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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 OSTI2026

Ab Initio Many Body Quantum Embedding and Local Correlation in Crystalline Materials using Interpolative Separable Density Fitting

We present an efficient implementation of ab initio many-body quantum embedding and local correlation methods for infinite periodic systems through translational symmetry adapted interpolative separable density fitting, an approach which reduces the scaling of the calculations to only linear with the number of k-points. Employing this methodology, we compute correlated ground-state coupled cluster energies within density matrix embedding and local natural orbital correlation frameworks for both weakly and strongly correlated solids, using up to 1000 k-points. By extrapolating the local correlation domains and k-point sampling we further obtain estimates of the full coupled cluster with singles, doubles, and perturbative triples ground-state energies in the thermodynamic limit.

Chemical Physics (physics.chem-ph)↗
DOE OSTI2025

Embedded random phase approximation for magnetic systems: H 2 dissociative adsorption on Fe(110)

The random phase approximation (RPA), a method for treating electron correlation, has been shown to be superior to standard density functional theory (DFT) approximations in numerous cases. However, the RPA’s computational cost is substantially higher than that of DFT, particularly restricting its application to extended surfaces. The recently introduced embedded RPA (emb-RPA) approach [Wei et al., J. Chem. Phys. 159(19), 194108 (2023)] reduces this computational cost by approximately two orders of magnitude. While previous applications of emb-RPA focused on non-spin-polarized systems, here we extend the approach to ferromagnetic ones. Unlike other embedded correlated wavefunction methods, such as embedded complete active space self-consistent field theory, emb-RPA is advantageous for spin-polarized systems because the RPA is compatible with unrestricted DFT solutions, which are eigenfunctions of the spin angular momentum operator S z but not the total spin-squared operator S 2 . By applying emb-RPA with specific magnetization constraints, we achieved a speedup of two to three orders of magnitude (one order when accounting for the one-time embedding potential optimization cost) with only small errors (∼50 meV) compared to full periodic RPA. Moreover, emb-RPA significantly reduces the over-binding errors of DFT approximations. In conclusion, we anticipate that the acceleration enabled by the spin-polarized emb-RPA approach will broaden the applicability of RPA to magnetic materials.

Density functional theory↗
DOE OSTI2026

ZTF-SEDm Type Ia supernova sample for Twins Embedding spectrophotometric standardization

Aims. This paper has two aims: the first aim is to build a large homogeneous spectrophotometric sample of Type Ia supernovae (SNe Ia) from the second data release of the Zwicky Transient Facility (ZTF DR2). We used the spectrum sample from the low-resolution ( R ∼ 100) SEDmachine (SEDm) Integral Field Spectrograph (IFS) that gathered 3069 spectra. This is one of the largest samples of such collections that can attempt to reproduce the Twins Embedding (TE) spectrophotometric standardization method. This is our second objective. The method was developed based on high-quality spectra from 200 SNe Ia of the Nearby Supernova factory (SNfactory) and led to an exceptionally low value of 0.073 mag for the intrinsic scatter. Methods. As the SEDm is not designed as a spectrophotometric instrument, we first improved the flux-calibration accuracy of the SN Ia spectrum sample using the ZTF photometric data, which were calibrated at the percent level. We corrected the spectra for second-order polynomials, fitted by comparing the synthetic photometry in the ZTF g , r , i filters with the light-curve (LC) data. We then applied the three steps of the TE parameterization to a subset of 783 ZTF SN spectra near maximum light while comparing results from SNfactory and ZTF. We finally analyzed the standardization methods based on the TE parameters. Results. The precision of the phase-correction model, which is the first step of the TE, is estimated at 0.01 mag in g band based on ZTF data. Despite the challenge posed by the spectrum-extraction pipeline associated with the SEDm (flux calibration, leftover host signal, low signal-to-noise ratio, and low resolution), we applied a first standardization in color based on the second step of the TE, called read between the lines (RBTL), to the ZTF sample. We reached a Hubble residual scatter of 0.153 mag, all in normalized median absolute deviation, which is to be compared to the ∼0.11 mag obtained with the SNfactory data. The SALT color and stretch standardization reaches a scatter of 0.164 mag for the same ZTF SN Ia sample, and its host steps are ∼0.1 mag and zero for RBTL. When considering the scatter due to the redshift error and flux calibration error, we estimated a RBTL scatter of ∼0.129 mag for this ZTF sample as an upper limit because we identified an additional contribution from a systematic error in color. We tested the standardization based on the nonlinear TE parameters, and, as expected from the low spectrum quality, it did not improve the overall dispersion. Conclusions. We release 1897 flux calibrated spectra of 1607 SNe Ia with an estimated photometric accuracy of 0.07 mag. We further demonstrate that some amount of spectrophotometric SN Ia standardization can be done with limited-quality spectra. The RBTL standardization is more efficient than that of SALT with one parameter less, and the resulting host steps are consistent with zero. This makes it less prone to astrophysical bias. For future spectroscopic surveys, targeting the extraction pipeline for a thorough flux calibration and good signal-to-noise ratio would enable us to compute the full TE standardization, which would further reduce the scatter in the distance estimate.

Ganot, C↗
DOE OSTI2026

Exploring the Feasibility of Modern Fiber Optics in Offshore Mooring Condition Monitoring

This project explored the feasibility of using fiber-optic sensing technologies for condition monitoring of offshore synthetic mooring lines used in marine renewable energy systems. The work focused on evaluating optical fiber materials, interrogation methods, and rope-embedment approaches capable of enabling distributed strain or elongation measurements along mooring lines.

16 TIDAL AND WAVE POWER↗
DOE OSTI2025

Exploring Continuous Seismic Data at an Industry Facility Using Unsupervised Machine Learning

Seismic data recorded at industrial sites contain valuable information on anthropogenic activities. With advances in machine learning and computing power, new opportunities have emerged to explore the seismic wavefield in these complex environments. We applied two unsupervised machine learning algorithms to analyze continuous seismic data collected from an industrial facility in Texas, United States. The Uniform Manifold Approximation and Projection for Dimension Reduction algorithm was used to reduce the dimensionality of the data and generate 2D embeddings. Then, the Hierarchical Density-Based Spatial Clustering of Applications with Noise method was employed to automatically group these embeddings into distinct signal clusters. Our analysis of over 1400 hr (around 59 days) of continuous seismic data revealed five and seven signal clusters at two separate stations. At both stations, we identified clusters associated with background noise and vehicle traffic, with the latter’s temporal patterns aligning closely with the facility’s work schedule. Furthermore, the algorithms detected signal clusters from unknown sources and underline the ability of unsupervised machine learning for uncovering previously unrecognized patterns. Our analysis demonstrates the effectiveness of unsupervised approaches in examining continuous seismic data without requiring prior knowledge or pre-existing labels.

58 GEOSCIENCES↗
DOE OSTI2024

AOI [1] Advanced Manufacturing of Ceramic Anchors with Embedded Sensors for Process and Health Monitoring of Coal Boilers

Researchers at West Virginia University (WVU) developed methods to fabricate and test ceramic anchors with an embedded sensor technology for monitoring the health and processing conditions within pulverized coal (PC) and fluidized-bed combustion (FBC) boiler systems. The technology included the development of advanced manufacturing processes for 2D/3D printing electroceramic (conductive ceramic) sensor designs within the ceramic anchor microstructure during the manufacturing process. This advanced manufacturing process would allow for the precise control of local microstructure and composition in order to engineer layer-by-layer any protective and electrically active materials within the refractory anchor. This 3D printing technology would permit the rapid and controlled design of the refractory microstructure and embedded sensor design throughout the volume of the ceramic anchor. The work also included a method to interconnect the sensors to boiler shell through the anchor clamp, where the sensor signals will be processed by low-power electronics and transmitted wirelessly to a central processing hub. The end-goal of the program was to produce a ceramic anchor sensor system which would be ready for implementation within a coal boiler, and/or other similar refractory liner systems (such as that in the glass and metal manufacturing areas). The project objectives were to: 1) Define the chemical and microstructural stability, in addition to the electrical properties, of oxide and non-oxide ceramic composites to be embedded within the ceramic anchor compositions that may operate up to 1400ºC; 2) Develop and implement the 2D/3D printing technology to pattern and control the microstructure of the ceramic anchor and embedded sensor circuits; 3) Develop an interconnect technology which will permit easy installation of the ceramic anchors and signal collection at the boiler shell; 4) Develop low power analog electronics and wireless communication hardware to efficiently collect the sensor signal at each processing unit and transmit data to a central hub for data analysis; 5) Demonstrate the smart ceramic anchor system for temperature and liner fracture within a high-temperature processing unit, such as a boiler furnace or glass melting furnace floor/wall liner.

20 FOSSIL-FUELED POWER PLANTS↗
DOE OSTI2026

Heliostat sizing methodology for concentrating solar thermal industrial process heat projects

This study presents a method to obtain a heliostat size that minimizes the levelized cost of heat (LCOH) of a heliostat-based concentrating solar thermal system for applications of solar heating for industrial processes at operating temperatures from 565 to 1550°C. The method extends prior work by embedding a routine for system design that obtains near-optimal subsystem sizes, increasing the fidelity of drive cost functions, and adding an optical performance model to supplement the previously developed cost models, which we update to reflect current pricing trends. An illustrative business case is developed for Daggett, California, targeting specified annual thermal energy outputs of 50 to 400 GWh th . Optical performance is modeled using verified estimates from the literature. A surrogate heliostat cost model, derived from commercial heliostat designs and scaled for production volume, installation, and operations and maintenance costs, is used to develop cost functions. Results show that heliostat size strongly affects the LCOH, producing a characteristic U-shaped trend with a robust near-optimal window of 7-20 m 2 ; the heliostat size producing the lowest project cost in our study grows slightly as the project size increases, and is reduced as the operating temperature increases. The findings in this study are consistent with the general trend of smaller heliostats being deployed at existing projects for high-temperature industrial process heat and reflect the significant reduction in power electronics and other per-heliostat costs. The methodology we propose is general and can be tailored to revised cost curves as the technology continues to evolve.

14 SOLAR ENERGY↗
DOE OSTI2025

Online learning of quadratic manifolds from streaming data for nonlinear dimensionality reduction and nonlinear model reduction

Here, this work introduces an online greedy method for constructing quadratic manifolds from streaming data, designed to enable in situ analysis of numerical simulation data on the Petabyte scale. Unlike traditional batch methods, which require all data to be available upfront and take multiple passes over the data, the proposed online greedy method incrementally updates quadratic manifolds in one pass as data points are received, eliminating the need for expensive disk input/output operations as well as storing and loading data points once they have been processed. A range of numerical examples demonstrate that the online greedy method learns accurate quadratic manifold embeddings while being capable of processing data that far exceed common disk input/output capabilities and volumes as well as main-memory sizes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Heliostat Sizing Methodology for Solar Heat for Industrial Processes

This study presents a method to obtain a heliostat size that minimizes the levelized cost of a heliostat-based concentrating solar thermal system for industrial process heat (IPH) applications at operating temperatures from 565 to 1550 degrees Celsius. The method extends prior work by embedding a routine for system design that obtains near-optimal subsystem sizes, increasing the fidelity of drive cost functions, and adding an optical performance model. An illustrative business case is developed for Daggett, California, targeting specified annual thermal energy outputs of 50 to 400 GWhth. Optical performance is modeled using verified estimates from the literature. A surrogate heliostat cost model, derived from commercial heliostat designs and scaled for production volume, installation, and operations and maintenance costs, is used to develop cost functions. Results show that heliostat size strongly affects the levelized cost of heat (LCOH), producing a characteristic U-shaped trend with a robust near-optimal window of 8 - 12 m2; the heliostat size producing the lowest project cost in our study grows slightly as the project size increases, and is reduced as the operating temperature increases. The findings in this study are consistent with the general trend of smaller heliostats under deployment at existing projects for high-temperature industrial process heat and reflect the significant reduction in power electronics and other per-heliostat costs. The methodology we propose is general and can be tailored to revised cost curves as the technology continues to evolve.

14 SOLAR ENERGY↗
DOE OSTI2025

DOME: Directional medical embedding vectors from Electronic Health Records

Motivation: The increasing availability of Electronic Health Record (EHR) systems has created enormous potential for translational research. Recent developments in representation learning techniques have led to effective large-scale representations of EHR concepts along with knowledge graphs that empower downstream EHR studies. However, most existing methods require training with patient-level data, limiting their abilities to expand the training with multi-institutional EHR data. On the other hand, scalable approaches that only require summary-level data do not incorporate temporal dependencies between concepts. Methods: We introduce a DirectiOnal Medical Embedding (DOME) algorithm to encode temporally directional relationships between medical concepts, using summary-level EHR data. Specifically, DOME first aggregates patient-level EHR data into an asymmetric co-occurrence matrix. Then it computes two Positive Pointwise Mutual Information (PPMI) matrices to correspondingly encode the pairwise prior and posterior dependencies between medical concepts. Following that, a joint matrix factorization is performed on the two PPMI matrices, which results in three vectors for each concept: a semantic embedding and two directional context embeddings. They collectively provide a comprehensive depiction of the temporal relationship between EHR concepts. Results: We highlight the advantages and translational potential of DOME through three sets of validation studies. First, DOME consistently improves existing direction-agnostic embedding vectors for disease risk prediction in several diseases, for example achieving a relative gain of 5.5% in the area under the receiver operating characteristic (AUROC) for lung cancer. Second, DOME excels in directional drug-disease relationship inference by successfully differentiating between drug side effects and indications, correspondingly achieving relative AUROC gain over the state-of-the-art methods by 10.8% and 6.6%. Finally, DOME effectively constructs directional knowledge graphs, which distinguish disease risk factors from comorbidities, thereby revealing disease progression trajectories. The source codes are provided at https://github.com/celehs/Directional-EHRembedding.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2026

Towards utility-scale electronic structure with sample-based quantum bootstrap embedding

One of the main applications for which quantum computers are hoped to find utility is in simulating ground state energies and other observables of molecular chemical systems. The recently proposed sample-based diagonalization method is a readily implementable method for this task on current-day hardware using short circuit depths and has been demonstrated on as many as 85 qubits in recent studies. In this work, we combine the recently proposed quantum bootstrap embedding (QBE) method with sampled-based diagonalization (QBE-SQD) and present the first benchmarking study of the QBE method on real quantum hardware, ibm_pittsburgh, a Heron r3 processor with 156 qubits. Our test system is a hydrogen ring with 8 hydrogen atoms in the cc-pVDZ basis. We show that for this system, QBE-SQD using an active space of (8e, 19o) per fragment with a 43 qubit footprint produces a ground state energy accuracy which exceeds that of an SQD calculation with an (8e, 30o) active space with a 67 qubit footprint when using a comparable number of Slater determinants. This demonstrates that the use of quantum bootstrap embedding techniques is a promising path towards extending the capabilities of state-of-the-art quantum eigensolvers on near-term devices.

Bierman, Joel [North Carolina State University, Ra↗
DOE OSTI2025

Chemical templates of the Central Molecular Zone

Context . The Central Molecular Zone (CMZ) of the Milky Way exhibits extreme conditions, including high gas densities, elevated temperatures, enhanced cosmic-ray ionization rates, and large-scale dynamics. This makes it a perfect laboratory for astrochemical studies. With large-scale molecular surveys revealing increasing chemical and physical complexity in the CMZ, it is essential to develop robust methods to decode the chemical information embedded in this extreme region. Aims . A key step to interpreting the molecular richness found in the CMZ is building chemical templates tailored to its diverse conditions. In particular, understanding how CMZ environments affect shock and protostellar chemistry is crucial. The combined impact of high ionization, elevated temperatures, and dense gas remains insufficiently explored for observable tracers. Methods . For this study, we utilized UCLCHEM , a gas-grain time-dependent chemical model, to link physical conditions with their corresponding molecular signatures and identify key tracers of temperature, density, ionization, and shock activity. To achieve this, we ran a grid of models of shocks and protostellar objects representative of typical CMZ conditions, focusing on 24 species, including complex organic molecules. Results . Shocked and protostellar environments show distinct evolutionary timescales (≲10 4 vs. ≳10 4 years); 300 K emerges as a key temperature threshold for chemical differentiation. We find that cosmic-ray ionization and temperature are the main drivers of chemical trends. HCO + , H 2 CO, and CH 3 SH trace ionization, while HCO, HCO + , CH 3 SH, CH 3 NCO, and HCOOCH 3 show consistent abundance contrasts between shocks and protostellar regions over similar temperature ranges. Conclusions . We characterized the behavior of 24 species in protostellar and shock-related environments. While our models underpredict some complex organics in shocks, they reproduce observed trends for most species, supporting scenarios involving a need for recurring shocks in Galactic Center clouds and enhanced ionization toward Sgr B2(N2). Future work should assess the role of shock recurrence and metallicity in shaping chemistry.

Galaxy: center↗
DOE OSTI2026

Divertor detachment and heat exhaust mitigation control in KSTAR with tungsten divertor

KSTAR has recently undergone an upgrade to use a new tungsten divertor to run experiments in ITER-relevant scenarios. Even with a high melting point of tungsten, it is important to control the heat flux impinging on tungsten divertor targets to minimize sputtering and contamination of the core plasma. Heat flux on the divertor is often controlled by increasing the degree of detachment of scrape-off layer plasma from the target plates. In this work, we have demonstrated successful divertor detachment and heat exhaust dissipation control experiments using two different methods. The first method uses attachment fraction as a control variable which is estimated using ion saturation current measurements from embedded Langmuir probes in the divertor. The second method uses a novel machine-learning-based surrogate model of 2D UEDGE simulation database, DivControlNN. We demonstrated running inference operation of DivControlNN in realtime to estimate heat flux at the divertor and use it as the control variable in a feedback loop with impurity gas flow. We present interesting insights from these experiments including a systematic approach to tuning controllers and discuss future improvements in the control infrastructure and control variables for future burning plasma experiments.

KSTAR tungsten divertor operations↗
DOE OSTI2025

FluxRETAP: a REaction TArget Prioritization genome-scale modeling technique for selecting genetic targets

MOTIVATION: Metabolic engineering is rapidly evolving as a result of new advances in synthetic biology tools and automation platforms that enable high throughput strain construction, as well as the development of machine learning tools (ML) for biology. However, selecting genetic engineering targets that effectively guide the metabolic engineering process is still challenging. ML can provide predictive power for synthetic biology, but current technical limitations prevent the independent use of ML approaches without previous biological knowledge. RESULTS: Here, we present FluxRETAP, a simple and computationally inexpensive method that leverages the prior mechanistic knowledge embedded in genome-scale models for suggesting targets for genetic overexpression, downregulation or deletion, with the final goal of increasing the production of a desired metabolite. This method can provide a list of desirable engineering targets that can be combined with current ML pipelines. FluxRETAP captured 100% of reaction targets experimentally verified to improve Escherichia coli isoprenol production, 50% of targets that experimentally improved taxadiene production in E. coli and ∼60% of genetic targets from a verified minimal constrained cut-set in Pseudomonas putida, while providing additional high priority targets that could be tested. Overall, FluxRETAP is an efficient algorithm for identifying a prioritized list of testable genetic and reaction targets. AVAILABILITY AND IMPLEMENTATION: FluxRETAP is implemented in python and released under the creative commons license. The implementation and code are freely available at: https://github.com/JBEI/FluxRETAP.

Czajka, Jeffrey J↗
DOE OSTI2026

Latent Catalysis as a Platform for Accessing Diverse Material Properties in Vat Photopolymerization 3D Printing

Vat photopolymerization (VP) 3D printing is an attractive strategy to manufacture customized polymer parts. The properties of printed materials are limited by the need to employ a low viscosity liquid resin and achieve rapid polymerization kinetics. To circumvent this limitation, dual‐cure methods have been developed using reagents embedded in the liquid resin formulation; however, the reagent‐based approach requires the discovery and optimization of new chemistry for each desired material. Here, in this work, we demonstrate a catalytic, dual‐cure platform that enables access to both Nylon‐6 and polyester interpenetrating networks through VP 3D printing under a universal approach. Structure–reactivity relationships of the latent NHC catalysts led to the identification of a magnesium chloride–NHC adduct as a latent catalyst that is orthogonal to radical polymerization and can be unmasked at elevated temperatures post‐printing to initiate ring‐opening polymerization of lactones and lactams. This strategy results in access to semicrystalline materials, which are a challenging morphology to access via VP 3D printing, that have attractive mechanical properties and can be printed at high resolution. This work represents the first photochemical‐based 3D printing of Nylon‐based materials and demonstrates the value of catalytic approaches to access new material properties in VP 3D printing.

Colliver, Cali N. [University of North Carolina, C↗
DOE OSTI2024

HAPPA: A Modular Platform for HPC Application Resilience Analysis with LLMs Embedded

High-performance computing (HPC) systems are increasingly vulnerable to soft errors, which pose significant challenges in maintaining computational accuracy and reliability. Predicting the resilience of HPC applications to these errors is crucial for robust code protection and detailed resilience analysis. In this study, we present HAppA, a modular platform designed for HPC Application Resilience Analysis. Embedding Large Language Models (LLMs), HAppA addresses understanding the context information of long code sequences typical in HPC applications. HAppA implements a novel code representation module that chunks the code into fixed-size segments and aggregates the embeddings of these segments. Three aggregation methods have been explored: MeanPooling, MaxPooling, and LSTM-based techniques. We built a DAtaset for REsilience analysis using Fault Injection (FI), named DARE. Using our DARE dataset, HAppA is trained for regression prediction tasks. Our evaluation results demonstrate the predictive accuracy of HAppA compared to other models, particularly noting that the LSTM-based aggregation method -- HAppA-LSTM -- achieves a mean squared error (MSE) of 0.078 for SDC prediction, surpassing the existing state-of-the-art PARIS model, which recorded an MSE of 0.1172. Additionally, HAppA with the KeyBERT model extracts a list of keywords representing the source code. A comprehensive importance analysis of these keywords further elucidates the code patterns contributing to the error rate. These findings highlight the effectiveness of HAppA in analyzing the resilience of HPC applications and establish a new benchmark for predictive accuracy in resilience.

Jiang, Hailong [Kent State University]↗
DOE OSTI2025

Accelerating Embedding Potential Optimization by Reconstructing the Pseudo-Valence Electron Density

Density functional embedding theory (DFET) enables use of electronic structure methods with higher accuracy than density functional theory in a local region, with applications thus far ranging from (photo/electro)catalysis to reactions in solution. DFET partitions a large collection of atoms into smaller groups that interact via a shared embedding (interaction) potential V emb , determined via functional optimization. The optimized effective potential (OEP) process used to optimize V emb is time-consuming and becomes a computational bottleneck due to sharp, oscillating features of V emb near nuclei. Here, similar to pseudopotential theory, by reconstructing electron densities used in the OEP process from smoother pseudo-valence-only (PVO) electron densities as proxies for total densities of the full system and subsystems, we can retain accuracy in the embedded electronic structure calculations while potentially reducing the overhead of V emb construction, within the projector augmented-wave (PAW) formalism. We explore three different chemical reactions as exemplars to test PVO–DFET, namely, H 2 dissociative adsorption on a Cu(111) surface, H 2 O adsorption on a Pt(111) surface, and aqueous [Ca 2+ –SO 4 2– ] ion-pair formation. The PVO approximation works well for all three systems with minimal loss of accuracy (∼10–70 meV error relative to the original exact-derivative (ED) approach) while accelerating V emb generation for the Cu and Pt systems respectively by 20× and 5×. Given proper numerical convergence parameters, the spatial distributions of differences between PVO- and ED-based V emb outside the core regions are small, explaining the exceptional agreement between the two approaches. Finally, we anticipate that this more efficient PVO–DFET approximation will be useful whenever computation of V emb is much more expensive than subsequent embedded high-level electron correlation calculations.

approximation↗
DOE OSTI2025

Visualizing Temporal Topic Embeddings with a Compass

—Dynamic topic modeling is useful at discovering the development and change in latent topics over time. However, present methodology relies on algorithms that separate document and word representations. This prevents the creation of a meaningful embedding space where changes in word usage and documents can be directly analyzed in a temporal context. This paper proposes an expansion of the compass-aligned temporal Word2Vec methodology into dynamic topic modeling. Such a method allows for the direct comparison of word and document embeddings across time in dynamic topics. This enables the creation of visualizations that incorporate temporal word embeddings within the context of documents into topic visualizations. In experiments against the current state-of-the-art, our proposed method demonstrates overall competitive performance in topic relevancy and diversity across temporal datasets of varying size. Simultaneously, it provides insightful visualizations focused on temporal word embeddings while maintaining the insights provided by global topic evolution, advancing our understanding of how topics evolve over time.

Cluster analysis↗