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At least 523 records · Page 29

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DOE OSTI2026

Spatiotemporal control of laser intensity using differentiable programming

Optical techniques for spatiotemporal control can produce laser pulses with custom amplitude, phase, or polarization structure. In nonlinear optics and plasma physics, the use of structured pulses typically follows a forward design approach, in which the efficacy of a known structure is analyzed for a particular application. Inverse approaches, in contrast, enable the discovery of new structures with the potential for superior performance. Here, an implementation of the unidirectional pulse propagation equation that supports automatic differentiation is combined with gradient-based optimization to design structured pulses with features that are advantageous for a range of nonlinear optical and plasma-based applications: (1) a longitudinally uniform intensity over an extended region, (2) a superluminal intensity peak that travels many Rayleigh ranges with constant duration, spot size, and amplitude, and (3) a laser pulse that ionizes a gas to form a uniform column of plasma. In the final case, optimizing the full spatiotemporal structure improves the performance by a factor of 15 compared to optimizing only spatial or only temporal structure, highlighting the advantage of spatiotemporal control.

automatic differentiation↗

NASA NTRS1991

An active set algorithm for tracing parametrized optima

Optimization problems often depend on parameters that define constraints or objective functions. It is often necessary to know the effect of a change in a parameter on the optimum solution. An algorithm is presented here for tracking paths of optimal solutions of inequality constrained nonlinear programming problems as a function of a parameter. The proposed algorithm employs homotopy zero-curve tracing techniques to track segments where the set of active constraints is unchanged. The transition between segments is handled by considering all possible sets of active constraints and eliminating nonoptimal ones based on the signs of the Lagrange multipliers and the derivatives of the optimal solutions with respect to the parameter. A spring-mass problem is used to illustrate all possible kinds of transition events, and the algorithm is applied to a well-known ten-bar truss structural optimization problem.

Rakowska, J.↗

NASA NTRS1993

Neighboring suboptimal control for vehicle guidance

The neighboring optimal feedback control law is developed for systems with a piecewise linear control for the case where the optimal control is obtained by nonlinear programming techniques. To develop the control perturbation for a given deviation from the nominal path, the second variation is minimized subject to the constraint that the final conditions be satisfied (neighboring suboptimal control). This process leads to a feedback relationship between the control perturbation and the measured deviation from the nominal state. Neighboring suboptimal control is applied to the lunar launch problem. Two approaches, single optimization and multiple optimization for calculating the gains are used, and the gains are tested in a guidance simulation with a mismatch in the acceleration of gravity. Both approaches give acceptable results, but multiple optimization keeps the perturbed path closer to the nominal path.

Hull, David G.↗

NASA NTRS1993

Neighboring suboptimal control for vehicle guidance

The neighboring optimal feedback control law is developed for systems with a piecewise linear control for the case where the optimal control is obtained by nonlinear programming techniques. To develop the control perturbation for a given deviation from the nominal path, the second variation is minimized subject to the constraint that the final conditions be satisfied (neighboring suboptimal control). This process leads to a feedback relationship between the control perturbation and the measured deviation from the nominal state. Neighboring suboptimal control is applied to the lunar launch problem. Two approaches, single optimization and multiple optimization, for calculating the gains are used, and the gains are tested in a guidance simulation with a mismatch in the acceleration of gravity. Both approaches give acceptable results, but multiple optimization keeps the perturbed path closer to the nominal path.

Hull, David G.↗

NASA NTRS2018

Instability Wave–Streak Interactions in a High Mach Number Boundary Layer at Flight Conditions

The interaction of stationary streaks undergoing nonmodal growth with modally unstable instability waves in a hypersonic boundary-layer flow is studied using numerical computations. The geometry and flow conditions are selected to match a relevant trajectory location from the ascent phase of the HIFiRE-1 flight experiment; namely, a 7 degree half-angle, circular cone with 2.5 mm nose radius, freestream Mach number equal to 5.30, unit Reynolds number equal to 13.42 m -1 , and wall-to-adiabatic temperature ratio of approximately 0.35 over most of the vehicle. This paper investigates the nonlinear evolution of initially linear optimal disturbances that evolve into finite-amplitude streaks, followed by an analysis of the modal instability characteristics of the perturbed, streaky boundary-layer flow. The investigation is performed with stationary direct numerical simulations (DNS) and plane-marching parabolized stability equations (PSE), in conjunction with partial-differential-equation-based planar eigenvalue analysis. The overall effect of streaks is to reduce the peak amplification factors of instability waves, indicating a possible downstream shift in the onset of laminar-turbulent transition. The present study confirms previous findings that the mean flow distortion of the nonlinear streak perturbation reduces the amplification rates of the Mack-mode instability. More importantly, however, the present results demonstrate that the spanwise varying component of the streak can produce a larger effect on the Mack-mode amplification. The study with selected azimuthal wavenumbers for the stationary streaks reveals that a wavenumber of approximately 1.4 times larger than the optimal wavenumber is more effective in stabilizing the planar Mack-mode instabilities. In the absence of unstable first-mode waves for the present cold-wall condition, transition onset is expected to be delayed until the peak streak amplitude increases to nearly 35 percent of the freestream velocity, when intrinsic instabilities of the boundary-layer streaks begin to dominate the transition process. For streak amplitudes below that limit a significant net stabilization is achieved, yielding a potential transition delay that can exceed 100 percent of the length of the laminar region in the uncontrolled case.

Boundary layer stability↗

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 NTRS1993

Multidisciplinary optimization of a controlled space structure using 150 design variables

A controls-structures interaction design method is presented. The method coordinates standard finite-element structural analysis, multivariable controls, and nonlinear programming codes and allows simultaneous optimization of the structure and control system of a spacecraft. Global sensitivity equations are used to account for coupling between the disciplines. Use of global sensitivity equations helps solve optimization problems that have a large number of design variables and a high degree of coupling between disciplines. The preliminary design of a generic geostationary platform is used to demonstrate the multidisciplinary optimization method. Design problems using 15, 63, and 150 design variables to optimize truss member sizes and feedback gain values are solved and the results are presented. The goal is to reduce the total mass of the structure and the vibration control system while satisfying constraints on vibration decay rate. Incorporation of the nonnegligible mass of actuators causes an essential coupling between structural design variables and control design variables.

James, Benjamin B.↗

NASA NTRS1995

Active control of panel vibrations induced by a boundary layer flow

The problems of active and passive control of sound and vibration has been investigated by many researchers for a number of years. However, few of the articles are concerned with the sound and vibration with flow-structure interaction. Experimental and numerical studies on the coupling between panel vibration and acoustic radiation due to flow excitation have been done by Maestrello and his associates at NASA/Langley Research Center. Since the coupled system of nonlinear partial differential equations is formidable, an analytical solution to the full problem seems impossible. For this reason, we have to simplify the problem to that of the nonlinear panel vibration induced by a uniform flow or a boundary-layer flow with a given wall pressure distribution. Based on this simplified model, we have been able to consider the control and stabilization of the nonlinear panel vibration, which have not been treated satisfactorily by other authors. Although the sound radiation has not been included, the vibration suppression will clearly reduce the sound radiation power from the panel. The major research findings are presented in three sections. In section two we describe results on the boundary control of nonlinear panel vibration, with or without flow excitation. Sections three and four are concerned with some analytical and numerical results in the optimal control of the linear and nonlinear panel vibrations, respectively, excited by the flow pressure fluctuations. Finally, in section five, we draw some conclusions from research findings.

Chow, Pao-Liu↗

NASA NTRS2004

A Resonator for Low-Threshold Frequency Conversion

A proposed toroidal or disklike dielectric optical resonator (dielectric optical cavity) would be made of an optically nonlinear material and would be optimized for use in parametric frequency conversion by imposition of a spatially periodic permanent electric polarization. The poling (see figure) would suppress dispersions caused by both the material and the geometry of the optical cavity, thereby effecting quasi-matching of the phases of high-resonance-quality (high-Q) whispering-gallery electromagnetic modes. The quasi-phase-matching of the modes would serve to maximize the interactions among them. Such a resonator might be a prototype of a family of compact, efficient nonlinear devices for operation over a broad range of optical wavelengths. A little background information is prerequisite to a meaningful description of this proposal: (1) Described in several prior NASA Tech Briefs articles, the whispering-gallery modes in a component of spheroidal, disklike, or toroidal shape are waveguide modes that propagate circumferentially and are concentrated in a narrow toroidal region centered on the equatorial plane and located near the outermost edge. (2) For the sake of completeness, it must be stated that even though optical resonators of the type considered here are solid dielectric objects and light is confined within them by total internal reflection at dielectric interfaces without need for mirrors, such components are sometimes traditionally called cavities because their effects upon the light propagating within them are similar to those of true cavities bounded by mirrors. (3) For a given set of electromagnetic modes interacting with each other in an optically nonlinear material (e.g., modes associated with the frequencies involved in a frequency-conversion scheme), the threshold power for oscillation depends on the mode volumes and the mode-overlap integral. (4) Whispering-gallery modes are attractive in nonlinear optics because they maximize the effects of nonlinearities by occupying small volumes and affording high Q values

Iltchenko, Vladimir↗

DOE OSTI2026

Economic NMPC for a Reversible Solid Oxide Cell

Reversible solid oxide fuel cells (rSOCs) offer the flexibility to operate in tandem with the electric grid by switching between fuel cell and electrolysis modes based on real-time electricity prices. However, their complex, tightly coupled dynamic behavior poses significant challenges in determining optimal operating strategies. In this work, we present an economic nonlinear model predictive control (E-NMPC) framework to optimize the operation of rSOCs. The proposed E-NMPC is applied to a detailed rSOC flowsheet model that includes a utility scale rSOC module as well as balance-of-plant equipment necessary for thermal management. Our results demonstrate that in fuel cell mode, the E-NMPC strategy reduces hydrogen consumption compared to conventional set-point tracking NMPC, while maintaining the same level of electricity output. Also, in electrolysis mode, the E-NMPC yields a marginal improvement in hydrogen production. In addition, we explore the integration of a battery with the rSOC system to enhance flexibility in meeting electricity production and consumption targets.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2025

Tandem neural network-based controller for x-ray bimorph mirrors

Nanometer-scale shape control of x-ray mirrors is crucial for coherent x-ray beam experiments at low-emittance synchrotron beamline instruments. Piezoelectric bimorph mirrors offer adaptive control but are hindered by nonlinearities such as cross talk, creep, and hysteresis. To overcome these limitations, we present a novel feedback-free control solution, inspired by the proportional–integral–derivative (PID) scheme, driven by tandem neural networks (TNNs). Using task-specific datasets, the TNN-based system predicts actuator voltages with greater speed, accuracy, and stability than a single NN-based model. This approach is ideal for real-time applications, such as adapting beam focus to dynamic sample sizes while maintaining precise wavefront quality. Our findings highlight the potential of artificial intelligence in rapidly optimizing adaptive optics and managing nonlinear control systems.

Zhang, Runyu↗

NASA NTRS1991

Multidisciplinary optimization of controlled space structures with global sensitivity equations

A new method for the preliminary design of controlled space structures is presented. The method coordinates standard finite element structural analysis, multivariable controls, and nonlinear programming codes and allows simultaneous optimization of the structures and control systems of a spacecraft. Global sensitivity equations are a key feature of this method. The preliminary design of a generic geostationary platform is used to demonstrate the multidisciplinary optimization method. Fifteen design variables are used to optimize truss member sizes and feedback gain values. The goal is to reduce the total mass of the structure and the vibration control system while satisfying constraints on vibration decay rate. Incorporating the nonnegligible mass of actuators causes an essential coupling between structural design variables and control design variables. The solution of the demonstration problem is an important step toward a comprehensive preliminary design capability for structures and control systems. Use of global sensitivity equations helps solve optimization problems that have a large number of design variables and a high degree of coupling between disciplines.

Padula, Sharon L.↗

NASA NTRS1974

Optimum propellant usage for reaction jet systems of space vehicles

The on-off type control for reaction jet systems is proven to be the optimal fuel scheme. However, due to the nonlinear characteristics of this type control, no direct method of solution is known for this optimal process being applied to the attitude control of space vehicles. This paper will discuss the optimization of fuel usage for an attitude control of space vehicles. A computation technique is developed for the calculation of optimal control law. The method of calculus of variations is applied to the estimation of the changes of performance index as well as terminal constraints. Thus an algorithm is obtained by the steepest descent method. A numerical example is given in the paper.

Liu, T. C.↗

NASA NTRS1981

Application of constrained optimization to active control of aeroelastic response

Active control of aeroelastic response is a complex in which the designer usually tries to satisfy many criteria which are often conflicting. To further complicate the design problem, the state space equations describing this type of control problem are usually of high order, involving a large number of states to represent the flexible structure and unsteady aerodynamics. Control laws based on the standard Linear-Quadratic-Gaussian (LQG) method are of the same high order as the aeroelastic plant. To overcome this disadvantage of the LQG mode, an approach developed for designing low order optimal control laws which uses a nonlinear programming algorithm to search for the values of the control law variables that minimize a composite performance index, was extended to the constrained optimization problem. The method involves searching for the values of the control law variables that minimize a basic performance index while satisfying several inequality constraints that describe the design criteria. The method is applied to gust load alleviation of a drone aircraft.

Newsom, J. R.↗

NASA NTRS1993

Actuator tuning for nonlinear truss structures - A neural network approach

The optimal actuator placement problem encompasses finding their best locations and best gains. The latter is referred to as tuning the actuators. This paper deals with tuning a given set of actuators in presence of known structural nonlinearities arising from gaps at some joints. For this purpose, an efficient neural network-based algorithm is proposed and illustrated using numerical simulations.

Toomarian, N.↗

NASA NTRS1986

A general-purpose optimization program for engineering design

A new general-purpose optimization program for engineering design is described. ADS (Automated Design Synthesis) is a FORTRAN program for nonlinear constrained (or unconstrained) function minimization. The optimization process is segmented into three levels: Strategy, Optimizer, and One-dimensional search. At each level, several options are available so that a total of nearly 100 possible combinations can be created. An example of available combinations is the Augmented Lagrange Multiplier method, using the BFGS variable metric unconstrained minimization together with polynomial interpolation for the one-dimensional search.

Vanderplaats, G. N.↗

DOE OSTI2026

Relaxations of the steady optimal gas flow problem for a non-Ideal gas

Natural gas ranks second in U.S. primary energy consumption. Because most production sites are remote, gas must be transported through pipeline networks equipped with compressors, valves, and other components. For both economic efficiency and system reliability, it is desirable to operate these networks optimally. The governing physics across pipeline components entails nonlinear, non-convex equality and inequality constraints, and the most general steady-flow operations problem is a Mixed-Integer Nonlinear Program (MINLP).This work focuses on one such steady-flow problem-the Optimal Gas Flow (OGF) for a natural gas pipeline network-which minimizes production cost subject to the steady-flow physics. For day-to-day operations, the ability to quickly compute a globally optimal solution and a strong lower bound for varying demand profiles is crucial. A promising strategy is to build tight relaxations of the OGF’s nonlinear constraints. However, many nonlinearities arising from non-ideal equations of state either lack relaxations or have relaxations that do not scale to realistic network sizes. We address this gap by combining recent advances in polyhedral relaxations for univariate functions to construct tight, computationally efficient relaxations of the OGF with a non-ideal equation of state. These relaxations solve within seconds on a standard laptop. In conclusion, we demonstrate their quality through extensive numerical experiments on very large-scale test networks from the literature and find that the proposed approach proves optimality in 92% of tested instances.

03 NATURAL GAS↗

DOE OSTI2026

A Flexible Quasi-Static Mooring Design Optimization Method for Floating Structures

This paper presents a flexible and efficient design method for optimizing the mooring systems of floating structures. Mooring system optimization is challenging because of the strong nonlinearity of mooring system behavior and the many technical constraints that must be satisfied. Furthermore, different mooring configurations can have very different design spaces. While some successful examples of mooring design optimization exist in the literature, developing an optimization approach that can work across various mooring design problems is a larger challenge. We present such a method based on a flexible parameterization that allows a wide variety of mooring designs to be described by a list of variables, a quasi-static mooring model that provides efficient evaluation of a mooring design without directly considering mooring system dynamics, and an optimization framework that generates, evaluates, and adjusts the mooring design while considering user-specified constraints such as offset limits, strength safety factors, and seabed contact limits. We demonstrate the design optimization framework on four mooring design problems, each for a different type of mooring system. We compare the use of different design modes to simplify the optimization problem, showing that they can reduce the computation time by up to 75%. We also compare different optimization algorithms and find that the resulting computational speed can vary by up to 51 times. We perform a sensitivity study on one design and find that the local sensitivity of anchoring radius to water depth has a positive correlation of 0.29, but the global sensitivity shows large nonlinearities. Lastly, we perform a coupled dynamic analysis on one of the optimized designs and find that the predicted mean platform motions and mooring line tensions are within 1% of dynamic results and the extreme motions and tensions are within 14%. Lastly, we show that a DEA-Chain-Polyester mooring configuration is cost-optimal for the given design problem of the demonstrations, which aligns with general industry practice.

16 TIDAL AND WAVE POWER↗