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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 325 records · Page 18
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Tunable phononic bandgap materials designed via topology optimization

Topology optimization is used to design phononic bandgap materials that are tunable by mechanical deformation. A periodic media is considered, which due to the assumption of length scale separation, allows the dispersion relations to be obtained by analyzing a single unit cell subjected to Floquet–Bloch boundary conditions. A finite macroscopic deformation is applied to the unit cell to affect its geometry and hence dispersion. We tune the dispersion–deformation relation to our liking by solving a topology optimization problem using nonlinear programming. The adjoint method is employed to compute the sensitivities, and the non-differentiability of degenerate eigenvalues is avoided using symmetric polynomials. Several tunable phononic crystal designs are presented. Also, a verification analysis is performed, wherein the optimized design is interpreted and analyzed using a conforming finite element mesh.

42 ENGINEERING↗
DOE OSTI2023

A Fast Temporal Decomposition Procedure for Long-Horizon Nonlinear Dynamic Programming

We propose a fast temporal decomposition procedure for solving long-horizon nonlinear dynamic programs. The core of the procedure is sequential quadratic programming (SQP) that utilizes a differentiable exact augmented Lagrangian as the merit function. Within each SQP iteration, we approximately solve the Newton system using an overlapping temporal decomposition strategy. We show that the approximate search direction is still a descent direction of the augmented Lagrangian provided the overlap size and penalty parameters are suitably chosen, which allows us to establish the global convergence. Moreover, we show that a unit step size is accepted locally for the approximate search direction and further establish a uniform, local linear convergence over stages. This local convergence rate matches the rate of the recent Schwarz scheme (Na et al. 2022). However, the Schwarz scheme has to solve nonlinear subproblems to optimality in each iteration, whereas we only perform a single Newton step instead. Numerical experiments validate our theories and demonstrate the superiority of our method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

A Generalized Variational Principle with Applications to Excited State Mean Field Theory

We present a generalization of the variational principle that is compatible with any Hamiltonian eigenstate that can be specified uniquely by a list of properties. This variational principle appears to be compatible with a wide range of electronic structure methods, including mean field theory, density functional theory, multireference theory, and quantum Monte Carlo. Like the standard variational principle, this generalized variational principle amounts to the optimization of a nonlinear function that, in the limit of an arbitrarily flexible wave function, has the desired Hamiltonian eigenstate as its global minimum. Unlike the standard variational principle, it can target excited states and select individual states in cases of degeneracy or near-degeneracy. As an initial demonstration of how this approach can be useful in practice, we employ it to improve the optimization efficiency of excited state mean field theory by an order of magnitude. With this improved optimization, we are able to demonstrate that the accuracy of the corresponding second-order perturbation theory rivals that of singles-and-doubles equation-of-motion coupled cluster in a substantially broader set of molecules than could be explored by our previous optimization methodology.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2011

PyRAT (Python Radiography Analysis Tool): Overview [Slides]

PyRAT was developed as a quantitative tool for robustly characterizing objects from radiographs to solve problems such as the hybrid nonlinear inverse problem. The optimization software library that was used is the nonsmooth optimization by MADS algorithm (NOMAD). Some of PyRAT's features are: (1) hybrid nonlinear inverse problem with calculated x-ray spectrum and detector response; (2) optimization based inversion approach with goal of identifying unknown object configurations - MVO problem; (3) using functionalities of Python libraries for radiographic image processing and analysis; (4) using the Tikhonov regularization method of linear inverse problem to recover partial information of object configurations; (5) using a priori knowledge of problem solutions to define feasible region and discrete neighbor for the MVO problem - initial data analysis + material library $\Rightarrow$ a priori knowledge; and (6) using the NOMAD (C++ version) software in the object.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2025

Analog Systems for Edge Optimization

Over the past decade, analog computing has the subject of substantial research interest providing a path toward improved computational efficiency in the post-Dennard era. Analog matrix vector multiplication (MVM) accelerators provide a popular approach given the ubiquity of MVM operations in numerous applications. However, historically analog computing systems can struggle with applications requiring high precision due to the inherent susceptibility of these systems to analog non-idealities. Therefore, prior work on analog systems has focused either on applications known to be tolerant of limited precision (e.g., neural network inference), or using expensive techniques to emulate high-precision using many analog MVM operations. In this work, we propose an alternative approach. Motivated by recent advances in inexact nonlinear solvers and optimizers, we explore the potential of co-designing optimization algorithms which can take full advantage of the fundamentally inexact analog MVM operations. To enable these co-designed algorithms we also develop a general mathematical theory of the precision and energy efficiency of analog operations, and a new system architecture for tightly-coupled analog and digital computation. Finally, we examine the applicability of analog computing to a wider class of symmetric positive definite systems and find potential in using analog operations as a sparse approximate inverse preconditioner. With these core innovations, this project provides a path toward effectively implementing optimization algorithms on power-constrained autonomous and semi-autonomous systems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

A time-parallel method for the solution of PDE-constrained optimization problems

We study a time-parallel approach to solving quadratic optimization problems with linear time-dependent partial differential equation (PDE) constraints. These problems arise in formulations of optimal control, optimal design and inverse problems that are governed by parabolic PDE models. They may also arise as subproblems in algorithms for the solution of optimization problems with nonlinear time-dependent PDE constraints, e.g., in sequential quadratic programming methods. We apply a piecewise linear finite element discretization in space to the PDE constraint, followed by the Crank-Nicolson discretization in time. The objective function is discretized using finite elements in space and the trapezoidal rule in time. At this point in the discretization, auxiliary state variables are introduced at each discrete time interval, with the goal to enable: (i) a decoupling in time; and (ii) a fixed-point iteration to recover the solution of the discrete optimality system. The fixed-point iterative schemes can be used either as preconditioners for Krylov subspace methods or as smoothers for multigrid (in time) schemes. We present promising numerical results for both use cases.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Joint Optimization of Multimodal Transit Frequency and Shared Autonomous Vehicle Fleet Size with Hybrid Metaheuristic and Nonlinear Programming

Shared autonomous vehicles (SAVs) bring competition to traditional transit services but redesigning multimodal transit network can utilize SAVs as feeders to enhance service efficiency and coverage. This paper presents an optimization framework for the joint multimodal transit frequency and SAV fleet size problem, a variant of the transit network frequency setting problem. The objective is to maximize total transit ridership (including SAV-fed trips and subtracting boarding rejections) across multiple time periods under budget constraints, considering endogenous mode choice (transit, point-to-point SAVs, driving) and route selection, while allowing for strategic route removal by setting frequencies to zero. Due to the problem’s non-linear, non-convex nature and the computational challenges of large-scale networks, we develop a hybrid solution approach that combines a metaheuristic approach (particle swarm optimization) with nonlinear programming for local solution refinement. To ensure computational tractability, the framework integrates analytical approximation models for SAV waiting times based on fleet utilization, multimodal network assignment for route choice, and multinomial logit mode choice behavior, bypassing the need for computationally intensive simulations within the main optimization loop. Applied to the Chicago metropolitan area’s multimodal network, our method illustrates a 33.3% increase in transit ridership through optimized transit route frequencies and SAV integration, particularly enhancing off-peak service accessibility and strategically reallocating resources.

Ng, Max↗
DOE OSTI2024

Nonlinear control of the minimum safety factor in tokamaks by optimal allocation of spatially moving electron cyclotron current drive

The minimum value of the safety factor profile is related to the magnetohydrodynamic (MHD) stability of the plasma confined in a tokamak. Therefore, active control of the minimum safety factor may mitigate MHD instabilities that can degrade or even terminate plasma confinement. Typically, in most tokamak scenarios, the minimum safety factor evolves spatially with time, i.e., the location at which the safety factor achieves the minimum value changes with time. In addition to the inherent nonlinearities in the minimum safety factor evolution, its spatial variation makes the control design challenging. In particular, complexity in control design may arise from the need for time-dependent nonlinear models that account for spatial variation of the minimum safety factor. Furthermore, the minimum safety factor may drift to locations where the actuator authority is low. The problem of minimum safety factor control with target location tracking and moving electron cyclotron current drive (ECCD) is addressed in this work. A nonlinear time-dependent model that incorporates the spatial variation of the minimum safety factor is presented. A nonlinear controller based on optimal feedback linearization is developed to track a target minimum safety factor. The proposed controller treats the ECCD position as a controllable variable. In other words, the controller prescribes the ECCD position (in addition to the non-inductive powers) in real time based on an optimal criterion that is defined a priori. This work also presents the steps necessary to integrate the minimum safety factor controller with a total energy controller to achieve multiple control objectives simultaneously. In conclusion, the proposed integrated control algorithm is tested using nonlinear simulations in the Control Oriented Transport SIMulator (COTSIM) for a DIII-D tokamak scenario.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2016

A superstructure-based framework for bio-separation network synthesis

Modern biotechnologies enable the production of chemicals using engineered microorganisms. However, the cost of downstream recovery and purification steps is high, which means that the feasibility of bio-based chemicals production depends heavily on the synthesis of cost-effective separation networks. To this end, we develop a superstructure-based framework for bio-separation network synthesis. Based on general separation principles and insights obtained from industrial processes for specific products, we first identify four separation stages: cell treatment, product phase isolation, concentration and purification, and refinement. For each stage, we systematically implement a set of connectivity rules to develop stage-superstructures, all of which are then integrated to generate a general superstructure that accounts for all types of chemicals that can be produced using microorganisms. Here we further develop a superstructure reduction method to solve specific instances, based on product attributes, technology availability, case-specific considerations, and final product stream specifications. A general optimization model, including short-cut models for all technologies, is formulated. The proposed framework enables preliminary synthesis and analysis of bio-separation networks, and thus estimation of separation costs.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Roadmap on thermodynamics and thermal metamaterials

Thermal metamaterials represent a transformative paradigm in modern physics, synergizing thermodynamic principles with metamaterial engineering to master heat flow at will. As next-generation technologies demand multi-scale thermal control, this field urgently requires systematic frameworks to unify its multidisciplinary advances. Curated through a global collaboration involving over 50 specialists across 25 subdisciplines, this review primarily summarizes two decades of advancements, ranging from theoretical breakthroughs to functional implementations. The review reveals groundbreaking innovations in heat manipulation through the exploration of both classical and non-classical transport regimes, topological thermal control mechanisms, and quantum-informed phonon engineering strategies. By bridging physical insights like non-Hermitian thermal dynamics and valleytronic phonon transport with cutting-edge applications, we demonstrate paradigm-shifting capabilities: environment-adaptive thermal cloaks, AI-optimized metamaterials, and nonlinear thermal circuits enabling heat-based computation. Experimental milestones include 3D thermal null media with reconfigurable invisibility and thermal designs breaking classical conductivity limits. Here, this collaborative effort establishes an indispensable roadmap for physicists, highlighting pathways to quantum thermal management, entropy-controlled energy systems, and topological devices. As thermal metamaterials transition from laboratory marvels to technological cornerstones, this work provides the foundational lexicon and design principles for the coming era of intelligent thermal matter.

heat conduction control↗
DOE OSTI2013

Adaptive Implicit Non-Equilibrium Radiation Diffusion

We describe methods for accurate and efficient long term time integra- tion of non-equilibrium radiation diffusion systems: implicit time integration for effi- cient long term time integration of stiff multiphysics systems, local control theory based step size control to minimize the required global number of time steps while control- ling accuracy, dynamic 3D adaptive mesh refinement (AMR) to minimize memory and computational costs, Jacobian Free Newton-Krylov methods on AMR grids for efficient nonlinear solution, and optimal multilevel preconditioner components that provide level independent solver convergence.

Philip, Bobby↗