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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 145 records · Page 8

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NASA NTRS2004

Subsonic Aircraft With Regression and Neural-Network Approximators Designed

At the NASA Glenn Research Center, NASA Langley Research Center's Flight Optimization System (FLOPS) and the design optimization testbed COMETBOARDS with regression and neural-network-analysis approximators have been coupled to obtain a preliminary aircraft design methodology. For a subsonic aircraft, the optimal design, that is the airframe-engine combination, is obtained by the simulation. The aircraft is powered by two high-bypass-ratio engines with a nominal thrust of about 35,000 lbf. It is to carry 150 passengers at a cruise speed of Mach 0.8 over a range of 3000 n mi and to operate on a 6000-ft runway. The aircraft design utilized a neural network and a regression-approximations-based analysis tool, along with a multioptimizer cascade algorithm that uses sequential linear programming, sequential quadratic programming, the method of feasible directions, and then sequential quadratic programming again. Optimal aircraft weight versus the number of design iterations is shown. The central processing unit (CPU) time to solution is given. It is shown that the regression-method-based analyzer exhibited a smoother convergence pattern than the FLOPS code. The optimum weight obtained by the approximation technique and the FLOPS code differed by 1.3 percent. Prediction by the approximation technique exhibited no error for the aircraft wing area and turbine entry temperature, whereas it was within 2 percent for most other parameters. Cascade strategy was required by FLOPS as well as the approximators. The regression method had a tendency to hug the data points, whereas the neural network exhibited a propensity to follow a mean path. The performance of the neural network and regression methods was considered adequate. It was at about the same level for small, standard, and large models with redundancy ratios (defined as the number of input-output pairs to the number of unknown coefficients) of 14, 28, and 57, respectively. In an SGI octane workstation (Silicon Graphics, Inc., Mountainview, CA), the regression training required a fraction of a CPU second, whereas neural network training was between 1 and 9 min, as given. For a single analysis cycle, the 3-sec CPU time required by the FLOPS code was reduced to milliseconds by the approximators. For design calculations, the time with the FLOPS code was 34 min. It was reduced to 2 sec with the regression method and to 4 min by the neural network technique. The performance of the regression and neural network methods was found to be satisfactory for the analysis and design optimization of the subsonic aircraft.

Patnaik, Surya N.↗

NASA NTRS2020

Verification of Anisotropic Mesh Adaptation for Turbulent Simulations over ONERA M6 Wing

Unstructured anisotropic mesh adaptation is known to be an efficient way to control discretization errors in Computational Fluid Dynamics (CFD) simulations. Method verification is required to provide the confidence for routine use in production analysis. The current work aims at verification of anisotropic mesh adaptation for RANS simulations over the ONERA M6 wing. The present verification study is performed using four different flow solvers, three different implementations of the metric field, and three mesh mechanics packages. Two of the flow solvers use stabilized finite-element discretizations (FUN3D-SFE and GGNS), one uses finite-volume discretization (FUN3D-FV), and the last one uses mixed finite-volume and finite element discretizations (Wolf). The mesh adaptation is based on an error estimator that aims to control the quadratic error term in the linear interpolation of Mach number. Two sets of adaptations were performed; the first one controls the interpolation error in L2 norm and the second one controls the interpolation error in L4 norm. Convergence studies were performed on the forces and the pitching moment using all four solvers, and the results are compared with previously verified convergence studies on fixed (nonadapted) meshes. Both forces and pitching moment on adapted meshes are found to be converging to the fine mesh values faster than those on fixed meshes. In addition to forces and moments, convergence of surface pressure and skin friction coefficients at various measurement locations on the wing are also presented. Adapted-mesh surface pressure distributions agree with the fine fixed mesh pressure distributions. Adapted-mesh skin friction distributions contain high frequency noise with mean values approaching the fixed mesh pressure skin friction distributions.

Aravind Balan↗

DOE OSTI2026

Integral Kernel Methods for Nonlinear Parabolic-Elliptic Systems

Nonlinear parabolic-elliptic systems arise in many physical, biological, and chemical phenomena such as chemotaxis, ion transport, self-gravitating particles, and Brownian vortices. Existing methods struggle with the strong coupling and high nonlinearity and nonlocality of some of these systems, especially the ill-conditioned, convection-dominated problems. To overcome numerical difficulties, current approaches rely on initial guesses, preconditioning, or iterative techniques with no convergence guarantees. They might suffer from poor scalability, large memory usage, and difficulty to parallelize. Inspired by the connection of parabolic-elliptic systems to stochastic processes, we introduce a novel meshless, monolithic, and fully explicit method that naturally encapsulates the elliptic and parabolic operators into a single step which updates each node deterministically with global information. By being fully quadrature-based, it avoids solving systems of discretized equations and does not utilize initial guesses or preconditioning, while requiring little memory and being easy to parallelize. We first derive the method in an integral kernel formulation with quadratic complexity in the number of integration nodes and then leverage kernel-independent fast multipole methods (FMM) to present a scalable algorithm with linear complexity. We provide numerical examples for the Poisson-Nernst-Planck equations in one, two, and three dimensions, together with the derivation of the integral kernel for each case. Furthermore, the examples demonstrate the fast convergence and scalability of the FMM-accelerated algorithm, as well as its suitability for convection-dominated problems, making it competitive against traditional PDE solvers.

PDE systems↗

DOE OSTI2023

Neural Network-Based Variational Methods for Solving Quadratic Porous Medium Equations in High Dimensions

Here, in this paper, we propose and study neural network-based methods for solutions of high-dimensional quadratic porous medium equation (QPME). Three variational formulations of this nonlinear PDE are presented: a strong formulation and two weak formulations. For the strong formulation, the solution is directly parameterized with a neural network and optimized by minimizing the PDE residual. It can be proved that the convergence of the optimization problem guarantees the convergence of the approximate solution in the $L^1$ sense. The weak formulations are derived following (Brenier in Examples of hidden convexity in nonlinear PDEs, 2020) which characterizes the very weak solutions of QPME. Specifically speaking, the solutions are represented with intermediate functions who are parameterized with neural networks and are trained to optimize the weak formulations. Extensive numerical tests are further carried out to investigate the pros and cons of each formulation in low and high dimensions. This is an initial exploration made along the line of solving high-dimensional nonlinear PDEs with neural network-based methods, which we hope can provide some useful experience for future investigations.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Extending a 10‐node composite tetrahedral finite element for solid mechanics

Abstract We propose to extend the composite tetrahedral finite element first introduced by Thoutireddy et al. (2002) and recently reformulated by Ostien et al. (2016). We generalize the gradient operator and mass matrix to curved domains through analytical expressions weighted by subtetrahedra Jacobians. Optimal integration weights are constructed to increase the accuracy of Gaussian quadrature. We preserve the variational structure of the formulation through a new five‐field functional with additional, independent fields for the Jacobian and the pressure. This approach not only obviates volumetric locking but also yields symmetry. A deleterious soft mode, common to both the quadratic and composite tetrahedral element with constant pressure formulations is effectively stabilized through a novel convex energy penalty function. Numerous numerical examples spanning a patch test to the impact of a Taylor bar demonstrate the accuracy, robustness, and convergence of the extended composite tetrahedral element for application to structural metals.

Foulk III, James W.↗

DOE OSTI2025

A time-parallel multiple-shooting method for large-scale quantum optimal control

Quantum optimal control plays a crucial role in quantum computing by providing the interface between compiler and hardware. Solving the optimal control problem is particularly challenging for multi-qubit gates, due to the exponential growth in computational complexity with the system's dimensionality and the deterioration of optimization convergence. To ameliorate the computational complexity of time-integration, this paper introduces a multiple-shooting approach in which the time domain is divided into multiple windows and the intermediate states at window boundaries are treated as additional optimization variables. Further, this enables parallel computation of state evolution across time-windows, significantly accelerating objective function and gradient evaluations. Since the initial state matrix in each window is only guaranteed to be unitary upon convergence of the optimization algorithm, the conventional gate trace infidelity is replaced by a generalized infidelity that is convex for non-unitary state matrices. Continuity of the state across window boundaries is enforced by equality constraints. A quadratic penalty optimization method is used to solve the constrained optimal control problem, and an efficient adjoint technique is employed to calculate the gradients in each iteration. We demonstrate the effectiveness of the proposed method through numerical experiments on quantum Fourier transform gates in systems with 2, 3, and 4 qubits, noting a speedup of 80x for evaluating the gradient in the 4-qubit case, highlighting the method's potential for optimizing control pulses in multi-qubit quantum systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Quantum simulation of bosons with the contracted quantum eigensolver

Abstract Quantum computers are promising tools for simulating many-body quantum systems due to their potential scaling advantage over classical computers. While significant effort has been expended on many-fermion systems, here we simulate a model entangled many-boson system with the contracted quantum eigensolver (CQE). We generalize the CQE to many-boson systems by encoding the bosonic wavefunction on qubits. The CQE provides a compact ansatz for the bosonic wave function whose gradient is proportional to the residual of a contracted Schrödinger equation. We apply the CQE to a bosonic system, where N quantum harmonic oscillators are coupled through a pairwise quadratic repulsion. The model is relevant to the study of coupled vibrations in molecular systems on quantum devices. Results demonstrate the potential efficiency of the CQE in simulating bosonic processes such as molecular vibrations with good accuracy and convergence even in the presence of noise.

Physics↗

NASA NTRS1995

Local multiplicative Schwarz algorithms for convection-diffusion equations

We develop a new class of overlapping Schwarz type algorithms for solving scalar convection-diffusion equations discretized by finite element or finite difference methods. The preconditioners consist of two components, namely, the usual two-level additive Schwarz preconditioner and the sum of some quadratic terms constructed by using products of ordered neighboring subdomain preconditioners. The ordering of the subdomain preconditioners is determined by considering the direction of the flow. We prove that the algorithms are optimal in the sense that the convergence rates are independent of the mesh size, as well as the number of subdomains. We show by numerical examples that the new algorithms are less sensitive to the direction of the flow than either the classical multiplicative Schwarz algorithms, and converge faster than the additive Schwarz algorithms. Thus, the new algorithms are more suitable for fluid flow applications than the classical additive or multiplicative Schwarz algorithms.

Cai, Xiao-Chuan↗

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 OSTI2023

Reinforcement Learning of Structured Stabilizing Control for Linear Systems With Unknown State Matrix

This paper delves into designing feedback control gains for a continuous-time linear quadratic regulator (LQR) problem that is constrained to certain predefined structure with unknown state matrix. We bring forth the ideas from reinforcement learning (RL) in conjunction with sufficient stability and performance guarantees in order to design these structured gains using the trajectory measurements of states and controls. Here we first formulate a model-based framework using dynamic programming (DP) to embed the structural constraint to the LQR gain computation in the continuous-time setting, and then subsequently, formulate a policy iteration RL algorithm that can alleviate the requirement of known state matrix in conjunction with maintaining the feedback gain structure. The design enables a distributed learning control design which is necessary for many large-scale cyber-physical systems. Theoretical guarantees are provided for stability and convergence of the structured reinforcement learning (SRL) algorithm. We validate our theoretical results with numerical simulations on a multi-agent networked linear time-invariant (LTI) dynamic system.

42 ENGINEERING↗

DOE OSTI2025

Factorization Machine‐Based Active Learning for Functional Materials Design with Optimal Initial Data

The optimization of functional materials is important to enhance their properties, but their complex geometries pose great challenges to optimization. Data-driven algorithms efficiently navigate such complex design spaces by learning relationships between material structures and performance metrics to discover high-performance functional materials. Surrogate-based active learning, continually improving its surrogate model by iteratively including high-quality data points, has emerged as a cost-effective data-driven approach. Furthermore, it can be coupled with quantum computing to enhance optimization processes, especially when paired with a special form of surrogate model (i.e., quadratic unconstrained binary optimization), formulated by factorization machine (FM). However, current practices often overlook the variability in design space sizes when determining the initial data size for optimization. In this work, we investigate the optimal initial data sizes required for efficient convergence across various design space sizes. By employing averaged piecewise linear regression, we identify initiation points where convergence begins, highlighting the crucial role of employing adequate initial data in achieving efficient optimization. These results contribute to the efficient optimization of functional materials by ensuring faster convergence and reducing computational costs in FM-based active learning.

active learning↗

NASA NTRS1988

Efficient approximation concepts using second order information

The application of second derivative information for solving structural optimization problems is considered. In the present method, rather than building approximate nonlinear forms for the objective function and constraints, only linear approximations are used. A separable quadratic approximation of the Lagrangian function is included in the subproblem statement. The method has been successfully used for simple problems that can be solved in closed form, in addition to the sizing optimization of trusses, and it is shown to converge faster than the convex linearization method or the method of moving asymptotes.

Fleury, Claude↗

DOE OSTI2022

An adaptive stochastic sequential quadratic programming with differentiable exact augmented lagrangians

In this study, we consider solving nonlinear optimization problems with a stochastic objective and deterministic equality constraints. We assume for the objective that its evaluation, gradient, and Hessian are inaccessible, while one can compute their stochastic estimates by, for example, subsampling. We propose a stochastic algorithm based on sequential quadratic programming (SQP) that uses a differentiable exact augmented Lagrangian as the merit function. To motivate our algorithm design, we first revisit and simplify an old SQP method Lucidi developed for solving deterministic problems, which serves as the skeleton of our stochastic algorithm. Based on the simplified deterministic algorithm, we then propose a non-adaptive SQP for dealing with stochastic objective, where the gradient and Hessian are replaced by stochastic estimates but the stepsizes are deterministic and prespecified. Finally, we incorporate a recent stochastic line search procedure Paquette and Scheinberg into the non-adaptive stochastic SQP to adaptively select the random stepsizes, which leads to an adaptive stochastic SQP. The global "almost sure" convergence for both non-adaptive and adaptive SQP methods is established. Numerical experiments on nonlinear problems in CUTEst test set demonstrate the superiority of the adaptive algorithm.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1975

A transformation method for constrained-function minimization

A direct method for constrained-function minimization is discussed. The method involves the construction of an appropriate function mapping all of one finite dimensional space onto the region defined by the constraints. Functions which produce such a transformation are constructed for a variety of constraint regions including, for example, those arising from linear and quadratic inequalities and equalities. In addition, the computational performance of this method is studied in the situation where the Davidon-Fletcher-Powell algorithm is used to solve the resulting unconstrained problem. Good performance is demonstrated for 19 test problems by achieving rapid convergence to a solution from several widely separated starting points.

Park, S. K.↗

NASA NTRS1986

Numerical approximation for the infinite-dimensional discrete-time optimal linear-quadratic regulator problem

An abstract approximation framework is developed for the finite and infinite time horizon discrete-time linear-quadratic regulator problem for systems whose state dynamics are described by a linear semigroup of operators on an infinite dimensional Hilbert space. The schemes included the framework yield finite dimensional approximations to the linear state feedback gains which determine the optimal control law. Convergence arguments are given. Examples involving hereditary and parabolic systems and the vibration of a flexible beam are considered. Spline-based finite element schemes for these classes of problems, together with numerical results, are presented and discussed.

Gibson, J. S.↗

NASA NTRS1988

Numerical approximation for the infinite-dimensional discrete-time optimal linear-quadratic regulator problem

Gibson, J. S.↗

NASA NTRS1990

A superlinear interior points algorithm for engineering design optimization

We present a quasi-Newton interior points algorithm for nonlinear constrained optimization. It is based on a general approach consisting of the iterative solution in the primal and dual spaces of the equalities in Karush-Kuhn-Tucker optimality conditions. This is done in such a way to have primal and dual feasibility at each iteration, which ensures satisfaction of those optimality conditions at the limit points. This approach is very strong and efficient, since at each iteration it only requires the solution of two linear systems with the same matrix, instead of quadratic programming subproblems. It is also particularly appropriate for engineering design optimization inasmuch at each iteration a feasible design is obtained. The present algorithm uses a quasi-Newton approximation of the second derivative of the Lagrangian function in order to have superlinear asymptotic convergence. We discuss theoretical aspects of the algorithm and its computer implementation.

Herskovits, J.↗

DOE OSTI2023

ALESQP: An Augmented Lagrangian Equality-Constrained SQP Method for Optimization with General Constraints

Here we present a new algorithm for infinite-dimensional optimization with general constraints, called ALESQP. In short, ALESQP is an augmented Lagrangian method that penalizes inequality constraints and solves equality-constrained nonlinear optimization subproblems at every iteration. The subproblems are solved using a matrix-free trust-region sequential quadratic programming (SQP) method that takes advantage of iterative, i.e., inexact linear solvers, and is suitable for large-scale applications. A key feature of ALESQP is a constraint decomposition strategy that allows it to exploit problem-specific variable scalings and inner products. We analyze convergence of ALESQP under different assumptions. We show that strong accumulation points are stationary. Consequently, in finite dimensions ALESQP converges to a stationary point. In infinite dimensions we establish that weak accumulation points are feasible in many practical situations. Under additional assumptions we show that weak accumulation points are stationary. We present several infinite-dimensional examples where ALESQP shows remarkable discretization-independent performance in all of its iterative components, requiring a modest number of iterations to meet constraint tolerances at the level of machine precision. Also, we demonstrate a fully matrix-free solution of an infinite-dimensional problem with nonlinear inequality constraints.

97 MATHEMATICS AND COMPUTING↗