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At least 1,567 records · Page 87

Long-Wave Infrared Dyson Spectrometer

Preliminary results are presented for an ultra compact long-wave infrared slit spectrometer based on the dyson concentric design. The dyson spectrometer has been integrated in a dewar environment with a quantum well infrared photodetecor (QWIP), concave electron beam fabricated diffraction grating and ultra precision slit. The entire system is cooled to cryogenic temperatures to maximize signal to noise ratio performance, hence eliminating thermal signal from transmissive elements and internal stray light. All of this is done while maintaining QWIP thermal control. A general description is given of the spectrometer, alignment technique and predicated performance. The spectrometer has been designed for optimal performance with respect to smile and keystone distortion. A spectral calibration is performed with NIST traceable targets. A 2-point non-uniformity correction is performed with a precision blackbody source to provide radiometric accuracy. Preliminary laboratory results show excellent agreement with modeled noise equivalent delta temperature and detector linearity over a broad temperature range.

imaging↗

Bioinspired Honeycomb Core Design: An Experimental Study of the Role of Corner Radius, Coping, and Interface

The honeybee’s nest has inspired the design of engineering honeycomb core that primarily abstract the hexagonal cell shape and exploit its mass minimizing properties to construct lightweight panels. This work explored three additional design features that are part of the natural honeybee comb but have not been traditionally considered as design features of interest in honeycomb design: the radius at the corner of each cell, the coping at the top of the cell walls, and the interface between cell arrays. These features were first characterized in natural honeycomb using optical and X-ray techniques, and then incorporated into honeycomb core design, and fabricated using an additive manufacturing process. The honeycomb cores were then tested in out-of-plane compression and bending, and since all three design features added mass to the overall structure, all metrics were examined per unit mass to assess performance gains. The study concluded that the addition of an interface increases specific flexural modulus but has little benefit in out-of-plane compression; coping radius positively impacts specific flexural strength; but that the corner radius has no significant effect in bending, and actually is slightly detrimental for out-of-plane compression testing.

honeycomb↗

A Monte Carlo Based Ray Tracing Tool for Evaluating Wolter-Type Prescriptions

Evaluating Wolter-like X-ray mirror prescriptions via ray tracing is useful for selecting and optimizing the right mirror prescriptions for a specified application. Moreover, incorporating real metrology data into a ray trace and simulating point spread functions (PSF) allows for performance predictions representative of real manufacturing errors and tolerances. In fulfillment of an internship project, an X-ray ray trace routine using a Monte-Carlo method has been developed to examine different Wolter-like prescriptions and characterize their theoretical performances over a specified field of view. This routine includes the ability to use real metrology data to evaluate the impact of figure error on imaging performance. As a test case, the Marshall Grazing Incidence X-ray Spectrometer (MaGIXS) Wolter-I mirror prescription and an equivalent Wolter-Schwarzschild prescription were traced and imaging performance of a specified field of view were mapped. Here we present the approach used in this routine, showcase example results, and discuss future goals for expanding the routine to address azimuthally varying figure errors and surface roughness.

X-ray optics↗

Towards Gbps Downlinks from Low-Cost Active Phased Arrays

Spacecraft performing science missions use high-directivity antennas to quickly downlink large amounts of collected data. Movement required to keep gimbaled reflector antennas trained on target receivers can impart blockages or vibrations which perturb precision science instruments. Recent manufacturing advances have made Ka-band electronically-steered antenna arrays a cost-effective option to mitigate these challenges, but only if these devices can be proven to deliver comparable quality of service. In this work we present a hardware and software architecture for high-rate links using an active phased array-based terminal in a 1U (10cm cube) form factor. Over-the-air tests in an antenna range characterize two key features of the architecture: high-order (32APSK and above) modulations and dual carriers. We calculate an optimal modulation-dependent input power backoff from array saturation and perform orbital simulations of the link at this operating point. We conclude that reliable links with rates in excess of 1Gbps are possible with current-generation hardware.

Adam Gannon↗

Evaluation of Regional Water and Energy Balance in Contemporary Reanalyses

Regional to continental water and energy balance in reanalyses provide crucial information on the climate and climate variations in that region and can contrast other regions. Reanalyses are a valuable tool in piecing together the complete balance owing to the incorporation of the budgets in the background model and the assimilation of observation. On the other hand, the background model has its own biases and observational assimilation can lead to non-negligible tendencies within the budgets, and these can vary over space and time. Here, we will compare the balance within several reanalyses and how they have evolved over recent decades. Several observational data products will provide reference points in the comparison. In addition, a recent project has integrated observations of the water and energy budgets in an optimization that aims to reduce the imbalance of regional budgets in using observational terms from disparate sources. In evaluating the regional balances, we will incorporate, when available, the water and energy convergence terms as well as their analysis increments (which may be diagnosed as residuals). The reanalyses considered here include: Japanese Reanalyses for Three Quarters Century (JRA3Q), ECMWF Reanalysis version 5 (ERA5), Modern Era Retrospective-analysis for Research and Applications version 2 (MERRA-2) and the NCEP Reanalysis II (NCEPR2). NCEPR2 is representative of the late 90s technology, while the others represent the contemporary climate reanalyses presently available. We will discuss the regional balances over key river basins (e.g. Mississippi and Amazon), and a range of continents including those well observed (North America and Europe) and those with fewer consistent observations (e.g. Africa). These contrasting regions show the degree of advancement in reanalyses and expose areas in need of improvement. The results also demonstrate the usefulness of producing complete atmospheric water and energy budgets as part of the diagnostic output.

Michael G Bosilovich↗

Evaluation of Regional Water and Energy Balance in Contemporary Reanalyses

Regional to continental water and energy balance in reanalyses provide crucial information on the climate and climate variations in that region and can contrast other regions. Reanalyses are a valuable tool in piecing together the complete balance owing to the incorporation of the budgets in the background model and the assimilation of observation. On the other hand, the background model has its own biases and observational assimilation can lead to non-negligible tendencies within the budgets, and these can vary over space and time. Here, we will compare the balance within several reanalyses and how they have evolved over recent decades. Several observational data products will provide reference points in the comparison. In addition, a recent project has integrated observations of the water and energy budgets in an optimization that aims to reduce the imbalance of regional budgets in using observational terms from disparate sources. In evaluating the regional balances, we will incorporate, when available, the water and energy convergence terms as well as their analysis increments (which may be diagnosed as residuals). The reanalyses considered here include: Japanese Reanalyses for Three Quarters Century (JRA3Q), ECMWF Reanalysis version 5 (ERA5), Modern Era Retrospective-analysis for Research and Applications version 2 (MERRA-2) and the NCEP Reanalysis II (NCEPR2). NCEPR2 is representative of the late 90s technology, while the others represent the contemporary climate reanalyses presently available. We will discuss the regional balances over key river basins (e.g. Mississippi and Amazon), and a range of continents including those well observed (North America and Europe) and those with fewer consistent observations (e.g. Africa). These contrasting regions show the degree of advancement in reanalyses and expose areas in need of improvement. The results also demonstrate the usefulness of producing complete atmospheric water and energy budgets as part of the diagnostic output.

Michael Bosilovich↗

Demonstration of Automatically-Generated Adjoint Code for Use in Aerodynamic Shape Optimization

Gradient-based optimization requires accurate derivatives of the objective function and constraints. These gradients may have previously been obtained by manual differentiation of analysis codes, symbolic manipulators, finite-difference approximations, or existing automatic differentiation (AD) tools such as ADIFOR (Automatic Differentiation in FORTRAN). Each of these methods has certain deficiencies, particularly when applied to complex, coupled analyses with many design variables. Recently, a new AD tool called ADJIFOR (Automatic Adjoint Generation in FORTRAN), based upon ADIFOR, was developed and demonstrated. Whereas ADIFOR implements forward-mode (direct) differentiation throughout an analysis program to obtain exact derivatives via the chain rule of calculus, ADJIFOR implements the reverse-mode counterpart of the chain rule to obtain exact adjoint form derivatives from FORTRAN code. Automatically-generated adjoint versions of the widely-used CFL3D computational fluid dynamics (CFD) code and an algebraic wing grid generation code were obtained with just a few hours processing time using the ADJIFOR tool. The codes were verified for accuracy and were shown to compute the exact gradient of the wing lift-to-drag ratio, with respect to any number of shape parameters, in about the time required for 7 to 20 function evaluations. The codes have now been executed on various computers with typical memory and disk space for problems with up to 129 x 65 x 33 grid points, and for hundreds to thousands of independent variables. These adjoint codes are now used in a gradient-based aerodynamic shape optimization problem for a swept, tapered wing. For each design iteration, the optimization package constructs an approximate, linear optimization problem, based upon the current objective function, constraints, and gradient values. The optimizer subroutines are called within a design loop employing the approximate linear problem until an optimum shape is found, the design loop limit is reached, or no further design improvement is possible due to active design variable bounds and/or constraints. The resulting shape parameters are then used by the grid generation code to define a new wing surface and computational grid. The lift-to-drag ratio and its gradient are computed for the new design by the automatically-generated adjoint codes. Several optimization iterations may be required to find an optimum wing shape. Results from two sample cases will be discussed. The reader should note that this work primarily represents a demonstration of use of automatically- generated adjoint code within an aerodynamic shape optimization. As such, little significance is placed upon the actual optimization results, relative to the method for obtaining the results.

Green, Lawrence↗

The scoping, design, and plasma physics optimization of the Eos neutron source stellarator

On the path to a fusion pilot plant, Thea Energy plans to build Eos, a sub-breakeven, deuterium-deuterium, beam-target fusion, stellarator neutron source facility for producing tritium and other valuable radioisotopes. In this paper, a set of 1D plasma physics models are coupled and used to design the operating point of the facility and predict performance. At this foundational stage of the design, analytic and approximate models are sufficient to capture the leading-order effects, and fast enough to run in the inner loop of an optimizer. Higher-fidelity analyses will follow. Models of 1D profile-dependent neutral beam stopping, ion beam slowing down, beam-target fusion, electron-ion classical heat transfer, energy confinement (ISS04), beam pressure, beam heating of ions and electrons, beam-beam fusion fraction, and neutral beam injection and gyrotron heating electrical efficiencies are included. A numerical optimizer is used to determine the minimum required facility electric power to generate tritium at a given rate. A potentially advantageous regime is described in which modern precisely-quasisymmetric stellarators, new high-temperature superconductors, ITER-derived neutral beam injection, and new high-frequency gyrotrons enable a suitible target plasma with hot electrons, cold ions, peaked density and temperature profiles, and high beam-injected ion density. It appears possible at this time for a facility with a medium-scale and medium-strength stellarator whose required facility electric power is less than 40 MW to produce $2.5\times 10^{17}$ neutrons s -1 for the production of radioisotopes. With the addition of a tritium breeding blanket, such a facility could produce 0.2 grams d -1 or 70 grams yr -1 of tritium.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

An Optimization-Based Coupling of Reduced Order Models with an Efficient Reduced Adjoint Basis Generation Approach

Optimization-based coupling (OBC) is an attractive alternative to traditional Lagrange multiplier approaches in multiple modeling and simulation contexts. However, application of OBC to time-dependent problems has been hindered by the computational cost of finding the stationary points of the associated Lagrangian, which requires primal and adjoint solves. This issue can be mitigated by using OBC in conjunction with computationally efficient reduced order models (ROMs). To demonstrate the potential of this combination, in this paper, we develop an optimization-based ROM-ROM coupling for a transient advection-diffusion transmission problem. We pursue the “optimize-then-reduce” path toward solving the minimization problem at each time step and solve reduced space adjoint system of equations, where the main challenge in this formulation is the generation of adjoint snapshots and reduced bases for the adjoint systems required by the optimizer. One of the main contributions of the paper is a new technique for an efficient adjoint snapshot collection for gradient-based optimizers in the context of optimization-based ROM-ROM couplings. In conclusion, we present numerical studies demonstrating the accuracy of the approach along with comparison between various approaches for selecting a reduced order basis for the adjoint systems, including decay of snapshot energy, average iteration counts, and timings.

coupled problems↗

Design optimization of an ethanol heavy-duty engine using design of experiments and bayesian optimization

Diesel-fueled engines still hold a large market share in the medium and heavy-duty transportation sector. However, the increase in fossil fuel prices and the strict emission regulations are leading engine manufacturers to seek cleaner alternatives without a compromise in performance. Alcohol-based fuels, such as ethanol, offer a promising alternative to diesel fuel in meeting regulatory demands. Ethanol provides cleaner combustion and lower levels of soot due to its chemical properties, in particular its lower level of carbon content. In addition, the stoichiometric operating conditions of alcohol fueled engines enable the mitigation of NOx emissions in aftertreatment stage. With the promise of retrofitting diesel engines to run on ethanol to reduce emissions, the thermal efficiency of these engines remains the primary optimization target. In order to find the optimal ethanol-fueled engine design that maximizes the thermal efficiency, a large design space needs to be investigated using engineering tools. In this study, previous research by the authors on optimizing the design of a single-cylinder ethanol-fueled engine was extended to explore the design space for a heavy-duty multi-cylinder engine configuration. A heavy-duty engine setup with multiple operating conditions at different engine speeds and loads were considered. A design optimization analysis was performed to identify the potential designs that maximize the indicated thermal efficiency in an ethanol-fueled compression ignition engine. First, a computational fluid dynamics (CFD) model of the engine was validated using experimental data for four drive cycle points. Using a design of experiments (DoE) approach and a parameterized piston bowl geometry, the model was then exercised to explore the relationship among geometric features of the piston bowl and spray targeting angle and indicated thermal efficiency across all tested operating conditions. After evaluating 165~candidate designs, a piston bowl geometry was identified that yielded an increase between 1.3 to 2.2 percentage points in indicated thermal efficiency for all tested conditions, while satisfying the operational design constraints for peak pressure and maximum pressure rise rate. The increased performance was attributed to enhanced mixing that led to the formation of a more homogeneous distribution of in-cylinder temperature and equivalence ratio, higher combustion temperatures, and shorter combustion duration. Finally, a Bayesian optimization (BOpt) analysis was employed to find the optimal piston bowl geometry with a fixed spray injector angle for one of the operating conditions. Using BOpt, a piston candidate was identified that resulted in a 1.9~percentage point increase in thermal efficiency from the baseline design, yet only required 65\% of the design samples investigated using the DoE approach.

Tekgul, Bulut↗

Ionomer Optimization for Water Uptake and Swelling in Anion Exchange Membrane Electrolyzer: Oxygen Evolution Electrode

Water electrolysis using an anion conductive, solid polymer electrolyte is an attractive method for point-of-use hydrogen production. Recent advances in catalysts and anion exchange membranes (AEM) have made alkaline devices increasingly competitive with their acidic counterparts. However, less attention has been paid to the anion conductive ionomers (ACI) used in the fabrication of electrodes for AEM electrolyzers. The ACI contributes to ion conduction between the catalyst and bulk electrolyte and serves as a binder for adhering the catalyst to the gas diffusion layer and AEM. Ionic conductivity, water uptake and ionomer swelling are critical properties for electrode performance. High ion exchange capacity (IEC) in the ionomer is desired for reduced electrode resistance, however, it can lead to excess water uptake (WU) and disruptive ACI swelling. In this study, a series of poly(norbornene)-based ionomers were synthesized, characterized and used to fabricate oxygen evolving anodes for low-temperature AEM water electrolysis. The IEC of the ionomers (0 to 4.73 meq g −1 ) was adjusted by controlling the ratio of ion conducting to non-ion conducting norbornene monomers in the ACI tetrablock copolymers. Low conductivity ionomers are shown to yield the best-performing oxygen evolution electrodes, in the absence of ACI polymer cross-linking because they do not experience excessive water swelling. Light cross-linking within the anode ACI was used as a means to independently lower WU of the ionomer without compromising ionic conductivity. This control over water swelling allows higher ionic conductivity within the ACI to be used in water-fed electrolyzer applications. Other methods of water management were compared including the use of hydrophobic additives and adjustment of the ionomer concentration in the electrode. As a result, it was shown that the cell performance greatly benefits from a highly conductive ionomer in the oxygen evolution reaction electrode if the WU is managed.

08 HYDROGEN↗

Robust measurement of microbial reduction of graphene oxide nanoparticles using image analysis

ABSTRACT Shewanella oneidensis ( S. oneidensis ) has the capacity to reduce electron acceptors within a medium and is thus used frequently in microbial fuel generation, pollutant breakdown, and nanoparticle fabrication. Microbial fuel setups, however, often require costly or labor-intensive components, thus making optimization of their performance onerous. For rapid optimization of setup conditions, a model reduction assay can be employed to allow simultaneous, large-scale experiments at lower cost and effort. Since S. oneidensis uses different extracellular electron transfer pathways depending on the electron acceptor, it is essential to use a reduction assay that mirrors the pathways employed in the microbial fuel system. For microbial fuel setups that use nanoparticles to stimulate electron transfer, reduction of graphene oxide provides a more accurate model than other commonly used assays as it is a bulk material that forms flocculates in solutions with a large ionic component. However, graphene oxide flocculates can interfere with traditional absorbance-based measurement techniques. This study introduces a novel image analysis method for quantifying graphene oxide reduction, showing improved performance and statistical accuracy over traditional methods. A comparative analysis shows that the image analysis method produces smaller errors between replicates and reveals more statistically significant differences between samples than traditional plate reader measurements under conditions causing graphene oxide flocculation. Image analysis can also detect reduction activity at earlier time points due to its use of larger solution volumes, enhancing color detection. These improvements in accuracy make image analysis a promising method for optimizing microbial fuel cells that use nanoparticles or bulk substrates. IMPORTANCE Shewanella oneidensis ( S. oneidensis ) is widely used in reduction processes such as microbial fuel generation due to its capacity to reduce electron acceptors. Often, these setups are labor-intensive to operate and require days to produce results, so use of a model assay would reduce the time and expenses needed for optimization. Our research developed a novel digital analysis method for analysis of graphene oxide flocculates that may be utilized as a model assay for reduction platforms featuring nanoparticles. Use of this model reduction assay will enable rapid optimization and drive improvements in the microbial fuel generation sector.

Bennett, Danielle T. (ORCID:0009000188748827)↗

Digital Twin Model for Advanced Manufacture of a Rotating Detonation Engine Injector

A digital twin material model (DTMM) of an additive manufacturing (AM) process was created to advance the state of the art in rotating detonation engine (RDE) injector design. Current RDE injectors are designed with large pressure drops, enabling a stable and repeatable combustion process. However, this comes at the cost of system efficiency. For the technology to transition to commercial fossil-based power generation, it is important to develop injectors with reduced flow losses. Low-loss injectors are difficult to design and manufacture with conventional manufacturing techniques. AM enables new design options, but the AM manufacturing process must be thoroughly understood to result in a robust design. A DTMM provides the necessary insight by defining the cause-effect relationships between process parameters, microstructure features, and properties. Therefore, a DTMM to support the design and manufacturing process was developed and applied to the design of a new additively manufactured low-loss injector. The injector combustion behavior was characterized through hot-fire tests, and mechanical performance was compared to the DTMM predictions. The two project goals were the successful development of the DTMM and the demonstration of an improved RDE injector design. The RDE injector design and DTMM developments occurred on parallel but dependent paths. The injector was designed to reduce pressure drop by increasing the cross-sectional flow area ratio between the injector air passages and the combustor annulus. This resulted in less structural material, raising the concern that thin members would be susceptible to high-cycle fatigue (HCF) under the periodic loading inherent to an RDE. It was most important for the DTMM to predict behavior in these features; therefore, the injector design concept guided the material thicknesses used in fatigue tests. The DTMM development started by manufacturing a series of coupons over the range of possible AM process variations. A design-of-experiment approach was used to select which process variable combinations gave the most efficient coverage relevant to the injector design space. The microstructure in each of these coupons was characterized, and then computational methods were used to create a numerical model of the correlation between process variables and microstructure. Next, a set of HCF samples were tested to calibrate existing models that map microstructure to HCF performance. Together, these two links formed the DTMM that calculates HCF behavior from AM process variables. Two injector prototypes were additively manufactured. The first injector design strategy aggressively pursued low-loss performance by substantially increasing the oxidizer flow area. The combination of manufacturing lead times and the fatigue testing schedule meant that the DTMM was not available when building this first prototype. Therefore, its process parameters were chosen based on a manual review of the available coupon data. This prototype was built successfully and evaluated in 58 combustion tests. Sustained detonation was achieved with remarkably reduced pressure loss, and some tests even displayed pressure loss characteristics similar to conventional gas turbine combustors. This achieved the project goal of improving RDE injector design. The second injector was manufactured according to the optimized parameters predicted by the DTMM. The flow area modifications of this injector were less aggressive than the first injector since demonstrating low pressure loss was not an objective of the second hot-fire test series. Rather, the test objective was to cause high cycle fatigue failure in the part due to periodic loading from the rotating detonation wave. The observed number of cycles to failure was to be compared to the number predicted by the DTMM and thereby assess the utility of the DTMM in component design. However, the required level of vibration was not obtained during combustion. Therefore, high cycle fatigue was not experienced in the hot-fire tests of the second injector. Fatigue data was obtained by further testing the second injector in a conventional HCF test apparatus. The injector demonstrated HCF strength above the DTMM prediction. In fact, it did not fail and testing was only discontinued due to reaching the end of the period of performance. This points to some success in the project’s primary goal of successfully developing and applying the DTMM to a component design. Implementing the DTMM recommendations for optimal processing parameters led to a part with acceptable properties. The DTMM was also shown to be an efficient correlator of data and to provide insight into the relationship between process settings, microstructure, and property performance. However, the failure of the DTMM prediction to match the experimental result of the injector fatigue test also points to the need to include significantly more data in the model development. In this project, coupons made with identical processing parameters exhibited drastically different properties from each other and from the injector part, which clearly influences the accuracy of a model that predicts performance based on parameters. Uncertainties in the build process must be quantified to develop more robust models. A denser and broader matrix of coupon process and geometry variations, several repeated builds of every point, more in-situ build process measurements, and direct observation of tensile and HCF sample microstructure (as opposed to separate microstructure specimens) are recommendations to improve future AM modeling efforts.

20 FOSSIL-FUELED POWER PLANTS↗

Generalized mathematical models in design optimization

The theory of optimality conditions of extremal problems can be extended to problems continuously deformed by an input vector. The connection between the sensitivity, well-posedness, stability and approximation of optimization problems is steadily emerging. The authors believe that the important realization here is that the underlying basis of all such work is still the study of point-to-set maps and of small perturbations, yet what has been identified previously as being just related to solution procedures is now being extended to study modeling itself in its own right. Many important studies related to the theoretical issues of parametric programming and large deformation in nonlinear programming have been reported in the last few years, and the challenge now seems to be in devising effective computational tools for solving these generalized design optimization models.

Papalambros, Panos Y.↗

Optimization-Based Model Reduction Scheme for Renewable Energy Power Plants Using Standardized Testing Scenarios

This paper presents an optimization-based model reduction scheme for renewable energy (RE) power plants consisting of inverter-based resources (IBRs) operating in grid-following (GFL) or grid-forming (GFM) modes. More importantly, the datasets feeding the optimization-based model reduction scheme are generated and re-used through the standardized grid-interactive testing scenarios. Particularly, the proposed scheme makes use of the power plant point of common coupling (PCC) measurements of various quantities specified by standardized tests (e.g., voltage and frequency ride through) as per IEEE 2800, to estimate the parameters of the reduced-order model such that its dynamic performance aligns with the original detailed power plant model. The proposed model reduction approach does not require the parameters of individual IBRs and using standardized test data as input to the formulated optimization problem simplifies the reduced-order modelling scheme. Extensive case studies following standardized test scenarios verified the remarkable accuracy of the proposed approach.

Yallamilli, Ram S. [Purdue University]↗

Simulating many-engine spacecraft: Exceeding 1 quadrillion degrees of freedom via information geometric regularization

We present an optimized implementation of the recently proposed information geometric regularization (IGR) for unprecedented scale simulation of compressible fluid flows applied to multi-engine spacecraft boosters. We improve upon state-of-the-art computational fluid dynamics (CFD) techniques in terms of computational cost, memory footprint, and energy-to-solution metrics. Unified memory on coupled CPU–GPU or APU platforms increases problem size with negligible overhead. Mixed half/single-precision storage and computation are used on well-conditioned numerics. We simulate flow at 200 trillion grid points and 1 quadrillion degrees of freedom, exceeding the current record by a factor of 20. A factor of 4 wall-time speedup is achieved over optimized baselines. Ideal weak scaling is observed on OLCF Frontier, LLNL El Capitan, and CSCS Alps using the full systems. Strong scaling is near ideal at extreme conditions, including 80% efficiency on CSCS Alps with an 8 node baseline and stretching to the full system.

Wilfong, Benjamin [Georgia Institute of Technology↗

Optimization on Manifolds via Graph Gaussian Processes

This paper integrates manifold learning techniques within a Gaussian process upper confidence bound algorithm to optimize an objective function on a manifold. Our approach is motivated by applications where a full representation of the manifold is not available and querying the objective is expensive. We rely on a point cloud of manifold samples to define a graph Gaussian process surrogate model for the objective. Query points are sequentially chosen using the posterior distribution of the surrogate model given all previous queries. We establish regret bounds in terms of the number of queries and the size of the point cloud. Several numerical examples complement the theory and illustrate the performance of our method.

Bayesian optimization↗