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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 361 records · Page 20

A comparative study of calibration techniques for finite strain elastoplasticity: Numerically-exact sensitivities for FEMU and VFM

Accurate identification of material parameters is crucial for predictive modeling in computational mechanics. Here, the two primary approaches in the experimental mechanics community for calibration from full-field digital image correlation data are known as finite element model updating (FEMU) and the virtual fields method (VFM). In VFM, the objective function is a squared mismatch between internal and external virtual work or power. In FEMU, the objective function quantifies the weighted mismatch between model predictions and corresponding experimentally measured quantities of interest. It is minimized by iteratively updating the parameters of an FE model. While FEMU is seen as more flexible, VFM is commonly used instead of FEMU due to its considerably greater computational expense. However, comparisons between the two methods usually involve approximations of gradients or sensitivities with finite difference schemes, thereby making direct assessments difficult. Hence, in this study, we compare VFM and FEMU in the context of numerically-exact sensitivities obtained through local sensitivity analyses and the application of automatic differentiation software. To this end, we conduct a series of test cases to assess both methods under practical challenges using a finite strain elastoplasticity model.

Automatic differentiation↗

Summer 2025 SULI: Nucleus ID, TinyTPC, and Scientific Communication

This paper summarizes my work during the Summer 2025 SULI internship, which focused on two main projects and broader scientific development. The first project involved improving the particle identification (PID) of protons, deuterons, and tritons using PIDA distributions and template fitting, with the goal of modeling nuclear final-state interactions (FSI) and testing the robustness of the method against systematic uncertainties. These techniques pave the way for future application to LArTPC data from the ICARUS detector. The second project centered on the optimization and data-taking of the TinyTPC detector, a compact LArTPC used for high-resolution low-energy measurements. I adjusted gain and threshold parameters, performed hardware validation tests, and developed analysis strategies to extract meaningful physics from collected data. Throughout the summer, I also enhanced my scientific communication and mentorship skills through presentations, collaborative analysis, and peer guidance.

McCright, Hannah [Maryland U.]↗

Low responsiveness of machine learning models to critical or deteriorating health conditions

Machine learning (ML) based mortality prediction models can be immensely useful in intensive care units. Such a model should generate warnings to alert physicians when a patient’s condition rapidly deteriorates, or their vitals are in highly abnormal ranges. Before clinical deployment, it is important to comprehensively assess a model’s ability to recognize critical patient conditions. We develop multiple medical ML testing approaches, including a gradient ascent method and neural activation map. We systematically assess these machine learning models’ ability to respond to serious medical conditions using additional test cases, some of which are time series. Guided by medical doctors, our evaluation involves multiple machine learning models, resampling techniques, and four datasets for two clinical prediction tasks. We identify serious deficiencies in the models’ responsiveness, with the models being unable to recognize severely impaired medical conditions or rapidly deteriorating health. For in-hospital mortality prediction, the models tested using our synthesized cases fail to recognize 66% of the injuries. In some instances, the models fail to generate adequate mortality risk scores for all test cases. Our study identifies similar kinds of deficiencies in the responsiveness of 5-year breast and lung cancer prediction models. Using generated test cases, we find that statistical machine-learning models trained solely from patient data are grossly insufficient and have many dangerous blind spots. Most of the ML models tested fail to respond adequately to critically ill patients. How to incorporate medical knowledge into clinical machine learning models is an important future research direction.

60 APPLIED LIFE SCIENCES↗

Direct Processing of Lithium Chloride Based Waste Salt in a Ceramic Waste Form

Ceramic waste form materials were fabricated with a LiCl based salt mixture to demonstrate the suitability of direct processing of waste salt from an all LiCl pyroprocessing flow sheet on the formation, microstructure, and durability of ceramic waste forms. Materials were successfully synthesized by using the simplified direct processing technique with salt loadings of 5, 7.5, and 10 wt% at the laboratory scale. Materials fabricated with LiCl based salt indicated full conversion of zeolite to sodalite occurred to form products with low open porosity. This indicates that the Na 2 O content of NBS4 glass is suitable for processing salt chemistries which do not contain NaCl. Generated sodalite was microencapsulated by the glass binder, halite occlusions were detected within sodalite domains at all salt loadings, and a Cs-rich phase believed to be Cs-pollucite was detected in the material made with the lowest salt loading (5 wt%). Salt inclusions were encapsulated within the binder glass at all loadings, and found to consist primarily of NaCl with Cs present. A small amount of salt was found at the surface of the wasteform made with the highest salt loading of 10 wt%, which may indicate an upper limit to the amount of salt that can be accommodated or incomplete mechanical mixing of the reagents. Durability testing by using the ASTM C1308 method indicated that initial rapid dissolution of exposed halite inclusion phases was directly correlated to salt loading. Wasteform degradation during all tests occurred primarily due to dissolution of the sodalite phase. Durability of the binder glass was found to increase as the waste salt loading increased. Results for the release of cations from the salt indicate the changes in wasteform durability and halite inclusion chemistry are strongly influenced by ion exchange phenomena between the salt and the glass. This appears to be the result of the relatively stronger affinity for the glass phase of Li, compared to that of other cations such as Na and Cs. The effects from cation exchange were diminished at lower salt loadings.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Bayesian Optimization for Reactor Design Optimization

This study present a test case in which the Bayesian Optimization method is applied to a simulation-based reactor core design optimization problem. The test case aims to showcase the potential of an automated design optimization algorithm for reactor designs by streamlining the reactor core design workflow, given the high computational cost of simulations. The contributions of this work are threefold. First, the existing HTGR model is converted into a simulation-based design optimization test case by developing a pipeline that enables modification of key design parameters and evaluates design performance based on simulation outputs. Second, Bayesian Optimization is implemented and adapted to demonstrate the feasibility of automatic design optimization for nuclear reactor core. Proposed approach leverages Gaussian Process models to characterize the relationship between design variables and performance metrics, while incorporating novel acquisition functions that balance exploration of the design space with exploitation of promising configurations. This implementation lays the foundation for the future developments of reactor design optimization algorithms.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗

Predicting Li-Ion Battery Capacity Fade Using Early-Life Data and a Hybrid Data-Driven Gaussian Process-Bayesian Regression Approach

Accurately predicting Li-ion battery capacity trajectories using early-life data can dramatically improve battery-life understandings and be used to rapidly evaluate design/cost/performance trade-offs when developing new battery materials. Accurate early-life predictions enable researchers to quickly iterate over cell designs and material precursor properties without consistently cycling cells to failure. To this end, we present a toolbox that uses a combined Gaussian Process and Bayesian regression approach that capitalizes on signals other than just capacity (e.g., dQ/dV, voltage drops) to rapidly predict capacity-fade trajectories. The prediction tool uses Bayesian regression to fit functional forms, e.g., power law, sigmoids, etc., to predict capacity-fade dynamics. By fitting functional forms, the capacity fade can be interrogated at any point in the future, allowing for early cell-failure prediction. Additionally, Bayesian regression allows for accurate uncertainty estimates that account for cell-to-cell variability (aleatoric uncertainty) and the lack of observation data (epistemic uncertainty). By only using early cycle data to predict the capacity fade trajectory, uncertainty bounds at end-of-life can be extremely large. The large uncertainty bounds are further exacerbated because there is no systematic way to define the prior distribution of the functional forms' parameters. We improve our the predicted trajectory confidence interval of our predicted trajectory using two methods. First, we shows that a small amount of held-out cycling data is sufficientuse some train cells, that have been cycled to failure to derive information regarding the appropriate prior distributions for the functional forms' parameters of the functional form, effectively leading to data-driven priors.. We propose constructing the data-driven priors by first running a Bayesian regression starting with uninformed priors to generate intermediate cell-specific posterior parameter distributions. These posterior distributions are combined using a Ggaussian mixture model for each parameter to create the data-driven priors. These mixture models serve as the data-driven prior distributions for the parameters for. Second, we derive multiple features, e.g., C_dchg 0.5 DoD 0.5, log (|mean(dQ/dV_(w_3-w_0 ) (V)|), etc., from the train cellsheld-out cycling data, identify which the features are that best predicting capacity at early/mid-life cycles, and then create Ggaussian process regression models that are used for predicting capacity at early/mid-life cycles for the test cells (see blue dots with error bars in Fig 1b). Finally, these predicted data-points are used in addition to the actual early cycle data capacity fade to construct the Bayesian regression trajectory for the test cell s. Notably. We note that these two methods are complementary and can be combined with each other. We evaluate the performance of our proposed method on an testing open-source dataset from Iowa State University and Iowa Lakes Community College (ISU-ILCC). This dataset comprises of 251 nickel-manganese-cobalt/graphite Lithium-ion cells that are cycled under 63 different conditions. We compute the mean average percentage error (MAPE) and negative log predictive density (NLPD) to quantify the efficacy of our method. Our initial findings suggest that, when only few observations are available, for test cells, when using only Bayesian regression with uninformed priors, a power law functional provides the most accurate predictions. with very few data points. However, asHowever, a the number of data points increases, a twin sigmoidal function becomes more accurate as the number of observations further increases. We also find that using as little as 10% of the data set towards generating data-driven priors can lead to significant improvement in prediction accuracy when using early cycle data. Lastly, we found that augmenting early-cycle data with Gaussian process-predicted capacity data for Bayesian regression greatly improves the prediction accuracy. We will present a comprehensive comparison of our methods to other methods available in the literature and apply this method to additional battery datasets.

42 ENGINEERING↗

Near-field passive sensor for the monitoring of high-temperature oxidative corrosion of metals

This study reports on the development and testing of a passive wireless device designed to track temperature and corrosion behavior in SS304H stainless steel under elevated temperatures. The ANSYS HFSS software was utilized to model and optimize the design of an inductor-capacitor (LC) resonator passive wireless sensors fabricated using platinum designs printed onto an aluminum oxide support operating at frequencies between (50–190 MHz). The optimal LC wireless sensor designs were then fabricated using screen-printing and sintering methods. Here, the sensors were tested by placing the sensor onto polished SS304H flat substrates and heated to 900–1050 °C in air. Wireless acquisition of sensor data during heating, cooling, and isothermal stages was achieved through a Pt loop antenna connected to an RF signal generator and a network analyzer.

20 FOSSIL-FUELED POWER PLANTS↗

Interpreting accelerated tests on perovskite modules using photooxidation of MAPbI 3 as an example

Solar panels (modules) based on metal halide perovskites are following a fast track to commercialization. Unlike more established solar cell materials, there are not yet decades-long field observations to increase consumer confidence. The "physics and chemistry of failure" approach is used in other industries and estimates product degradation based on laboratory accelerated tests integrated with an understanding of degradation mechanisms. This work uses that approach to quantify the relationship between accelerated tests and projected product behavior for metal halide perovskite modules. Degradation involving photooxidation of methylammonium lead iodide is used to illustrate the method. Acceleration factors in common accelerated tests are found to be low. Conclusions emphasize that the accelerated tests on photovoltaics should not be interpreted as equivalent across module types or as a green light for commercialization unless supported by the appropriate field data or physics and chemistry of failure analysis.

14 SOLAR ENERGY↗

Extraction and Analysis of Time Series Data from Building Automation Systems Using Large Language Models

Semantic schemas like Haystack 4, Brick and ASHRAE standard 223 enable the structured, standardized, and machine-readable representation of building data, facilitating interoperability, data integration, and advanced analytics. However, extracting information from these models requires specialized expertise in SPARQL and other programming languages, skills that are not commonly found among building professionals. Recent advancements in Large Language Models (LLMs), such as ChatGPT, enable the construction of queries using natural language, making it easier for individuals to interact with these systems in a manner that resembles everyday speech. However, these methods have not yet been tested on building semantic ontologies. This paper introduces a novel workflow and tool for enabling users to ask questions about a specific building's data, using natural language and receive answers automatically generated by GPT-4o. Our approach integrates semantic ontologies with advanced LLM capabilities to automate three critical steps: (1) generating SPARQL queries to retrieve time series references from ontological models, (2) extracting the corresponding time series data from the Building Automation System, and (3) performing computations and visualizations tailored to the user's query. The proposed method simplifies access to BAS data, allowing both domain experts and non-specialists to conduct sophisticated analyses without needing extensive technical knowledge of semantic web technologies. By demonstrating this pipeline, we facilitate more accessible and scalable data-driven decision-making in building operations and management.

Mulayim, Ozan Baris↗

Extraction and Analysis of Time Series Data from Building Automation Systems Using Large Language Models

Semantic schemas like Haystack 4, Brick and ASHRAE standard 223 enable the structured, standardized, and machine-readable representation of building data, facilitating interoperability, data integration, and advanced analytics. However, extracting information from these models requires specialized expertise in SPARQL and other programming languages, skills that are not commonly found among building professionals. Recent advancements in Large Language Models (LLMs), such as ChatGPT, enable the construction of queries using natural language, making it easier for individuals to interact with these systems in a manner that resembles everyday speech. However, these methods have not yet been tested on building semantic ontologies. This paper introduces a novel workflow and tool for enabling users to ask questions about a specific building's data, using natural language and receive answers automatically generated by GPT-4o. Our approach integrates semantic ontologies with advanced LLM capabilities to automate three critical steps: (1) generating SPARQL queries to retrieve time series references from ontological models, (2) extracting the corresponding time series data from the Building Automation System, and (3) performing computations and visualizations tailored to the user's query. The proposed method simplifies access to BAS data, allowing both domain experts and non-specialists to conduct sophisticated analyses without needing extensive technical knowledge of semantic web technologies. By demonstrating this pipeline, we facilitate more accessible and scalable data-driven decision-making in building operations and management.

Mulayim, Ozan Baris↗

Twins in rotational spectroscopy: Does a rotational spectrum uniquely identify a molecule?

Rotational spectroscopy is the most accurate method for determining structures of molecules in the gas phase. It is often assumed that a rotational spectrum is a unique “fingerprint” of a molecule. The availability of large molecular databases and the development of artificial intelligence methods for spectroscopy make the testing of this assumption timely. In this paper, we pose the determination of molecular structures from rotational spectra as an inverse problem. Within this framework, we adopt a funnel-based approach to search for molecular twins, which are two or more molecules, which have similar rotational spectra but distinctly different molecular structures. Here we demonstrate that there are twins within standard levels of computational accuracy by generating rotational constants for many molecules from several large molecular databases, indicating that the inverse problem is ill-posed. However, some twins can be distinguished by increasing the accuracy of the theoretical methods or by performing additional experiments.

74 ATOMIC AND MOLECULAR PHYSICS↗

An improved guess for the variational calculation of charge-transfer excitations in large systems

Ab initio quantum-chemical methods that perform well for computing the electronic ground state are not straightforwardly transferable to electronically excited states, particularly in large molecular systems. Wave function theory offers high accuracy, but is often prohibitively expensive. Methods based on time-dependent density functional theory (TD-DFT) are crucially sensitive to the chosen exchange-correlation functional (XCF) parameterization, and system-specific tuning protocols were therefore proposed to address the method's robustness. Methods based on the variational relaxation of the excited-state electron density showcased promising results for the calculation of charge-transfer excitations, but the complex shape of the electronic hypersurface makes convergence to a specific excited state much more difficult than for the ground state when standard variational techniques are applied. We address the latter aspect by providing suitable initial guesses, which we obtain by two separate constrained algorithms. Combined with the squared-gradient minimization algorithm for all-electrons relaxation in a freeze-and-release scheme (FRZ-SGM), we demonstrate that orbital-optimized density functional theory (OO-DFT) calculations can reliably converge to the charge-transfer states of interest even for large molecular systems. We test the FRZ-SGM method on a phenothiazine-anthraquinone CT excitation in a supramolecular Pd(II) coordination cage complex as a function of the cage conformation. This compound has been studied experimentally prior to our work. We compare this freeze-and-release scheme to two XCF reparameterizations, which were recently proposed as low-cost TD-DFT-based alternatives to variational methods. Two dye-semiconductor complexes, which were previously investigated in the context of photovoltaic applications, serve as a second example to investigate the convergence and stability of the FRZ-SGM approach. Our results demonstrate that FRZ-SGM provides reliable convergence for charge-transfer excited states and avoids variational collapse to lower-lying electronic states, whereas time-dependent DFT calculations with an adequate tuning procedure for the range-separation parameter provide a computationally efficient initial estimate of the corresponding energies, with a computational cost comparable to that of configuration-interaction singles (CIS) calculations.

Bogo, Nicola↗

STRUCTURAL MODELING TO SUPPORT POST-YIELD ACCEPTANCE CRITERIA FOR SPENT NUCLEAR FUEL CLADDING

Spent nuclear fuel (SNF) is evaluated for structural failure during storage and transportation scenarios. The U.S. Department of Energy’s Spent Fuel and Waste Science and Technology (SFWST) program has sponsored significant research in quantifying mechanical loads on SNF during storage and transportation scenarios using experimental and modeling methods. The SFWST program has also performed significant research on measuring the mechanical behavior of irradiated SNF as defueled cladding segments and cladding with fuel pellets to measure composite behavior. This paper considers some of the key material data from the Sibling Pin testing and uses structural modeling and analysis methods that have been informed by testing to consider post-yield acceptance criteria for SNF cladding structural analysis. Test data published by Oak Ridge National Laboratory (ORNL) and Pacific Northwest National Laboratory (PNNL) are the foundation for informing the material behavior of the models developed in this study. In particular, four-point bend (4PB) tests of fueled and defueled cladding segments provide significant information about the bending failure mode of SNF. ORNL’s 4PB test data is on fueled cladding segments, so the composite behavior of SNF is demonstrated. This paper describes PNNL’s coincident beam model that was developed to approximate the composite behavior of SNF. This paper also presents PNNL’s structural dynamic finite element models of a cask tip-over scenario, which is predicted to cause the strongest mechanical loads on SNF of all postulated storage and transportation scenarios. SNF bending loads predicted in the cask tip-over scenario and cladding acceptance criteria beyond yield are considered, with justification based on the Sibling Pin test data. ASME Boiler and Pressure Vessel code stress intensity limits are also considered. The ultimate goal of this work is to aid in the justification of structural acceptance criteria for SNF cladding beyond the cladding’s irradiated yield strength for use in structural analysis of all storage and transportation scenarios.

Klymyshyn, Nicholas A.↗

Nondestructive Evaluation of Carbon Fiber Reinforced Polymers

The American Society of Mechanical Engineers Boiler and Pressure Vessel Code requires repair and replacement of safety-related piping materials to meet the original Construction Code; however, no construction criteria currently exist for carbon fiber reinforced polymer (CFRP) materials in the nuclear industry. Although nondestructive examination (NDE) techniques for cast and wrought ferritic and austenitic steels are well established, licensees are increasingly deploying novel materials such as CFRP for which assessment of the use of NDE is required, as the inspectability of such materials and the influence of manufacturing processes on inspectability remain insufficiently understood. To address these gaps, Pacific Northwest National Laboratory (PNNL) evaluated the fabrication of several CFRP repair mockups and the effectiveness of NDE methods to support regulatory review of CFRP repairs in nuclear power plant applications. Representative flat-plate mockups containing realistic fabrication defects were manufactured and inspected using manual and automated tap testing, dynamic response spectroscopy (DRS), and ultrasonic testing (UT). The study identified significant fabrication variability, particularly in controlling defect size and epoxy thickness, which strongly influenced defect detectability by NDE methods. Tap testing was effective for shallow defects in thin epoxy configurations but unreliable for thicker repairs and deeper flaws. DRS demonstrated higher sensitivity to dry spots but produced unconfirmed indications for thicker plates, requiring further validation. Conventional UT, particularly at 1.0 MHz, showed the strongest overall capability for detecting a range of defects, although performance degraded with increasing repair thickness and complexity. The results highlight the need to better define critical defect sizes, develop reliable mockup fabrication methods, and validate NDE methods needed to support CFRP repairs.

36 MATERIALS SCIENCE↗

Multiphysics Degradation Modeling of Energy Storage Materials via RKPM with a Neural Network-Enhancement

In energy storage materials, strong electrochemical-mechanical coupling and highly anisotropic material properties contribute to the formation and propagation of micro-cracking during charge/discharge cycling, resulting in reduced performance and service life. A coupled electro-chemo-mechanical reproducing kernel particle method (RKPM) formulation is developed, and a patch-test is formulated to certify optimal convergence of the proposed RKPM method for the coupled physics system. With microstructural images supplied by the National Renewable Energy Laboratory (NREL), pixel-based model construction by RKPM is then used to represent the complex material microstructures for modeling the coupled physics of these systems. Further, a neural network-enhanced reproducing kernel particle method (NN-RKPM) [1, 2] is introduced to effectively model damage and crack propagation in the material microstructures; the location, orientation, and solution transition near a localization are automatically captured by superimposed block-level NN optimizations. This NN enrichment approach allows for effective modeling of localizations via a fixed background discretization, relieving tedious efforts for adaptive refinement in traditional mesh-based methods. Applications to the heterogeneous microstructures of Li-ion battery cathodes will be presented to demonstrate the effectiveness of the proposed methods. Reference: [1] Baek, J., Chen, J. S., Susuki, K., "Neural Network enhanced Reproducing Kernel Particle Method for Modeling Localizations," International Journal for Numerical Methods in Engineering, Vol. 123, pp 4422-4454, https://doi.org/10.1002/nme.7040, 2022. [2] Baek, J., Chen, J. S., "A Neural Network-Based Enrichment of Reproducing Kernel Approximation for Modeling Brittle Fracture", Computer Methods in Applied Mechanics and Engineering Vol. 410, 116590, 2024.

electro-chemo-mechanical coupling↗

Updated ASME design correlations and qualification plan for powder bed fusion 316H stainless steel

This report provides an update on the Advanced Materials and Manufacturing Technologies (AMMT) program effort to qualify Laser-Powder Bed Fusion (L-PBF) 316H stainless steel for use with the ASME Boiler & Pressure Vessel Code Section III, Division 5 rules. The report summarizes progress in testing and characterizing L-PBF material at elevated temperatures by providing preliminary design data for L-PBF 316H and by comparing the elevated temperature performance of the L-PBF material to wrought and conventional fusion welded 316H. The report then updates the initial AMMT qualification plan for L-PBF 316H, originally developed in 2023, to update the accelerated qualification strategy adopted in that plan to account for the new high temperature test data. The report also explores a few methods for further accelerating the qualification process using machine learning techniques to supplement the more conventional, empirical analysis methods typically used by ASME to correlate and extrapolate time-dependent material test data.

36 MATERIALS SCIENCE↗

Towards robust surrogate models: Benchmarking machine learning approaches to expediting phase field simulations of brittle fracture

Data-driven approaches have the potential to make modeling complex, nonlinear physical phenomena significantly more computationally tractable. For example, computational modeling of fracture is a core challenge where machine learning techniques have the potential to provide a much needed speedup that would enable progress in areas such as multi-scale modeling and uncertainty quantification. Currently, phase field modeling (PFM) of fracture is one such approach that offers a convenient variational formulation to model crack nucleation, branching and propagation. To date, machine learning techniques have shown promise in approximating PFM simulations. While standard fracture benchmarks represent realistic scenarios frequently observed in practice, they typically do not provide sufficiently challenging tests for data-driven methods. Here, to address this gap, we introduce a challenging dataset based on PFM simulations designed to benchmark and advance ML methods for fracture modeling. This dataset includes three energy decomposition methods, two boundary conditions, and 1000 random initial crack configurations for a total of 6000 simulations. Each sample contains 100 time steps capturing the temporal evolution of the crack field. Alongside this dataset, we also implement and evaluate Physics Informed Neural Networks (PINN), Fourier Neural Operators (FNO), and UNet models as baselines, and explore the impact of ensembling strategies on prediction accuracy. With this combination of our dataset and baseline models drawn from the literature we aim to provide a standardized and challenging benchmark for evaluating machine learning approaches to solid mechanics. Our results highlight both the promise and limitations of popular current models, and demonstrate the utility of this dataset as a testbed for advancing machine learning in fracture mechanics research.

Benchmark dataset↗

Polynomial chaos expansions on principal geodesic Grassmannian submanifolds for surrogate modeling and uncertainty quantification

In this work we introduce a manifold learning-based surrogate modeling framework for uncertainty quantification in high-dimensional stochastic systems. Our first goal is to perform data mining on the available simulation data to identify a set of low-dimensional (latent) descriptors that efficiently parameterize the response of the high-dimensional computational model. To this end, we employ Principal Geodesic Analysis on the Grassmann manifold of the response to identify a set of disjoint principal geodesic submanifolds, of possibly different dimension, that captures the variation in the data. Since operations on the Grassmann require the data to be concentrated, we propose an adaptive algorithm based on Riemannian K-means and the minimization of the sample Fréchet variance on the Grassmann manifold to identify “local” principal geodesic submanifolds that represent different system behavior across the parameter space. Polynomial chaos expansion is then used to construct a mapping between the random input parameters and the projection of the response on these local principal geodesic submanifolds. Here, the method is demonstrated on four test cases, a toy-example that involves points on a hypersphere, a Lotka-Volterra dynamical system, a continuous-flow stirred-tank chemical reactor system, and a two-dimensional Rayleigh-Bénard convection problem.

42 ENGINEERING↗