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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 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Structure-aware Initialization via Numerical Continuation and Informed Priors

Scientific machine learning (SciML) often operates in ill-conditioned, weakly identifiable regimes due to limited data or indirect observations. In such settings, optimization and inference are highly sensitive to the starting point, making initialization--often under-reported--a consequential degree of freedom. Random initialization is not a neutral default as it induces an implicit prior over candidate solutions and can systematically bias the result, producing large run-to-run variability. Here, we formalize this view by treating initialization as a hidden confounder in SciML and develop a unifying theory for structure-aware initialization via numerical continuation, constructing warm starts from related problem instances. Across representative tasks, including physics-informed neural networks, maximum likelihood estimation, and variational inference, warm starts have been shown to consistently reduce optimization effort and improve reliability.

Data integrity↗
NASA NTRS2014

Bifurcation Analysis Using Rigorous Branch and Bound Methods

For the study of nonlinear dynamic systems, it is important to locate the equilibria and bifurcations occurring within a specified computational domain. This paper proposes a new approach for solving these problems and compares it to the numerical continuation method. The new approach is based upon branch and bound and utilizes rigorous enclosure techniques to yield outer bounding sets of both the equilibrium and local bifurcation manifolds. These sets, which comprise the union of hyper-rectangles, can be made to be as tight as desired. Sufficient conditions for the existence of equilibrium and bifurcation points taking the form of algebraic inequality constraints in the state-parameter space are used to calculate their enclosures directly. The enclosures for the bifurcation sets can be computed independently of the equilibrium manifold, and are guaranteed to contain all solutions within the computational domain. A further advantage of this method is the ability to compute a near-maximally sized hyper-rectangle of high dimension centered at a fixed parameter-state point whose elements are guaranteed to exclude all bifurcation points. This hyper-rectangle, which requires a global description of the bifurcation manifold within the computational domain, cannot be obtained otherwise. A test case, based on the dynamics of a UAV subject to uncertain center of gravity location, is used to illustrate the efficacy of the method by comparing it with numerical continuation and to evaluate its computational complexity.

Smith, Andrew P.↗
DOE OSTI2023

Spatially quasi-periodic bifurcations from periodic traveling water waves and a method for detecting bifurcations using signed singular values

We present a method of detecting bifurcations by locating zeros of a signed version of the smallest singular value of the Jacobian. This enables the use of quadratically convergent root-bracketing techniques or Chebyshev interpolation to locate bifurcation points. Only positive singular values have to be computed, though the method relies on the existence of an analytic or smooth singular value decomposition (SVD). The sign of the determinant of the Jacobian, computed as part of the bidiagonal reduction in the SVD algorithm, eliminates slope discontinuities at the zeros of the smallest singular value. We use the method to search for spatially quasi-periodic traveling water waves that bifurcate from large-amplitude periodic waves. The water wave equations are formulated in a conformal mapping framework to facilitate the computation of the quasi-periodic Dirichlet-Neumann operator. We find examples of pure gravity waves with zero surface tension and overhanging gravity-capillary waves. In both cases, the waves have two spatial quasi-periods whose ratio is irrational. We follow the secondary branches via numerical continuation beyond the realm of linearization about solutions on the primary branch to obtain traveling water waves that extend over the real line with no two crests or troughs of exactly the same shape. The pure gravity wave problem is of relevance to ocean waves, where capillary effects can be neglected. Such waves can only exist through secondary bifurcation as they do not persist to zero amplitude. The gravity-capillary wave problem demonstrates the effectiveness of using the signed smallest singular value as a test function for multi-parameter bifurcation problems. This test function becomes mesh independent once the mesh is fine enough.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1975

A two parameter survey of periodic orbits in the restricted problem of three bodies

Within the context of the restricted problem of three bodies the effects caused by varying the mass ratio of the primaries and the eccentricity of their orbits, upon periodic orbits of the infinitesimal mass which are numerical continuations of circular orbits in the ordinary problem of two bodies are shown. A recursive power series technique is used to numerically integrate the equations of motion as well as the first variational equations in order to generate a two parameter family of perodic orbits and identify the linear stability characteristics. Seven such families are investigated with equally spaced mass ratios from 0.0 to 1.0 and eccentricities of the orbits of the primaries in a range 0.0 to 0.6. Stable orbits are associated with large distances of the infinitesimal mass from the perturbing primary, nearly circular motion of the primaries, and small mass ratios of the primaries. Unstable orbits for the infinitesimal mass are associated with small distances from the perturbing primary, highly elliptic orbits of the primaries and large mass ratios.

Shelus, P. J.↗
NASA NTRS1990

Bifurcations and sensitivity in parametric nonlinear programming

The parametric nonlinear programming problem is that of determining the behavior of solution(s) as a parameter or vector of parameters alpha belonging to R(sup r) varies over a region of interest for the problem: Minimize over x the set f(x, alpha):h(x, alpha) = 0, g(x, alpha) is greater than or equal to 0, where f:R(sup (n+r)) approaches R, h:R(sup (n+r)) approaches R(sup q) and g:R(sup (n+r)) approaches R(sup p) are assumed to be at least twice continuously differentiable. Some of these parameters may be fixed but not known precisely and others may be varied to enhance the performance of the system. In both cases a fundamentally important problem in the investigation of global sensitivity of the system is to determine the stability boundaries of the regions in parameter space which define regions of qualitatively similar solutions. The objective is to explain how numerical continuation and bifurcation techniques can be used to investigate the parametric nonlinear programming problem in a global sense. Thus, first the problem is converted to a closed system of parameterized nonlinear equations whose solution set contains all local minimizers of the original problem. This system, which will be represented as F(z,alpha) = O, will include all Karush-Kuhn-Tucker and Fritz John points, both feasible and infeasible solutions, and relative minima, maxima, and saddle points of the problem. The local existence and uniqueness of a solution path (z(alpha), alpha) of this system as well as the solution type persist as long as a singularity in the Jacobian D(sub z)F(z,alpha) is not encountered. Thus the nonsingularity of this Jacobian is characterized in terms of conditions on the problem itself. Then, a class of efficient predictor-corrector continuation procedures for tracing solution paths of the system F(z,alpha) = O which are tailored specifically to the parametric programming problem are described. Finally, these procedures and the obtained information are illustrated within the context of design optimization.

Lundberg, Bruce N.↗
DOE OSTI2023

Method for simultaneous characterization and expansion of reference libraries for small molecule identification

A variational autoencoder (VAE) has been developed to learn a continuous numerical, or latent, representation of molecular structure to expand reference libraries for small molecule identification. The VAE has been extended to include a chemical property decoder, trained as a multitask network, to shape the latent representation such that it assembles according to desired chemical properties. The approach is unique in its application to metabolomics and small molecule identification, focused on properties that are obtained from experimental measurements (m/z, CCS) paired with its training paradigm, which involves a cascade of transfer learning iterations. First, molecular representation is learned from a large dataset of structures with m/z labels. Next, in silico property values are used to continue training. Finally, the network is further refined by being trained with the experimental data. The trained network is used to predict chemical properties directly from structure and generate candidate structures with desired chemical properties. The network is extensible to other training data and molecular representations, and for use with other analytical platforms, for both chemical property and feature prediction as well as molecular structure generation.

Colby, Sean M.↗
DOE OSTI2024

Large-scale harmonic balance simulations with Krylov subspace and preconditioner recycling

The multi-harmonic balance method combined with numerical continuation provides an efficient framework to compute a family of time-periodic solutions, or response curves, for large-scale, nonlinear mechanical systems. The predictor and corrector steps repeatedly solve a sequence of linear systems that scale by the model size and number of harmonics in the assumed Fourier series approximation. In this paper, a novel Newton–Krylov iterative method is embedded within the multi-harmonic balance and continuation algorithm to efficiently compute the approximate solutions from the sequence of linear systems that arise during the prediction and correction steps. Further, the method recycles, or reuses, both the preconditioner and the Krylov subspace generated by previous linear systems in the solution sequence. A delayed frequency preconditioner refactorizes the preconditioner only when the performance of the iterative solver deteriorates. The GCRO-DR iterative solver recycles a subset of harmonic Ritz vectors to initialize the solution subspace for the next linear system in the sequence. The performance of the iterative solver is demonstrated on two exemplars with contact-type nonlinearities and benchmarked against a direct solver with traditional Newton–Raphson iterations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

A numerical approach for detecting switch-like bistability in mass action chemical reaction networks with conservation laws

Theoretical analysis of signaling pathways can provide a substantial amount of insight into their function. One particular area of research considers signaling pathways capable of assuming two or more stable states given the same amount of signaling ligand. This phenomenon of bistability can give rise to switch-like behavior, a mechanism that governs cellular decision making. Investigation of whether or not a signaling pathway can confer bistability and switch-like behavior, without knowledge of specific kinetic rate constant values, is a mathematically challenging problem. Recently a technique based on optimization has been introduced, which is capable of finding example parameter values that confer switch-like behavior for a given pathway. Although this approach has made it possible to analyze moderately sized pathways, it is limited to reaction networks that presume a uniterminal structure. It is this limited structure we address by developing a general technique that applies to any mass action reaction network with conservation laws. In this paper we developed a generalized method for detecting switch-like bistable behavior in any mass action reaction network with conservation laws. The method involves (1) construction of a constrained optimization problem using the determinant of the Jacobian of the underlying rate equations, (2) minimization of the objective function to search for conditions resulting in a zero eigenvalue, (3) computation of a confidence level that describes if the global minimum has been found and (4) evaluation of optimization values, using either numerical continuation or directly simulating the ODE system, to verify that a bistability region exists. The generalized method has been tested on three motifs known to be capable of bistability. We have developed a variation of an optimization-based method for the discovery of bistability, which is not limited to uniterminal chemical reaction networks. Successful completion of the method provides an S-shaped bifurcation diagram, which indicates that the network acts as a bistable switch for the given optimization parameters.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1978

Flow field visualization about external axial corners

An experimental investigation was conducted to visualize the flow field about external axial corners. The investigation was initiated to provide answers to questions about the inviscid flow pattern for continuing numerical investigations. Symmetrical and asymmetrical corner models were tested at a Reynolds number per meter of 60,700,000. Oil-flow and vapor-screen photographs were taken for both models at angle of attack and yaw. The paper presents the results of the investigation in the form of oil-flow photographs and the surrounding shock wave location obtained from the vapor screens.

Talcott, N. A., Jr.↗
NASA NTRS1982

Periodic orbits of the elliptic restricted problem for the Sun-Jupiter-Saturn system

A systematic approach to generate periodic orbits in the elliptic restricted problem of three bodies is introduced. The approach is based on (numerical) continuation from periodic orbits of the first and second kind in the circular restricted problem to periodic orbits in the elliptic restricted problem. Two families of periodic orbits of the elliptic restricted problem are found by this approach. The mass ratio of the primaries of these orbits is equal to that of the Sun-Jupiter system. The sidereal mean motions between the infinitesimal body and the smaller primary are in a 2:5 resonance, so as to approximate the Sun-Jupiter-Saturn system. The lineaar stabilities of these periodic orbits are studied as functions of the eccentricities of the primaries and of the infinitesimal body. The results show that both stable and unstable periodic orbits exist in the elliptic restricted problem that are close to the actual Sun-Jupiter-Saturn system. However, the periodic orbit closest to the actual Sun-Jupiter-Saturn system is (linearly) stable.

Kwok, J. H.↗
NASA NTRS1985

Periodic orbits of the general three-body problem for the sun-Jupiter-Saturn system

Two families of symmetric periodic orbits of the planar, general, three-body problem are presented. The masses of the three bodies include ratios equal to the sun-Jupiter-Saturn system and the periods of the orbits of Jupiter and Saturn are in a 2:5 resonance. The (linear) stability of the orbits are studied in relation to eccentricity and mass variations. The generation of the two families of periodic orbits follows a systematic approach and employs (numerical) continuation from periodic orbits of the first and second kind in the circular restricted problem to the elliptic restricted problem and from the circular and elliptic problems to the general problem through bifurcation phenomena relating the three dynamical systems. The approach also provides insight into the evolutionary process of periodic orbits continued from the restricted problems to the general problem.

Kwok, J. H.↗
NASA NTRS1993

Multi-layered reasoning by means of conceptual fuzzy sets

The real world consists of a very large number of instances of events and continuous numeric values. On the other hand, people represent and process their knowledge in terms of abstracted concepts derived from generalization of these instances and numeric values. Logic based paradigms for knowledge representation use symbolic processing both for concept representation and inference. Their underlying assumption is that a concept can be defined precisely. However, as this assumption hardly holds for natural concepts, it follows that symbolic processing cannot deal with such concepts. Thus symbolic processing has essential problems from a practical point of view of applications in the real world. In contrast, fuzzy set theory can be viewed as a stronger and more practical notation than formal, logic based theories because it supports both symbolic processing and numeric processing, connecting the logic based world and the real world. In this paper, we propose multi-layered reasoning by using conceptual fuzzy sets (CFS). The general characteristics of CFS are discussed along with upper layer supervision and context dependent processing.

Takagi, Tomohiro↗
NASA NTRS2006

Uncertainty Analysis for a Jet Flap Airfoil

An analysis of variance (ANOVA) study was performed to quantify the potential uncertainties of lift and pitching moment coefficient calculations from a computational fluid dynamics code, relative to an experiment, for a jet flap airfoil configuration. Uncertainties due to a number of factors including grid density, angle of attack and jet flap blowing coefficient were examined. The ANOVA software produced a numerical model of the input coefficient data, as functions of the selected factors, to a user-specified order (linear, 2-factor interference, quadratic, or cubic). Residuals between the model and actual data were also produced at each of the input conditions, and uncertainty confidence intervals (in the form of Least Significant Differences or LSD) for experimental, computational, and combined experimental / computational data sets were computed. The LSD bars indicate the smallest resolvable differences in the functional values (lift or pitching moment coefficient) attributable solely to changes in independent variable, given just the input data points from selected data sets. The software also provided a collection of diagnostics which evaluate the suitability of the input data set for use within the ANOVA process, and which examine the behavior of the resultant data, possibly suggesting transformations which should be applied to the data to reduce the LSD. The results illustrate some of the key features of, and results from, the uncertainty analysis studies, including the use of both numerical (continuous) and categorical (discrete) factors, the effects of the number and range of the input data points, and the effects of the number of factors considered simultaneously.

Green, Lawrence L.↗
NASA NTRS1989

Experimental and numerical investigation of an oblique shock wave/turbulent boundary layer interaction with continuous suction

An numerical and experimental investigation has been conducted into the interaction of an incident oblique shock wave with a turbulent boundary layer, for the cases of a rough plate and a porous plate with suction, at a nominal Mach number of 2.5 and flow deflection angles of 0, 4, 6, and 8 deg. Attention is given to the pitot pressure profiles, wall static pressures, and porous plate local bleed distributions measured for the two plates. Suction is found to increase the strength of the incident shock required to separate the boundary layer; for all shock strengths tested, separation is completely eliminated.

Benhachmi, Driss↗
DOE OSTI2021

Automatically adaptive stabilized finite elements and continuation analysis for compaction banding in geomaterials

Under compressive creep, viscoplastic solids experiencing internal mass transfer processes can accommodate singular cnoidal wave solutions as material instabilities at the stationary wave limit. These instabilities appear when the loading rate is significantly faster than the material's capacity to diffusive internal perturbations, leading to localized failure features (e.g., cracks and compaction bands). These cnoidal waves, generally found in fluids, have strong nonlinearities that produce periodic patterns. Due to the singular nature of the solutions, the applicability of the theory is currently limited. Additionally, practical simulation tools require proper regularization to overcome the challenges that singularity induces. We focus on the numerical treatment of the governing equation using a nonlinear approach building on a recent adaptive stabilized finite element method. This automatic refinement method provides an error estimate that drives mesh adaptivity, a crucial feature for the problem at hand. We compare the performance of this adaptive strategy against analytical and standard finite element solutions. We then investigate the sensitivity of the diffusivity ratio, the parameter controlling the process, and identify multiple possible solutions with several stress peaks. We also show the evolution of the spacing between peaks for all solutions as a function of that parameter.

42 ENGINEERING↗
NASA NTRS2015

Numerical Computation of a Continuous-thrust State Transition Matrix Incorporating Accurate Hardware and Ephemeris Models

A significant body of work exists showing that providing a nonlinear programming (NLP) solver with expressions for the problem constraint gradient substantially increases the speed of program execution and can also improve the robustness of convergence, especially for local optimizers. Calculation of these derivatives is often accomplished through the computation of spacecraft's state transition matrix (STM). If the two-body gravitational model is employed as is often done in the context of preliminary design, closed form expressions for these derivatives may be provided. If a high fidelity dynamics model, that might include perturbing forces such as the gravitational effect from multiple third bodies and solar radiation pressure is used then these STM's must be computed numerically. We present a method for the power hardward model and a full ephemeris model. An adaptive-step embedded eight order Dormand-Prince numerical integrator is discussed and a method for the computation of the time of flight derivatives in this framework is presented. The use of these numerically calculated derivatieves offer a substantial improvement over finite differencing in the context of a global optimizer. Specifically the inclusion of these STM's into the low thrust missiondesign tool chain in use at NASA Goddard Spaceflight Center allows for an increased preliminary mission design cadence.

Low Thrust↗