph adjacency matrices, and kernel matrices. Moreover, this proximity-based decomposition can offer additional interpretability in applications that involve, e.g., capturing the inner low-dimensional structure of the data, retaining graph connectivity structure, and preserving the acutance of images.

Rebrova, Elizaveta↗
DOE OSTI2019

An adaptive, multivariate partitioning algorithm for global optimization of nonconvex programs

We develop an adaptive, multivariate partitioning algorithm for solving nonconvex, Mixed-Integer Nonlinear Programs (MINLPs) with polynomial functions to global optimality. In particular, we present an iterative algorithm that exploits piecewise, convex relaxation approaches via disjunctive formulations to solve MINLPs that is different than conventional spatial branch-and-bound approaches. The algorithm partitions the domains of variables in an adaptive and non-uniform manner at every iteration to focus on productive areas of the search space. Furthermore, domain reduction techniques based on sequential, optimization-based bound-tightening and piecewise relaxation techniques, as a part of a presolve step, are integrated into the main algorithm. Finally, we demonstrate the effectiveness of the algorithm on well-known benchmark problems (including Pooling and Blending instances) from MINLPLib and compare our algorithm with state-of-the-art global optimization solvers. With our novel approach, we solve several large-scale instances, some of which are not solvable by state-of-the-art solvers. We also succeed in reducing the best known optimality gap for a hard, generalized pooling problem instance.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Optimal Control of SOEC-Based Hydrogen Production Systems for Demand Response Using Deep Reinforcement Learning in Smart Grids

Solid oxide electrolysis cell (SOEC) hydrogen production technology can range in size from small, appliance-size equipment to large-scale, central production facilities that can be tied directly to renewable or non-greenhouse-gas-emitting forms of electricity production, making it an ideal resource for demand response (DR). The SOEC hydrogen production system is a complex integrated system that encompasses fluid dynamics, electrical dynamics, and electrochemical and thermal dynamics, all of which involve non-linearity and non-convexity. Proper control of the SOEC hydrogen production system is crucial to enable its participation in the DR program. Here, to overcome the difficulty of designing an explicit control law for such nonlinear systems with nonconvex optimization features in DR applications, deep reinforcement learning (DRL) is explored to achieve the optimal control of the SOEC system for DR participation. Specifically, a twin delayed deterministic policy gradient (TD3) control framework is applied to achieve optimal response performance during DR events by considering power tracking error and hydrogen production efficiency with a suitable reward function. Two case studies with grid connections for tracking different DR commands were investigated. The first case study involved operating conditions reaching the boundaries, while the second involved operating conditions within the boundaries. The results showed that the proposed DRL-based control for SOEC can track the DR signal in a timely manner while maintaining high energy efficiency.

08 HYDROGEN↗
DOE OSTI2014

Prediction of U-Mo dispersion nuclear fuels with Al-Si alloy using artificial neural network

Dispersion nuclear fuels, consisting of U-Mo particles dispersed in an Al-Si matrix, are being developed as fuel for research reactors. The equilibrium relationship for a mixture component can be expressed in the phase diagram. It is important to analyze whether a mixture component is in equilibrium phase or another phase. The purpose of this research it is needed to built the model of the phase diagram, so the mixture component is in the stable or melting condition. Artificial neural network (ANN) is a modeling tool for processes involving multivariable non-linear relationships. The objective of the present work is to develop code based on artificial neural network models of system equilibrium relationship of U-Mo in Al-Si matrix. This model can be used for prediction of type of resulting mixture, and whether the point is on the equilibrium phase or in another phase region. The equilibrium model data for prediction and modeling generated from experimentally data. The artificial neural network with resilient backpropagation method was chosen to predict the dispersion of nuclear fuels U-Mo in Al-Si matrix. This developed code was built with some function in MATLAB. For simulations using ANN, the Levenberg-Marquardt method was also used for optimization. The artificial neural network is able to predict the equilibrium phase or in the phase region. The develop code based on artificial neural network models was built, for analyze equilibrium relationship of U-Mo in Al-Si matrix.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2025

Mixed-Integer Linear Programming Formulation with Embedded Machine Learning Surrogates for the Design of Chemical Process Families

In previous work, we introduced process family design. The main idea is to design a platform of common elements, and, allowing us to capture additional cost savings, simultaneously design a family of processes, and reducing both engineering and deployment timelines. We formulate this as an optimization problem, specifically a nonlinear generalized disjunctive program (GDP). We have proposed two approaches for reformulating and solving this problem: one based on full-discretization of the design space and one that uses Machine Learning (ML) surrogates to replace the nonlinear process models. Using ML surrogates to predict required system costs and performance indicators allows us to reformulate the nonlinearities in the GDP generate an efficient MILP formulation. In this work, we apply the ML surrogate approach to two case studies. One case study involves designing a family of carbon capture systems to cover a set of different flue gas flow rates and inlet CO 2 concentrations, where we consider the absorber and stripper as common unit module types. The second case study focuses on a water-desalination process, where we design a family of these processes for a variety of salt concentrations and flow rates. In both of these case studies, we demonstrate a scalable optimization approach that enables the design of multiple processes simultaneously, reducing the time-to-market and overall costs by maximizing the cost savings due to both economies of scale and economies of numbers.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Optimal Membrane Cascade Design for Critical Mineral Recovery Through Logic-based Superstructure Optimization

Critical minerals and rare earth elements play an important role in our climate change initiatives, particularly in applications related with energy storage. Here, we use discrete optimization approaches to design a process for the recovery of Lithium and Cobalt from battery recycling, through membrane separation. Our contribution involves proposing a Generalized Disjunctive Programming (GDP) model for the optimal design of a multistage diafiltration cascade for Li-Co separation. By solving the resulting nonconvex mixed-integer nonlinear program model to global optimality, we investigated scalability and solution quality variations with changes in the number of stages and elements per stage. Results demonstrate the computational tractability of the nonlinear GDP formulation for design of membrane separation processes while opening the door for decom-position strategies for multicomponent separation cascades. Future work aims to extend the GDP formulation to account for stage installation and explore various decomposition techniques to enhance solution efficiency.

Ovalle, Daniel↗
DOE OSTI2016

Optimization of laser energy deposition for single-shot high aspect-ratio microstructuring of thick BK7 glass

We investigate the generation of high aspect ratio microstructures across 0.7 mm thick glass by means of single shot Bessel beam laser direct writing. We study the effect on the photoinscription of the cone angle, as well as of the energy and duration of the ultrashort laser pulse. The aim of the study is to optimize the parameters for the writing of a regular microstructure due to index modification along the whole sample thickness. By using a spectrally resolved single pulse transmission diagnostics at the output surface of the glass, we correlate the single shot material modification with observations of the absorption in different portions of the retrieved spectra, and with the absence or presence of spectral modulation. Numerical simulations of the evolution of the Bessel pulse intensity and of the energy deposition inside the sample help us interpret the experimental results that suggest to use picosecond pulses for an efficient and more regular energy deposition. Picosecond pulses take advantage of nonlinear plasma absorption and avoid temporal dynamics effects which can compromise the stationarity of the Bessel beam propagation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Optimizing multiple reliable forward contracts for reservoir allocation using multitime scale streamflow forecasts

Streamflow forecasts at multiple time scales provide a new opportunity for reservoir management to address competing objectives. Market instruments such as forward contracts with specified reliability are considered as a tool that may help address the perceived risk associated with the use of such forecasts in lieu of traditional operation and allocation strategies. A water allocation process that enables multiple contracts for water supply and hydropower production with different durations, while maintaining a prescribed level of flood risk reduction, is presented. The allocation process is supported by an optimization model that considers multitime scale ensemble forecasts of monthly streamflow and flood volume over the upcoming season and year, the desired reliability and pricing of proposed contracts for hydropower and water supply. It solves for the size of contracts at each reliability level that can be allocated for each future period, while meeting target end of period reservoir storage with a prescribed reliability. The contracts may be insurable, given that their reliability is verified through retrospective modeling. The process can allow reservoir operators to overcome their concerns as to the appropriate skill of probabilistic forecasts, while providing water users with short–term and long–term guarantees as to how much water or energy they may be allocated. An application of the optimization model to the Bhakra Dam, India, provides an illustration of the process. In conclusion, the issues of forecast skill and contract performance are examined. A field engagement of the idea is useful to develop a real–world perspective and needs a suitable institutional environment.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2015

Gompertzian stochastic model with delay effect to cervical cancer growth

In this paper, a Gompertzian stochastic model with time delay is introduced to describe the cervical cancer growth. The parameters values of the mathematical model are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic model numerically. The efficiency of mathematical model is measured by comparing the simulated result and the clinical data of cervical cancer growth. Low values of Mean-Square Error (MSE) of Gompertzian stochastic model with delay effect indicate good fits.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2018

A new modified BFGS method for unconstrained optimization problems

Using chain rule, we propose a modified secant equation to get a more accurate approximation of the second curvature of the objective function. Then, based on this modified secant equation we present a new BFGS method for solving unconstrained optimization problems. The proposed method makes use of both gradient and function values, and utilizes information from two most recent steps, while the usual secant relation uses only the latest step information. Under appropriate conditions, we show that the proposed method is globally convergent without convexity assumption on the objective function. Comparative numerical results show computational efficiency of the proposed method in the sense of the Dolan–Moré performance profiles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

High-contrast imaging with an arbitrary aperture: Active compensation of aperture discontinuities

We present a new method to achieve high-contrast images using segmented and/or on-axis telescopes. Our approach relies on using two sequential deformable mirrors (DMs) to compensate for the large amplitude excursions in the telescope aperture due to secondary support structures and/or segment gaps. In this configuration the parameter landscape of DM surfaces that yield high-contrast point-spread functions is not linear, and nonlinear methods are needed to find the true minimum in the optimization topology. We solve the highly nonlinear Monge-Ampere equation that is the fundamental equation describing the physics of phase-induced amplitude modulation. We determine the optimum configuration for our two sequential DM system and show that high-throughput and high-contrast solutions can be achieved using realistic surface deformations that are accessible using existing technologies. We name this process Active Compensation of Aperture Discontinuities (ACAD). We show that for geometries similar to the James Webb Space Telescope, ACAD can attain at least 10{sup –7} in contrast and an order of magnitude higher for both the future extremely large telescopes and on-axis architectures reminiscent of the Hubble Space Telescope. We show that the converging nonlinear mappings resulting from our DM shapes actually damp near-field diffraction artifacts in the vicinity of the discontinuities. Thus, ACAD actually lowers the chromatic ringing due to diffraction by segment gaps and struts while not amplifying the diffraction at the aperture edges beyond the Fresnel regime. This outer Fresnel ringing can be mitigated by properly designing the optical system. Consequently, ACAD is a true broadband solution to the problem of high-contrast imaging with segmented and/or on-axis apertures. We finally show that once the nonlinear solution is found, fine tuning with linear methods used in wavefront control can be applied to further contrast by another order of magnitude. Generally speaking, the ACAD technique can be used to significantly improve a broad class of telescope designs for a variety of problems.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

Optimizing BAO measurements with non-linear transformations of the Lyman-α forest

We explore the effect of applying a non-linear transformation to the Lyman-α forest transmitted flux F=e{sup −τ} and the ability of analytic models to predict the resulting clustering amplitude. Both the large-scale bias of the transformed field (signal) and the amplitude of small scale fluctuations (noise) can be arbitrarily modified, but we were unable to find a transformation that increases significantly the signal-to-noise ratio on large scales using Taylor expansion up to the third order. In particular, however, we achieve a 33% improvement in signal to noise for Gaussianized field in transverse direction. On the other hand, we explore an analytic model for the large-scale biasing of the Lyα forest, and present an extension of this model to describe the biasing of the transformed fields. Using hydrodynamic simulations we show that the model works best to describe the biasing with respect to velocity gradients, but is less successful in predicting the biasing with respect to large-scale density fluctuations, especially for very nonlinear transformations.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Stochastic growth logistic model with aftereffect for batch fermentation process

In this paper, the stochastic growth logistic model with aftereffect for the cell growth of C. acetobutylicum P262 and Luedeking-Piret equations for solvent production in batch fermentation system is introduced. The parameters values of the mathematical models are estimated via Levenberg-Marquardt optimization method of non-linear least squares. We apply Milstein scheme for solving the stochastic models numerically. The effciency of mathematical models is measured by comparing the simulated result and the experimental data of the microbial growth and solvent production in batch system. Low values of Root Mean-Square Error (RMSE) of stochastic models with aftereffect indicate good fits.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

A Review: Indirect Optimal Control of Wave Energy Converters

Wave energy conversion has been the subject of interest in the past several years. While there are several concepts for converting wave power into electric power, the cost of the electric power harvested from ocean waves remains high. One of the main challenges, though it receives less attention, is the control of the wave energy converter (WEC). This paper presents a treatment for the WEC control problem within the context of optimal control theory. The result is systematic development for an explicit expression for a control that maximizes the harvested energy while meeting operational constraints such as the maximum device stroke and the maximum control force. The control presented here can also be adjusted to meet device design constraints such as a limitation on the amount of reactive power available from the power take-off (PTO) unit; this feature enables a control co-design for the PTO unit. Numerical simulations are presented in this paper for demonstration.

control design↗
DOE OSTI2024

Stochastic average model methods

We consider the solution of finite-sum minimization problems, such as those appearing in nonlinear least-squares or general empirical risk minimization problems. We are motivated by problems in which the summand functions are computationally expensive and evaluating all summands on every iteration of an optimization method may be undesirable. Here we present the idea of stochastic average model (SAM) methods, inspired by stochastic average gradient methods. SAM methods sample component functions on each iteration of a trust-region method according to a discrete probability distribution on component functions; the distribution is designed to minimize an upper bound on the variance of the resulting stochastic model. We present promising numerical results concerning an implemented variant extending the derivative-free model-based trust-region solver POUNDERS, which we name SAM-POUNDERS.

97 MATHEMATICS AND COMPUTING↗