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DOE OSTI2025

Generative learning for slow manifolds and bifurcation diagrams

In dynamical systems characterized by separation of time scales, the approximation of so called “slow manifolds”, on which the long term dynamics lie, is a useful step for model reduction. Initializing on such slow manifolds is a useful step in modeling, since it circumvents fast transients, and is crucial in multiscale algorithms (like the equation-free approach) alternating between fine scale (fast) and coarser scale (slow) simulations. In a similar spirit, when one studies the infinite time dynamics of systems depending on parameters, the system attractors (e.g., its steady states) lie on bifurcation diagrams (curves for one-parameter continuation, and more generally, on manifolds in state parameter space. Sampling these manifolds gives us representative attractors (here, steady states of ODEs or PDEs) at different parameter values. Algorithms for the systematic construction of these manifolds (slow manifolds, bifurcation diagrams) are required parts of the “traditional” numerical nonlinear dynamics toolkit. In more recent years, as the field of Machine Learning develops, conditional score-based generative models (cSGMs) have been demonstrated to exhibit remarkable capabilities in generating plausible data from target distributions that are conditioned on some given label. It is tempting to exploit such generative models to produce samples of data distributions (points on a slow manifold, steady states on a bifurcation surface) conditioned on (consistent with) some quantity of interest (QoI, observable). In this work, we present a framework for using cSGMs to quickly (a) initialize on a low-dimensional (reduced-order) slow manifold of a multi-time-scale system consistent with desired value(s) of a QoI (a “label”) on the manifold, and (b) approximate steady states in a bifurcation diagram consistent with a (new, out-of-sample) parameter value. This conditional sampling can help uncover the geometry of the reduced slow-manifold and/or approximately “fill in” missing segments of steady states in a bifurcation diagram. Finally, the quantity of interest, which determines how the sampling is conditioned, is either known a priori or identified using manifold learning-based dimensionality reduction techniques applied to the training data.

Dynamical systems↗

NASA NTRS1931

A Method for Reducing the Temperature of Exhaust Manifolds

This report describes tests conducted at the Langley Memorial Aeronautical Laboratory on an "air-inducting" exhaust manifold for aircraft engines. The exhaust gases from each cylinder port are discharged into the throat of an exhaust pipe which has a frontal bellmouth. Cooling air is drawn into the pipe, where it surrounds and mixes with the exhaust gases. Temperatures of the manifold shell and of the exhaust gases were obtained in flight for both a conventional manifold and the air-inducting manifold. The air-inducting manifold was installed on an engine which was placed on a test stand. Different fuels were sprayed on and into the manifold to determine whether the use of this manifold reduced the fire hazard. The flight tests showed reductions in manifold temperatures of several hundred degrees, to values below the ignition point of aviation gasoline. On the test stand when the engine was run at idling speeds fuels sprayed into the manifold ignited. It is believed that at low engine speeds the fuel remained in the manifold long enough to become thoroughly heated, and was then ignited by the exhaust gas which had not mixed with cooling air. The use of the air-inducting exhaust manifold must reduce the fire hazard by virtue of its lower operating temperature, but it is not a completely satisfactory solution of the problem.

Schey, Oscar W↗

NASA NTRS2011

Failure Investigation of an Intra-Manifold Explosion in a Horizontally-Mounted 870 lbf Reaction Control Thruster

In June 2010, an 870 lbf Space Shuttle Orbiter Reaction Control System Primary Thruster experienced an unintended shutdown during a test being performed at the NASA White Sands Test Facility. Subsequent removal and inspection of the thruster revealed permanent deformation and misalignment of the thruster valve mounting plate. Destructive evaluation determined that after three nominal firing sequences, the thruster had experienced an energetic event within the fuel (monomethylhydrazine) manifold at the start of the fourth firing sequence. The current understanding of the phenomenon of intra-manifold explosions in hypergolic bipropellant thrusters is documented in literature where it is colloquially referred to as a ZOT. The typical ZOT scenario involves operation of a thruster in a gravitational field with environmental pressures above the triple point pressure of the propellants. Post-firing, when the thruster valves are commanded closed, there remains a residual quantity of propellant in both the fuel and oxidizer (nitrogen tetroxide) injector manifolds known as the "dribble volume". In an ambient ground test configuration, these propellant volumes will drain from the injector manifolds but are impeded by the local atmospheric pressure. The evacuation of propellants from the thruster injector manifolds relies on the fluids vapor pressure to expel the liquid. The higher vapor pressure oxidizer will evacuate from the manifold before the lower vapor pressure fuel. The localized cooling resulting from the oxidizer boiling during manifold draining can result in fuel vapor migration and condensation in the oxidizer passage. The liquid fuel will then react with the oxidizer that enters the manifold during the next firing and may produce a localized high pressure reaction or explosion within the confines of the oxidizer injector manifold. The typical ZOT scenario was considered during this failure investigation, but was ultimately ruled out as a cause of the explosion. Converse to the typical ZOT failure mechanism, the failure of this particular thruster was determined to be the result of liquid oxidizer being present within the fuel manifold.

Durning, Joseph G., III↗

DOE OSTI2025

Low‐dimensional manifold learning for uncertainty quantification in complex multi‐scale stochastic systems

Broadly speaking, the goals of the project are to develop techniques to use manifold learning to develop reduced‐order and surrogate models for "hyper‐reduction" of very high‐dimensional complex multi‐scale systems. This is being achieved by employing a newly proposed form of manifold projection and learning that leverages recent advancements in computational geometry and data‐driven modeling. In particular, we are applying a manifold projection technique to project the solutions of very high‐dimensional systems onto the so‐called Grassmannmanifold, a Reimannian manifold comprised of orthonormal matrices. We then apply data‐driven machine learning techniques to classify the solutions on the manifold (e.g. clustering techniques) according to their proximity on the manifold and leverage a further nonlinear dimension reduction to organize the structured data on the manifold. Finally, we are developing novel techniques that enable us to directly interpolate the hyper‐reduced data such that we can predict the solution of the complex, high‐ dimensional system without need to call the full expensive computational model. Given their adherence to the underlying structure of the solution of the physical system, it is expected that these approximate solutions will be sufficiently constrained so as to (approximately) adhere to physical principles.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1972

Experimental study of flow distribution and pressure loss with circumferential inlet and outlet manifolds

Water flow tests with circumferential inlet and outlet manifolds were conducted to determine factors affecting fluid distribution and pressure losses. Various orifice sizes and manifold geometries were tested over a range of flow velocities. With inlet manifolds, flow distribution was related directly to orifice discharge coefficients. A correlation indicated that nonuniform distribution resulted when the velocity head ratio at the orifice was not in the range of constant discharge coefficient. With outlet manifolds, nonuniform flow was related to static pressure variations along the manifold. Outlet manifolds had appreciably greater pressure losses than comparable inlet manifolds.

Dittrich, R. T.↗

DOE OSTI2024

Tracking the topology of neural manifolds across populations

Neural manifolds summarize the intrinsic structure of the information encoded by a population of neurons. Advances in experimental techniques have made simultaneous recordings from multiple brain regions increasingly commonplace, raising the possibility of studying how these manifolds relate across populations. However, when the manifolds are nonlinear and possibly code for multiple unknown variables, it is challenging to extract robust and falsifiable information about their relationships. We introduce a framework, called the method of analogous cycles, for matching topological features of neural manifolds using only observed dissimilarity matrices within and between neural populations. We demonstrate via analysis of simulations and in vivo experimental data that this method can be used to correctly identify multiple shared circular coordinate systems across both stimuli and inferred neural manifolds. Conversely, the method rejects matching features that are not intrinsic to one of the systems. Further, as this method is deterministic and does not rely on dimensionality reduction or optimization methods, it is amenable to direct mathematical investigation and interpretation in terms of the underlying neural activity. We thus propose the method of analogous cycles as a suitable foundation for a theory of cross-population analysis via neural manifolds.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Porous mesh manifold for enhanced boiling performance

High-performance electronics are continuously demanding cooling of higher heat fluxes. Phase-change cooling, including pool boiling, is a useful approach to address this challenge; however, competition between liquid and vapor flows generally limit the heat fluxes that can be dissipated. A range of strategies to control these flows have been investigated previously, including capillary guides. Here a manifold structure formed from a metallic mesh is investigated to control the disposition of liquid and vapor phases above a pool fed boiling surface enhanced with porous structures. Copper mesh forms defined liquid flow paths, using capillary action to guide and distribute liquid evenly over the heated surface, along with open channels to facilitate vapor escape. The mesh provides a novel structure for liquid guidance that imposes low resistance to liquid flow while occluding a minimal area of heated surface underneath. The manifold performance is characterized in boiling fed by a pool of water above a laser-textured aluminum nitride heat dissipation surface with pin–fin structures having heights of 110 µm and spacing of 30 µm with a heated area of 5 mm x 5 mm. A maximum heat flux of 490 W/cm 2 is reached with the manifold in the pool fed configuration, representing an increase of more than 65% over the porous pin fin surface alone. The maximum stable superheat observed for the manifold of 36K is 14K higher than that for the porous surface without the manifold. The factors limiting performance of the manifold are analyzed. High superheat is attributed to partial flooding of the boiling surface as suggested by the reduction in superheat using external suction. Similar systems and structures for enhanced two-phase cooling are compared.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1986

Advanced Vapor-Supply Manifold

Advanced vapor-supply manifold solves problem of manifold purging. Design virtually eliminates dead gas volumes in manifold system. System incorporates special valve into manifold in way that leaks and contamination problems of previous systems, which use tees and three-port valves, are minimized or eliminated in both main manifold line and in supply line. Of considerable use in gas manifold systems where even small amounts of gaseous impurities constitute problem or where more than one gaseous material used in single system.

Clark, I. O.↗

DOE OSTI2025

Construction of 3D MHD pressure drop correlation and flow characterization in the contraction region of a fusion blanket manifold

Inlet and outlet manifolds are typical components of liquid metal (LM) blanket designs of a fusion power reactor to be used to distribute the LM flow into breeding channels and collect it at the exit of the blanket. High pressure loss in the magnetohydrodynamic (MHD) flows featuring abrupt geometrical changes is one of the main feasibility issues of such designs. Recently, optimization studies were conducted to construct 3D MHD pressure drop correlations for a LM flow in an electrically insulating manifold with gradual expansion. Here, the 3D computational approach developed in that study is applied to the outlet manifold featuring gradual contraction. A systematic analysis was performed with a total number of 135 flow cases computed with COMSOL Multiphysics for Hartmann numbers 1000 < Ha < 10,000, Reynolds numbers 100 < Re < 12,000, and contraction angles 45° < θ < 75° for a fixed contraction ratio of 4. The effects of Ha, Re and θ on the flow recirculation, development length and the total pressure drop were carefully examined. A linear regression analysis was used to determine the power rule of pressure drop coefficient k related to Ha and Re, demonstrating a good match with the Ludford layer theory. Eventually, a correlation for the 3D MHD pressure drop coefficient was constructed as a function of Ha, Re and θ. Further, the results were compared against the inlet manifold. It was found that the flow in the inlet manifold exhibits larger recirculation zones. In the investigated range of Ha, Re and θ, the pressure drop coefficient k of the LM MHD flow in the gradual contraction is only slightly lower (< 8 %) than that in the gradual expansion.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1991

MOCVD manifold switching effects on growth and characterization

A combined modeling and experimental approach is used to quantify the effects of various manifold components on the switching speed in metalorganic chemical vapor deposition (MOCVD). In particular, two alternative vent-run high-speed switching manifold designs suitable for either continuous or interrupted growth have been investigated. Both designs are incorporated in a common manifold, instrumented with a mass spectrometer. The experiments have been performed using nitrogen as the transport gas and argon as the simulated source gas. The advantages and limitations of two designs are discussed. It is found that while constant flow manifold switching systems may have fluid dynamic advantages, care must be taken to minimize sections of the supply manifold with low flow rates if rapid changes in alloy composition are required.

Clark, Ivan O.↗

NASA NTRS2005

The world problem: on the computability of the topology of 4-manifolds

Topological classification of the 4-manifolds bridges computation theory and physics. A proof of the undecidability of the homeomorphy problem for 4-manifolds is outlined here in a clarifying way. It is shown that an arbitrary Turing machine with an arbitrary input can be encoded into the topology of a 4-manifold, such that the 4-manifold is homeomorphic to a certain other 4-manifold if and only if the corresponding Turing machine halts on the associated input. Physical implications are briefly discussed.

vanMeter, J. R.↗

NASA NTRS2006

The role of invariant manifolds in lowthrust trajectory design (part III)

This paper is the third in a series to explore the role of invariant manifolds in the design of low thrust trajectories. In previous papers, we analyzed an impulsive thrust resonant gravity assist flyby trajectory to capture into Europa orbit using the invariant manifolds of unstable resonant periodic orbits and libration orbits. The energy savings provided by the gravity assist may be interpreted dynamically as the result of a finite number of intersecting invariant manifolds. In this paper we demonstrate that the same dynamics is at work for low thrust trajectories with resonant flybys and low energy capture. However, in this case, the flybys and capture are effected by continuous families of intersecting invariant manifolds.

low thrust trajectories↗

DOE OSTI2025

Link Scheduling in Satellite Networks via Machine Learning Over Riemannian Manifolds

Low Earth Orbit (LEO) satellites play a crucial role in enhancing global connectivity, serving a complementary solution to existing terrestrial systems. In wireless networks, scheduling is a vital process that allocates time-frequency resources to users for interference management. However, LEO satellite networks face significant challenges in scheduling their links towards ground users due to the satellites’ mobility and overlapping coverage. This paper addresses the dynamic link scheduling problem in LEO satellite networks by considering spatio-temporal correlations introduced by the satellites’ movements. The first step in the proposed solution involves modeling the network over Riemannian manifolds, thanks to their representation as symmetric positive definite matrices. We introduce two machine learning (ML)-based link scheduling techniques that model the dynamic evolution of satellite positions and link conditions over time and space. To accurately predict satellite link states, we present a recurrent neural network (RNN) over Riemannian manifolds, which captures spatio-temporal characteristics over time. Furthermore, we introduce a separate model, the convolutional neural network (CNN) over Riemannian manifolds, which captures geometric relationships between satellites and users by extracting spatial features from the network topology across all links. Simulation results demonstrate that both RNN and CNN over Riemannian manifolds deliver comparable performance to the fractional programming-based link scheduling (FPLinQ) benchmark. Remarkably, unlike other ML-based models that require extensive training data, both models only need 30 training samples to achieve over 99% of the sum rate while maintaining similar computational complexity relative to the benchmark.

42 ENGINEERING↗

NASA NTRS1972

Experimental study of flow distribution with circumferential manifolds

Water flow test results on fluid flow distribution and pressure loss in curved manifolds with tangential or radial entry are reported. Manifolds were studied both as inlet and outlet manifolds. Manifolds can be used for boilers and/or heat exchangers for advanced space electric power plants.

Dittrich, R. T.↗

NASA NTRS1975

Fluid manifold design for a solar energy storage tank

A design technique for a fluid manifold for use in a solar energy storage tank is given. This analytical treatment generalizes the fluid equations pertinent to manifold design, giving manifold pressures, velocities, and orifice pressure differentials in terms of appropriate fluid and manifold geometry parameters. Experimental results used to corroborate analytical predictions are presented. These data indicate that variations in discharge coefficients due to variations in orifices can cause deviations between analytical predictions and actual performance values.

Humphries, W. R.↗

NASA NTRS1982

Manifold Insulation for Solar Collectors

Results of computer analysis of effects of various manifold insulation detailed in 23-page report show that if fluid is distributed to and gathered from array of solar collectors by external rather than internal manifold, effectiveness of manifold insulation has major influence on efficiency. Report describes required input data and presents equations that govern computer model. Provides graphs comparing collector efficiencies for representative manifold sizes and insulations.

Source record↗

NASA NTRS1985

Aerodynamic evaluation of the redesigned Space Shuttle Main Engine hot-gas manifold

The current Space Shuttle Main Engine hot-gas manifold configuration contains three transfer ducts connecting the fuel bowl and the main injector torus. For the current study, a new hot-gas manifold was designed to improve on a previously tested two-duct concept. This was accomplished by eliminating separated flow regions, reducing local velocities, and providing as uniform a flowfield as possible. The two-duct hot-gas manifold tested in this study showed significant improvement over the existing three-duct design. The circumferential pressure gradient was reduced by 67 percent. The system total pressure loss from the discharge of the 180-degree turn to the transfer duct exit was 60 percent less than with the three duct hot gas manifold. Although only limited fluctuating pressure data were taken in the main injector, indications are that the environment there has been improved.

Vogt, S. T.↗

NASA NTRS1993

Methodology for CFD Design Analysis of National Launch System Nozzle Manifold

The current design environment dictates that high technology CFD (Computational Fluid Dynamics) analysis produce quality results in a timely manner if it is to be integrated into the design process. The design methodology outlined describes the CFD analysis of an NLS (National Launch System) nozzle film cooling manifold. The objective of the analysis was to obtain a qualitative estimate for the flow distribution within the manifold. A complex, 3D, multiple zone, structured grid was generated from a 3D CAD file of the geometry. A Euler solution was computed with a fully implicit compressible flow solver. Post processing consisted of full 3D color graphics and mass averaged performance. The result was a qualitative CFD solution that provided the design team with relevant information concerning the flow distribution in and performance characteristics of the film cooling manifold within an effective time frame. Also, this design methodology was the foundation for a quick turnaround CFD analysis of the next iteration in the manifold design.

Haire, Scot L.↗