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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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

On the dual advantage of placing observations through forward sensitivity analysis

The four-dimensional variational data assimilation methodology for assimilating noisy observations into a deterministic model has been the workhorse in forecasting centres for over three decades. While this method provides a computationally efficient framework for dynamic data assimilation, it is largely silent on the important question concerning the minimum number and placement of observations. To answer this question, we demonstrate the dual advantage of placing the observations where the square of the sensitivity of the model solution with respect to the unknown control variables, called forward sensitivities, attains its maximum. By following this approach, we can force the observability Gramian to be of full rank, which in turn guarantees efficient recovery of the optimal values of the control variables, which is the first of the two advantages of this strategy. We further show that the proposed strategy of placing observations has another inherent optimality: the square of the sensitivity of the optimal estimates of the control with respect to the observations (used to obtain these estimates) attains its minimum value, a second advantage that is a direct consequence of the above strategy for placing observations. Our analytical framework and numerical experiments on linear and nonlinear systems confirm the effectiveness of our proposed strategy.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Mitigating Algorithmic Bias in Cancer Site Classification Models

Purpose Integrating artificial intelligence in cancer diagnostics has improved tumor classification beyond rule-based systems. Despite these advancements, these models may still encode demographic biases. We conducted a large-scale, applied bias-probing study of a deep learning–based cancer site classifier to quantify race information encoded in document embeddings. We then evaluated how performance changes when race-correlated embedding dimensions are removed in a post-training sensitivity analysis. Methods The cancer site classifier was trained using 3.5 million electronic cancer pathology reports from six of the National Cancer Institute's SEER registries. We trained a hierarchical self-attention network to generate 400-dimensional document embeddings. These embeddings were used to train two downstream, gradient-boosted decision tree classifiers: one to classify the cancer sites and another to predict racial categories. We identified overlapping features by intersecting the top 50 feature-importance rankings from the site and race models and computed their cumulative feature importance in each model. As a post hoc sensitivity analysis, we progressively pruned these overlapping dimensions, retrained the site model, and compared overall macro-F1 and accuracy, race-stratified macro-F1, and group fairness metrics on the basis of demographic parity and equalized odds before and after pruning. Results The analysis revealed minimal feature overlap between the cancer site and race prediction models, and the cumulative importance scores indicated a negligible influence of racial information on clinical predictions. Post-training pruning of overlapping features did not compromise the models' diagnostic accuracy, with a 0.07% loss in accuracy. Conclusion Our findings demonstrate that HiSAN-generated embeddings from SEER data can be used effectively in cancer site classification without significant demographic bias influencing the outcomes. Post-training pruning therefore functions as a practical audit and sensitivity check.

Shivanna, Abhishek [ORNL] (ORCID:0009000665228593)↗
DOE OSTI2025

DeepDiagnostics: A Software Package for Streamlined Posterior Evaluation

Automated prediction techniques like simulation-based inference (SBI) are important tasks for science experiments that produce large amounts of complex, raw data. However, their development remains in its early stages because the uncertainties of these techniques lack sufficient trustworthiness and interpretability. Packages for SBI provide a growing set of diagnostics; however, the software requirements are substantial, as they are tied to the inference technology itself, and the APIs lack adaptability. We introduce the DeepDiagnostics package for diagnosing posteriors from analytic likelihood-based methods and SBI methods, such as neural posterior estimation. DeepDiagnostics produces a comprehensive set of high-quality visualizations and metrics in a highly accessible, easy-to-use, and flexible package. We address all of these goals by providing a command-line inference tool and a Python API that is controlled through a configuration file. The package includes common diagnostics, such as parity plots, corner (covariance) plots, simulation-based calibration (SBC) diagnostics (including posterior coverage and rank histograms), Lemos et al. s PQMass and TARP, Masserano et al. s WALDO, Linhart et al. s LC2ST, as well as credible region diagnostics developed by our group.

Voetberg, Maggie [Fermilab]↗
DOE OSTI2021

An evaluation of prognostic factors, oncologic outcomes, and management for primary and recurrent squamous cell carcinoma of the vulva

Objective: To evaluate prognostic factors, outcomes, and management patterns of patients treated for squamous cell carcinoma of the vulva. Methods: One hundred sixty-four women were retrospectively identified with primary squamous cell carcinoma of the vulva treated at our institution between 1/1996–12/2018. Descriptive statistics were performed on patient, tumor, and treatment characteristics. The χ 2 tests and t-tests were used to compare categorical variables and continuous variables, respectively. Recurrence free survival (RFS), overall survival (OS), and disease-specific survival (DSS) were analyzed with Kaplan-Meier estimates, the log-rank test, and Cox proportional hazards. Results: Median follow-up was 52.5 months. Five-year RFS was 67.9%, 60.0%, 42.1%, and 20.0% for stage I–IV, respectively. Five-year DSS was 86.2%, 81.6%, 65.0%, and 42.9% for stage I–IV, respectively. On multivariate analysis, positive margins predicted overall RFS (hazard ratio [HR]=3.55; 95% confidence interval [CI]=1.18–10.73; p=0.025), while presence of lichen sclerosus on pathology (HR=2.78; 95% CI=1.30–5.91; p=0.008) predicted local RFS. OS was predicted by nodal involvement (HR=2.51; 95% CI=1.02–6.13; p=0.043) and positive margins (HR=5.19; 95% CI=2.03–13.26; p=0.001). Adjuvant radiotherapy significantly improved RFS (p=0.016) and DSS (p=0.012) in node-positive patients. Median survival after treatment of local, groin, and pelvic/distant recurrence was 52, 8, and 5 months, respectively. Conclusion: For primary treatment, more conservative surgical approaches can be considered with escalation of treatment in patients with concurrent precursor lesions, positive margins, and/or nodal involvement. Further studies are warranted to improve risk stratification in order to optimize treatment paradigms for vulvar cancer patients.

60 APPLIED LIFE SCIENCES↗
NASA NTRS1989

Analysis of Modified SMI Method for Adaptive Array Weight Control

An adaptive array is used to receive a desired signal in the presence of weak interference signals which need to be suppressed. A modified sample matrix inversion (SMI) algorithm controls the array weights. The modification leads to increased interference suppression by subtracting a fraction of the noise power from the diagonal elements of the covariance matrix. The modified algorithm maximizes an intuitive power ratio criterion. The expected values and variances of the array weights, output powers, and power ratios as functions of the fraction and the number of snapshots are found and compared to computer simulation and real experimental array performance. Reduced-rank covariance approximations and errors in the estimated covariance are also described.

Dilsavor, Ronald Louis↗
DOE OSTI2024

The endocannabinoid system in bovine tissues: characterization of transcript abundance in the growing Holstein steer

Abstract Background The endocannabinoid system (ECS) is highly integrated with seemingly all physiological and pathophysiological processes in the body. There is increasing interest in utilizing bioactive plant compounds, for promoting health and improving production in livestock. Given the established interaction between phytochemicals and the ECS, there are many opportunities for identification and development of therapies to address a range of diseases and disorders. However, the ECS has not been thoroughly characterized in cattle, especially in the gastrointestinal tract. The objective of this study was to characterize the distribution and transcriptional abundance of genes associated with the endocannabinoid system in bovine tissues. Methods Tissues including brain, spleen, thyroid, lung, liver, kidney, mesenteric vein, tongue, sublingual mucosa, rumen, omasum, duodenum, jejunum, ileum and colon were collected from 10-mo old Holstein steers (n = 6). Total RNA was extracted and gene expression was measured using absolute quantification real time qPCR. Gene expression of endocannabinoid receptorsCNR1andCNR2, synthesis enzymesDAGLA,DAGLBandNAPEPLD, degradation enzymesMGLLandFAAH, and transient receptor potential vanilloidsTRPV3andTRPV6was measured. Data were analyzed in R using a Kruskal-Wallis followed by a Wilcoxon rank-sum test. Results are reported as the median copy number/20 ng of equivalent cDNA (CN) with interquartile range (IQR). Results The greatest expression ofCNR1andCNR2was in the brain and spleen, respectively. Expression of either receptor was not detected in any gastrointestinal tissues, however there was a tendency (P = 0.095) forCNR2to be expressed above background in rumen. Expression of endocannabinoid synthesis and degradation enzymes varied greatly across tissues. Brain tissue had the greatestDAGLAexpression at 641 CN (IQR 52;P ≤ 0.05).DAGLBwas detected in all tissues, with brain and spleen having the greatest expression (P ≤ 0.05). Expression ofNAPEPLDin the gastrointestinal tract was lowest in tongue and sublingual mucosal. There was no difference in expression ofNAPEPLDbetween hindgut tissues, however these tissues collectively had 592% greater expression than rumen and omasum (P ≤ 0.05). WhileMGLLwas found to be expressed in all tissues, expression ofFAAHwas only above the limit of detection in brain, liver, kidney, jejunum and ileum.TRPV3was expressed above background in tongue, rumen, omasum and colon. Although not different from each other, thyroid and duodenum had the greatest expression ofTRPV6, with 285 (IQR 164) and 563 (IQR 467) CN compared to all other tissues (P < 0.05). Conclusions These data demonstrate the complex distribution and variation of the ECS in bovine tissues. Expression patterns suggest that regulatory functions of this system are tissue dependent, providing initial insight into potential target tissues for manipulation of the ECS.

Veterinary Sciences↗
NASA NTRS2001

A New Method for Evaluating Elastomeric Materials for Use in High Pressure Oxygen

The seal configuration tester (SCT) developed at the Stennis Space Center (SSC) was designed to replicate the intended application of different seat and seal materials in a high pressure oxygen system and assess the wearibility of those materials. Statistical models were used to test the reliability of the SCT in its intended application, and the tests showed very consistent measurements over time, indicating that the device was working as intended. Other statistical designs were used to test different O-ring materials in a high-pressure oxygen system. Those tests indicated that the SCT could be used to rank the performance of O-ring materials in certain environments. The results indicated that some cheaper materials performed as well as, if not better than, other more expensive materials. Different lubrications were integrated in the testing as well and had a significant impact on the performance of the materials. Testing of seat materials is the next stage of this project. An augmentation grant (JAG) was obtained to further this experimental testing at the Stennis Space Center. This part of the project is ongoing at this time and therefore there are no significant accomplishments with respect to seat materials as of yet.

Jordan, Scott M.↗
DOE OSTI2024

Digitalization mapping and assessment process supporting ION strategic transformation activities

The existing fleet of commercial nuclear power plants (NPPs) are an important asset in the nation’s portfolio of electrical generating resources. Their continued safe and reliable operation are critical to providing a large source of carbon-free electricity to power the nation’s economy. The United States Department of Energy’s (DOE) Light Water Reactor Sustainability (LWRS) Program develops the scientific bases, methods, and tools, for the continued safe and economical operation of the nation's commercial NPPs. The Plant Modernization Pathway within LWRS Program focuses on providing guidance to industry on the full-scale implementation of modernization solutions for NPPs that significantly reduce the technical and financial risks associated with modernization. This research is focused on helping the nuclear industry understand how to digitize and digitalize their NPPs so that they can design their modernization solutions to be scalable, sustainable, and integrated both laterally and horizontally within their organization. That is, this research creates a digital transformation in NPPs by reshaping cultural mindsets and by identifying business efficiencies. In partnership with industry, and using four previously established guiding principles for digitalization, this research supported NPP modernization through assessing readiness for digitalization as a means to achieve integrated operations for nuclear. Specifically, this research created an assessment to review an entire organization’s work processes to gather information about the digitalization health of the plant. The assessment tools were administered to plant employees, and the results were used to develop a digitalization plan. The survey assessment identified the optimal candidate processes that would most benefit from a digitalization initiative which were revealed through analytical frameworks. One analysis calculated mean digitalization health indicator scores for all endorsed activities which allowed the researchers to rank and color code the results for easy identification. Individual health indicator scores are also provided, should our industry partner wish to understand these findings according to their own organizational priorities, business considerations and desired end-state. The results were also analyzed from the perspective that organizations are comprised of different types of innovators (e.g., generators, optimizers, conceptualizers, and implementers), which differentially affects the organization’s ability to comprehend and adapt to change (i.e., opportunities to innovate). Understanding the relative composition of innovator types at an NPP allows them to gather insights into the strengths and weaknesses they have in innovating how work is performed. For the utility that partnered with this research team, the results showed that implementers make up the largest portion of respondents and conceptualizers the smallest portion. Knowing the proportion of innovator types gave this organization insights on how they can effectively implement their innovation solutions. Additionally, the results were analyzed from a technical, economic, and risk perspective to identify and quantify work reduction opportunities (WROs). Recognizing that not all cost-saving opportunities are the same, a Technical, Economic and Risk Assessment (TERA) was performed to evaluate WROs to identify areas of greatest potential and lowest risk. The key results from TERA included a digitalization opportunity score for each activity, and a calculation of potential cost savings. These two outputs formed the bases for calculating a priority index and rank for the activities/processes assessed. From the prioritization calculations, TERA can then help the utility 1) decide what digitalization priorities to invest money in implementing and then 2) calculates how much should be invested in the digitalization initiatives selected to achieve cost savings and/or an acceptable return on investment. Last, onsite interviews revealed several inefficiencies in the standard work processes that occur cross-departmentally that are due to the absence of digitized and digitalized processes. Examples of these include time spent scanning paper documents and then uploading the documents electronically, obtaining signatures, and searching for desired information. This represents a digital but not digitalized process. Over 15 opportunities to improve work processes were identified through this multi-method digitalization assessment. The various analytical assessments used (e.g., TERA, digitalization health indicator scores), as well as discussions with the utility partner, corroborated that all the opportunities identified had a strong potential to make work processes more efficient and to improve overall performance of the NPP.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2021

Evolutionary inverse design of defects at graphene 2D lateral interfaces

Grain boundaries (GBs) in two-dimensional (2D) materials often have a profound impact on various material properties from mechanical to optical to electronic, yet predicting all possible GB formations is a challenge. Here, we introduce a workflow based on an evolutionary algorithm for exploring possible GBs formed at a lateral 2D interface. In a departure from conventional genetic algorithm based structure optimization methods, we perform genetic operations in the near interface region that allow us to be computationally efficient. We benchmark our method using graphene, which is a well-studied 2D material with a wide range of point defects. An empirical potential was used as the surrogate of the evolutionary search. More than 11.5 × 106 structures in total were evaluated for 128 GB orientations, and for each orientation, the ten best structures are recorded. A subset of low energy GBs predicted by empirical potential based search was relaxed by first-principles calculations and used to validate the energetic rank order. With the validated formation energy, we rank-ordered the best 128 GB structures and performed a detailed statistical analysis of primitive rings to find the correlation between the ring distribution and the formation energy. We found that for low energy GBs (below 0.5eV/Å), Stone–Wales defects will dominate, while structures with a higher energy (0.5–1.1eV/Å) show an increasing population of heptagons and nine-membered rings to form seven-nine defect pairs. For structures with energy higher than 1.1eV/Å, the percentage of octagons and nine-membered rings increases, which indicates that these two types of rings are not energetically favorable. Our proposed methodology is broadly applicable to explore defective low dimensional materials and represents a powerful tool that enables a systematic search of GBs of lateral interfaces for 2D materials.

Zhang, Jianan↗
DOE OSTI2026

An immersed interface method for microstructure-scale electrochemical battery models: numerical formulation and performance portable implementation

We present the numerical formulation, verification, and performance portable implementation of an immersed interface method for microstructure scale electrochemical modeling of batteries. The innovation in this approach is the resolution of chemical species and electrostatic potential discontinuities at active interfaces without the use of interface conforming unstructured grids. A unified formulation on Cartesian grids for all domains (electrodes and electrolyte) is used with interfacial flux conditions applied using volume fraction or “color” function gradients. We have developed one dimensional and two dimensional test cases with analytic solutions for electrochemical modeling using which we verified the consistency and accuracy of our scheme. Our solver is also validated against solutions from a macroscale model and an unstructured multi-subdomain solver for a full lithium ion cell. We then demonstrated the utility of our solver on an image-based complex battery electrode microstructure at high charging rate. Our technique also exhibits good scalability on distributed memory architectures using central processing units (CPU), with problem sizes up to 1.8 billion degrees of freedom and with 5400 ranks. Initial performance studies of our open-source performance portable solver showed about 70 times speed up using a graphics processing unit (GPU) compared to single compute core for a problem with 4 million cells.

25 ENERGY STORAGE↗
DOE OSTI2021

Local and Global Sensitivity Analysis of a Reactive Transport Model Simulating Floodplain Redox Cycling

Reactive transport models (RTMs) are essential tools that simulate the coupling of advective, diffusive, and reactive processes in the subsurface, but their complexity makes them difficult to understand, develop and improve without accompanying statistical analyses. Although global sensitivity analysis (SA) can address these issues, the computational cost associated with most global SA techniques limits their use with RTMs. In this study, we apply distance-based generalized sensitivity analysis (DGSA), a novel and computationally efficient method of global SA, to a floodplain-scale RTM and compare DGSA results to those from local SA. Our test case focuses on the impact of 17 uncertain environmental parameters on spatially and temporally variable redox conditions within a floodplain aquifer. The input parameters considered include flow and diffusion rates, geochemical reaction rates, and the spatial distribution of sediment facies. Sensitivity was evaluated for three distinct components of the model response, encompassing both multidimensional and categorical output. Parameter rankings differ between local SA and DGSA, due to nonlinear effects of individual parameters and interaction effects between parameters. DGSA results show that fluid residence time, which is controlled by aquifer permeability, generally exerts a stronger control on redox conditions than do geochemical reaction rates. Sensitivity indices also demonstrate that sulfate reduction is key for establishing and maintaining reducing conditions throughout the aquifer. Furthermore, these results provide insights into the key drivers of heterogeneous redox processes within floodplain aquifers, as well as the main sources of uncertainty when modeling complex subsurface systems.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1977

The influence of various test plans on mission reliability

Methods have been developed for the evaluation of cost effective vibroacoustic test plans for Shuttle Spacelab payloads. The shock and vibration environments of components have been statistically represented, and statistical decision theory has been used to evaluate the cost effectiveness of five basic test plans with structural test options for two of the plans. Component, subassembly, and payload testing have been performed for each plan along with calculations of optimum test levels and expected costs. The tests have been ranked according to both minimizing expected project costs and vibroacoustic reliability. It was found that optimum costs may vary up to $6 million with the lowest plan eliminating component testing and maintaining flight vibration reliability via subassembly tests at high acoustic levels.

Stahle, C. V.↗
DOE OSTI2025

A machine learning method of modern urban building energy modeling: A case study of Chicago

Urban-scale building energy modeling is vital for urban planning. However, it can be challenging to assimilate reliable non-geometry building data for urban-scale modeling without extensive investment. Here, this study introduces a novel approach to developing modern urban-scale building energy stock data using geographic information systems and machine learning algorithms without necessarily requiring pre-supplied non-geometric metadata. The proposed framework integrates building footprint and height data to estimate gross floor areas, and matches each building to a pool of candidate records from ComStock or ResStock—filtered to the same county and ranked by geometric similarity—demonstrate a proof-of-concept case study in Chicago for predicting energy use intensity (EUI) using scalable datasets. The model achieved a mean bias error (MBE) of 0.08 kWh/m² and root mean square error (RMSE) of 14.84 kWh/m² under full metadata input for EUI prediction. With only location inputs, the model captured 69.2 % of EUI within predicted ranges. These results demonstrate the model’s potential to support early-stage urban planning, identify candidates for energy-efficient retrofits. By removing the dependency on detailed pre-surveys or extensive building metadata, the approach overcomes a key barrier in traditional urban-scale building energy modeling, illustrating a pathway toward broader and more cost-effective application, though further multi-city validation and improved treatment of pre-1925 buildings are needed.

Energy Use Intensity↗
DOE OSTI2021

Neutron diffraction discriminates between models for the nanoarchitecture of graphene sheets in glassy carbon

Glassy carbon is a chemically inert, biocompatible, disordered material with the graphene sheet as its basic building block. Structural characterisation techniques have so far been unable to provide definitive distinction between the many proposed models for its structure. Computer based simulation methods have made a step forward by predicting structure from interaction potentials, but the results are sensitive to the choice of the potential. Here we use the white neutron beam of the Spallation Neutron Source at Oak Ridge National Laboratory coupled with the SNAP time-of-flight diffractometer to sample the reciprocal space of glassy carbon and calculate accurate radial distribution functions. From the radial distribution information, we determine graphene sheet dimensions, registration, curvature, and assess defect content to rank the proposed structures in terms of their agreement with experimental data. In this work, we find that the recent models derived from empirical potentials give the best agreement.

36 MATERIALS SCIENCE↗
DOE OSTI2020

A long short-term memory embedding for hybrid uplifted reduced order models

In this paper, we introduce an uplifted reduced order modeling (UROM) approach through the integration of standard projection based methods with long short-term memory (LSTM) embedding. Our approach has three modeling layers or components. In the first layer, we utilize an intrusive projection approach to model dynamics represented by the largest modes. The second layer consists of an LSTM model to account for residuals beyond this truncation. This closure layer refers to the process of including the residual effect of the discarded modes into the dynamics of the largest scales. However, the feasibility of generating a low rank approximation tails off for higher Kolmogorov n -width systems due to the underlying nonlinear processes. The third uplifting layer, called super-resolution, addresses this limited representation issue by expanding the span into a larger number of modes utilizing the versatility of LSTM. Therefore, our model integrates a physics-based projection model with a memory embedded LSTM closure and an LSTM based super-resolution model. In several applications, we exploit the use of Grassmann manifold to construct UROM for unseen conditions. We performed numerical experiments by using the Burgers and Navier-Stokes equations with quadratic nonlinearity. Finally, our results show robustness of the proposed approach in building reduced order models for parameterized systems and confirm the improved trade-off between accuracy and efficiency.

42 ENGINEERING↗
DOE OSTI2024

Anomaly Detection in Connected and Autonomous Vehicle Trajectories Using LSTM Autoencoder and Gaussian Mixture Model

Connected and Autonomous Vehicles (CAVs) technology has the potential to transform the transportation system. Although these new technologies have many advantages, the implementation raises significant concerns regarding safety, security, and privacy. Anomalies in sensor data caused by errors or cyberattacks can cause severe accidents. To address the issue, this study proposed an innovative anomaly detection algorithm, namely the LSTM Autoencoder with Gaussian Mixture Model (LAGMM). This model supports anomalous CAV trajectory detection in the real-time leveraging communication capabilities of CAV sensors. The LSTM Autoencoder is applied to generate low-rank representations and reconstruct errors for each input data point, while the Gaussian Mixture Model (GMM) is employed for its strength in density estimation. The proposed model was jointly optimized for the LSTM Autoencoder and GMM simultaneously. The study utilizes realistic CAV data from a platooning experiment conducted for Cooperative Automated Research Mobility Applications (CARMAs). The experiment findings indicate that the proposed LAGMM approach enhances detection accuracy by 3% and precision by 6.4% compared to the existing state-of-the-art methods, suggesting a significant improvement in the field.

33 ADVANCED PROPULSION SYSTEMS↗
NASA NTRS1989

MIL-C-38999 electrical connector applicability tests for on-orbit EVA satellite servicing

MIL-C-38999 electrical connectors were tested for their applicability to the on-orbit EVA satellite servicing environment. The investigation provided a methodical approach to the evaluation of the human-machine interface of these connectors. The physical characteristics of thirty-five MIL-C-38999 connectors were tested in two simulated space environments, the NASA Johnson Space Center Weightless Environment Training Facility and an evacuated glovebox which incorporated the Extravehicular Maneuvering Unit series 3000 gloves. Physical characteristics of the connectors were documented, including operating torque and work profiles. STS crewmembers tested a select group of connectors in two WETF test and subjectively ranked the G&H PMM Wing-Tab connectors as most applicable to the on-orbit servicing environment. WETF performance times indicated that the G&H PMM Wing-Tab connector had the fastest operating time. The evacuated glovebox participants ranked the G&H 64600 Wing-Tab and the G&H PMM Wing-Tab connectors as those most applicable to the on-orbit servicing environment. During the evacuated glovebox tests, the G&H 64600 Wing-Tab connector had the fastest operating time.

Griffin, Thomas J.↗
DOE OSTI2021

A Flexible Power Method for Solving Infinite Dimensional Tensor Eigenvalue Problems

We propose a flexible power method for computing the leftmost, i.e., algebraically smallest, eigenvalue of an infinite dimensional tensor eigenvalue problem, $H x = \lambda x$, where the infinite dimensional symmetric matrix $H$ exhibits a translational invariant structure. We assume the smallest eigenvalue of $H$ is simple and apply a power iteration of $e^{-H}$ with the eigenvector represented in a compact way as a translational invariant infinite Tensor Ring (iTR). Hence, the infinite dimensional eigenvector can be represented by a finite number of iTR cores of finite rank. In order to implement this power iteration, we use a small parameter $t$ so that the infinite matrix-vector operation $e^{-Ht}x$ can efficiently be approximated by the Lie product formula, also known as Suzuki--Trotter splitting, and we employ a low rank approximation through a truncated singular value decomposition on the iTR cores in order to keep the cost of subsequent power iterations bounded. We also use an efficient way for computing the iTR Rayleigh quotient and introduce a finite size iTR residual which is used to monitor the convergence of the Rayleigh quotient and to modify the timestep $t$. In this paper, we discuss 2 different implementations of the flexible power algorithm and illustrate the automatic timestep adaption approach for several numerical examples.

Beeumen, Roel Van↗