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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 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Improved stellarator permanent magnet designs through combined discrete and continuous optimizations

A common optimization problem in the areas of magnetized plasmas and fusion energy is the design of magnets to produce a given three-dimensional magnetic field distribution to high precision. When designing arrays of permanent magnets for stellarator plasma confinement, such problems have tens of thousands of degrees of freedom whose solutions, for practical reasons, should be constrained to discrete spaces. We perform a direct comparison between two algorithms that have been developed previously for this purpose, and demonstrate that composite procedures that apply both algorithms in sequence can produce substantially improved results. One approach uses a continuous, quasi-Newton procedure to optimize the dipole moments of a set of magnets and then projects the solution onto a discrete space. The second uses an inherently discrete greedy optimization procedure that has been enhanced and generalized for this work. Further, the approaches are both applied to design arrays cubic rare-Earth permanent magnets to confine a quasi-axisymmetric plasma with a magnetic field on axis of 0.5 T. The first approach tends to find solutions with higher field accuracy, whereas the second can find solutions with substantially (up to 30%) fewer magnets. When the approaches are combined, they can obtain solutions with magnet quantities comparable to the second approach while matching the field accuracy of the first.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

A Stochastic Quasi-Newton Method in the Absence of Common Random Numbers

We present Q-SASS, a quasi-Newton method for unconstrained stochastic optimization that does not rely on common random numbers. Most existing quasi-Newton approaches leverage common random numbers to construct second-order updates. However, motivated by challenges in variational quantum algorithms—where such coordination is not possible—we consider the setting in which function values and gradients are accessible only through noisy probabilistic zeroth- and first-order oracles, and no common random numbers can be exploited. We derive high-probability tail bounds on the iteration complexity of our algorithm for nonconvex, convex, and strongly convex (more generally, those satisfying the PL condition) objective functions. Finally, we demonstrate the empirical benefits of our quasi-Newton updating scheme on both synthetic and quantum chemistry problems.

Complexity bound↗
DOE OSTI2022

Forward and inverse modeling of fault transmissibility in subsurface flows

Characterizing physical properties of faults, such as their transmissibility, is crucial for performing predictive numerical simulation of subsurface flows, such as those encountered in petroleum engineering and remediation of subsurface contamination. Here, this paper provides a complete investigation of the inverse problem for fault transmissibility in subsurface flow models, under appropriate assumptions on fault structure. In particular, the following aspects are considered: 1) fault modeling and well-posedness of the forward problem; 2) finite element (FEM) discretizations of the forward problem and their rigorous a priori convergence analysis; 3) Well-posedness of the Bayesian inverse problem, FEM discretization of the infinite dimensional Bayesian inverse formulation, and its rigorous a priori analysis. Moreover, computation of the maximum a posteriori (MAP) point via fast inexact Newton-conjugate gradient optimization and a Laplace approximation of the Bayesian posterior are also presented. Numerical results illustrate the use of the proposed fault model in forward and inverse problems for subsurface flows in two dimensional domains with multiple faults.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1977

The terminal area automated path generation problem

The automated terminal area path generation problem in the advanced Air Traffic Control System (ATC), has been studied. Definitions, input, output and the interrelationships with other ATC functions have been discussed. Alternatives in modeling the problem have been identified. Problem formulations and solution techniques are presented. In particular, the solution of a minimum effort path stretching problem (path generation on a given schedule) has been carried out using the Newton-Raphson trajectory optimization method. Discussions are presented on the effect of different delivery time, aircraft entry position, initial guess on the boundary conditions, etc. Recommendations are made on real-world implementations.

Hsin, C.-C.↗
NASA NTRS1992

First MEM task IRMEO in IRAF

The first task for image restoration using the Maximum Entropy Method (MEM) in IRAF, called IRMEO, is described. The underlining algorithm is the approximate Newton method for optimization. The basic input images and parameters for deconvolution are described in some detail. Results of preliminary tests, including the number of iterations, required CPU time on a variety of computers, and deconvolved images are reported and compared with those from other deconvolution methods. The merits and limitations of this task are pointed out. The possible development of better MEM tasks on the basis of IRMEO is also discussed.

Wu, Nailong↗
NASA NTRS2005

What Information Theory Says about Bounded Rational Best Response

Probability Collectives (PC) provides the information-theoretic extension of conventional full-rationality game theory to bounded rational games. Here an explicit solution to the equations giving the bounded rationality equilibrium of a game is presented. Then PC is used to investigate games in which the players use bounded rational best-response strategies. Next it is shown that in the continuum-time limit, bounded rational best response games result in a variant of the replicator dynamics of evolutionary game theory. It is then shown that for team (shared-payoff) games, this variant of replicator dynamics is identical to Newton-Raphson iterative optimization of the shared utility function.

Wolpert, David H.↗
DOE OSTI2023

The DESC stellarator code suite Part 3: Quasi-symmetry optimization

The DESC stellarator optimization code takes advantage of advanced numerical methods to search the full parameter space much faster than conventional tools. Only a single equilibrium solution is needed at each optimization step thanks to automatic differentiation, which efficiently provides exact derivative information. A Gauss–Newton trust-region optimization method uses second-order derivative information to take large steps in parameter space and converges rapidly. With just-in-time compilation and GPU portability, high-dimensional stellarator optimization runs take orders of magnitude less computation time with DESC compared to other approaches. This paper presents the theory of the DESC fixed-boundary local optimization algorithm along with demonstrations of how to easily implement it in the code. Example quasi-symmetry optimizations are shown and compared to results from conventional tools. Three different forms of quasi-symmetry objectives are available in DESC, and their relative advantages are discussed in detail. In the examples presented, the triple product formulation yields the best optimization results in terms of minimized computation time and particle transport. This paper concludes with an explanation of how the modular code suite can be extended to accommodate other types of optimization problems.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1997

Neural Generalized Predictive Control: A Newton-Raphson Implementation

An efficient implementation of Generalized Predictive Control using a multi-layer feedforward neural network as the plant's nonlinear model is presented. In using Newton-Raphson as the optimization algorithm, the number of iterations needed for convergence is significantly reduced from other techniques. The main cost of the Newton-Raphson algorithm is in the calculation of the Hessian, but even with this overhead the low iteration numbers make Newton-Raphson faster than other techniques and a viable algorithm for real-time control. This paper presents a detailed derivation of the Neural Generalized Predictive Control algorithm with Newton-Raphson as the minimization algorithm. Simulation results show convergence to a good solution within two iterations and timing data show that real-time control is possible. Comments about the algorithm's implementation are also included.

Soloway, Donald↗
DOE OSTI2025

Optimizing the optimizer for physics-informed neural networks and Kolmogorov-Arnold networks

Physics-Informed Neural Networks (PINNs) have revolutionized the computation of PDE solutions by integrating partial differential equations (PDEs) into the neural network’s training process as soft constraints, becoming an important component of the scientific machine learning (SciML) ecosystem. More recently, physics-informed Kolmogorv-Arnold networks (PIKANs) have also shown to be effective and comparable in accuracy with PINNs. In their current implementation, both PINNs and PIKANs are mainly optimized using first-order methods like Adam, as well as quasi-Newton methods such as BFGS and its low-memory variant, L-BFGS. However, these optimizers often struggle with highly nonlinear and non-convex loss landscapes, leading to challenges such as slow convergence, local minima entrapment, and (non)degenerate saddle points. In this study, we investigate the performance of Self- Scaled BFGS (SSBFGS), Self-Scaled Broyden (SSBroyden) methods and other advanced quasi-Newton schemes, including BFGS and L-BFGS with different line search strategies. These methods dynamically rescale updates based on historical gradient information, thus enhancing training efficiency and accuracy. We systematically compare these optimizers – using both PINNs and PIKANs – on key challenging PDEs, including the Burgers, Allen-Cahn, Kuramoto-Sivashinsky, Ginzburg-Landau, and Stokes equations. Additionally, we evaluate the performance of SSBFGS and SSBroyden for Deep Operator Network (DeepONet) architectures, demonstrating their effectiveness for data-driven operator learning. Our findings provide state-of-the-art results with orders-of-magnitude accuracy improvements without the use of adaptive weights or any other enhancements typically employed in PINNs. More broadly, our work reveal insights into the effectiveness of quasi-Newton optimization strategies in significantly improving the convergence and accurate generalization of PINNs and PIKANs.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1980

A new method for optimizing multiple flyby trajectories

A new procedure has been developed which minimizes total impulsive Delta V for multiple flyby trajectories with constraints on flyby parameters and maneuver times. The method involves solving a bounds-constrained parameter optimization problem with a Newton algorithm utilizing analytic first and second derivatives. Each trajectory segment connecting consecutive maneuver points is found by first targeting from the preceding maneuver point to the parameters of the upcoming flyby and then propagating the resulting trajectory to the next maneuver point. Multi-conic techniques are used for trajectory propagation and for computation of the state transition matrix. This procedure has successfully optimized Galileo satellite tours containing up to 11 flybys.

Damario, L. A.↗
NASA NTRS1991

Airfoil optimization with efficient gradient calculations

The viscous airfoil design analysis code XFOIL was extended to allow optimization using conformal mapping coefficients as design variables. The optimization technique used was the Steepest Descent method applied to a Penalty Function. The gradients of the aerodynamic variables with respect to the design variables were cheaply calculated as by-products of XFOIL's integral boundary layer Newton solver. The speed of the optimization process further increased by updating the Newton system boundary layer variables after each optimization step using the available gradient information. Two examples are presented.

Sorensen, Thomas↗
DOE OSTI2025

Efficient proximal subproblem solvers for a nonsmooth trust-region method

In [R. J. Baraldi and D. P. Kouri, Mathematical Programming, (2022), pp. 1-40], we introduced an inexact trust-region algorithm for minimizing the sum of a smooth nonconvex and nonsmooth convex function. The principle expense of this method is in computing a trial iterate that satisfies the so-called fraction of Cauchy decrease condition—a bound that ensures the trial iterate produces sufficient decrease of the subproblem model. In this paper, we expound on various proximal trust-region subproblem solvers that generalize traditional trust-region methods for smooth unconstrained and convex-constrained problems. We introduce a simplified spectral proximal gradient solver, a truncated nonlinear conjugate gradient solver, and a dogleg method. Finally, we compare algorithm performance on examples from data science and PDE-constrained optimization.

97 MATHEMATICS AND COMPUTING↗