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NASA NTRSDate not supplied

Harmonized Sentinel-1 SAR Global River Geometry and Inundation Database

Satellite-based observations on river geometries are sporadic in time, space, or both. Most satellite-based surface water maps, river widths, water surface elevations (WSE), slopes, and bathymetry are asynchronized in time and space. The current configuration of satellites such as Sentinel-6 measured the WSE but is missing the river width, slopes, and depths. To advance hydrological sciences research, there is a need to produce a harmonized time series of river geometry data of non-SWOT satellites in partnership with the upcoming SWOT mission. The SWOT satellite will measure river width, height, and slope but missing river depth measurements in space and time. Further, none of these current satellites measure the WSE, river width, and slopes synchronously. In this work, we use the Sentinel-1 SAR satellite data archive from 2015 to the present to create a global river width and surface water database at the reach scale. A modified version of the Sentinel SAR surface water classification algorithm from ASF is used to quantify the surface water extent on the stream approximately every six days (at the equator) at 10m spatial resolution globally. This 10m water mask is fed into a workflow to quantify the river widths, surface water inundations, slopes, and synthetic bathymetry in SWORD (SWOT River Database) stream networks. A Satellite HAND is used to address the cloud obscured surface water observations using a trained machine learning algorithm. We use WSE derived from the Global Water Monitor from NASA GSFC, Hydroweb from LEGOS, and ICESat-2 to harmonize the WSE observation. And Landsat-8/9 and Sentinel-2 water observations to fill the gaps in the Sentinel-1 SAR database. We use Congo River Basin as a test case where we have more than 500 radar altimetry-based WSE, continuous series of Sentinel-1, ICESat-2, Landsat-8/9, and Sentinel-2 observations. A Congo River hydrologic model is used to generate the streamflow discharge. The satellite observed river reaches are assimilated with the stream flows computed by the routing models. And the downstream reaches in the river network without satellite observations get optimized for discharge/river geometry at each observation cycle. Our final product is a harmonized river geometry dataset (reach's water extent, WSE, slope, synthetic bathymetry) for Congo Basin's SWORD reaches.

Chandana Gangodagamage↗

DOE OSTI2025

Feature engineering descriptors, transforms, and machine learning for grain boundaries and variable-sized atom clusters

Abstract Obtaining microscopic structure-property relationships for grain boundaries is challenging due to their complex atomic structures. Recent efforts use machine learning to derive these relationships, but the way the atomic grain boundary structure is represented can have a significant impact on the predictions. Key steps for property prediction common to grain boundaries and other variable-sized atom clustered structures include: (1) describing the atomic structure as a feature matrix, (2) transforming the variable-sized feature matrix to a fixed length common to all structures, and (3) applying a machine learning algorithm to predict properties from the transformed matrices. We examine how these steps and different combinations of engineered features impact the accuracy of grain boundary energy predictions using a database of over 7000 grain boundaries. Additionally, we assess how different engineered features support interpretability, offering insights into the physics of the structure-property relationships.

36 MATERIALS SCIENCE↗

DOE OSTI2024

A high-throughput workflow to analyze sequence-conformation relationships and explore hydrophobic patterning in disordered peptoids

Understanding how a macromolecule’s primary sequence governs its conformational landscape is crucial for elucidating its function, yet these design principles are still emerging for macromolecules with intrinsic disorder. Herein, we introduce a high-throughput workflow that implements a practical colorimetric conformational assay, introduces a semi-automated sequencing protocol using matrix-assisted laser desorption/ionization and tandem mass spectrometry (MALDI-MS/MS), and develops a generalizable sequence-structure algorithm. Using a model system of 20mer peptidomimetics containing polar glycine and hydrophobic N-butylglycine residues, we identified nine classifications of conformational disorder and isolated 122 unique sequences across varied compositions and conformations. Conformational distributions of three compositionally identical library sequences were corroborated through atomistic simulations and ion mobility spectrometry coupled with liquid chromatography. A data-driven strategy was developed using existing sequence variables and data-derived “motifs” to inform a machine-learning algorithm toward conformation prediction. Here, this multifaceted approach enhances our understanding of sequence-conformation relationships and offers a powerful tool for accelerating the discovery of materials with conformational control.

data-driven analysis↗

NASA NTRS2004

Automatic Generation of Algorithms for the Statistical Analysis of Planetary Nebulae Images

Analyzing data sets collected in experiments or by observations is a Core scientific activity. Typically, experimentd and observational data are &aught with uncertainty, and the analysis is based on a statistical model of the conjectured underlying processes, The large data volumes collected by modern instruments make computer support indispensible for this. Consequently, scientists spend significant amounts of their time with the development and refinement of the data analysis programs. AutoBayes [GF+02, FS03] is a fully automatic synthesis system for generating statistical data analysis programs. Externally, it looks like a compiler: it takes an abstract problem specification and translates it into executable code. Its input is a concise description of a data analysis problem in the form of a statistical model as shown in Figure 1; its output is optimized and fully documented C/C++ code which can be linked dynamically into the Matlab and Octave environments. Internally, however, it is quite different: AutoBayes derives a customized algorithm implementing the given model using a schema-based process, and then further refines and optimizes the algorithm into code. A schema is a parameterized code template with associated semantic constraints which define and restrict the template s applicability. The schema parameters are instantiated in a problem-specific way during synthesis as AutoBayes checks the constraints against the original model or, recursively, against emerging sub-problems. AutoBayes schema library contains problem decomposition operators (which are justified by theorems in a formal logic in the domain of Bayesian networks) as well as machine learning algorithms (e.g., EM, k-Means) and nu- meric optimization methods (e.g., Nelder-Mead simplex, conjugate gradient). AutoBayes augments this schema-based approach by symbolic computation to derive closed-form solutions whenever possible. This is a major advantage over other statistical data analysis systems which use numerical approximations even in cases where closed-form solutions exist. AutoBayes is implemented in Prolog and comprises approximately 75.000 lines of code. In this paper, we take one typical scientific data analysis problem-analyzing planetary nebulae images taken by the Hubble Space Telescope-and show how AutoBayes can be used to automate the implementation of the necessary anal- ysis programs. We initially follow the analysis described by Knuth and Hajian [KHO2] and use AutoBayes to derive code for the published models. We show the details of the code derivation process, including the symbolic computations and automatic integration of library procedures, and compare the results of the automatically generated and manually implemented code. We then go beyond the original analysis and use AutoBayes to derive code for a simple image segmentation procedure based on a mixture model which can be used to automate a manual preproceesing step. Finally, we combine the original approach with the simple segmentation which yields a more detailed analysis. This also demonstrates that AutoBayes makes it easy to combine different aspects of data analysis.

Fischer, Bernd↗

NASA NTRS2021

Predicting Arrival and Departure Runway Assignments with Machine Learning

Runway assignments at major airports are made by air traffic controllers subject to various constraints, and to achieve various objectives. In this research, we describe our efforts training machine learning (ML) models to predict both departure and arrival runway assignments using an entirely data-driven approach. This approach is compared to existing rule-based approaches developed in previous research using input from Subject Matter Experts. The models have features derived from various FAA data feeds, and leverage multiple machine learning algorithms. Results for models trained for nine major U.S. airports are described and compared to one another across various important dimensions. Particular attention was paid to developing a repeatable framework for training these models so the approach could be scaled to other airports, and to developing models that are useful in a real-time environment. In addition, the models were designed to be functional in a real-time environment to support NASA’s ATD-2 project, as part of an ML-powered shadow system to compare against the performance of the fielded system.

machine learning↗

NASA NTRS2021

Predicting Arrival and Departure Runway Assignments with Machine Learning

machine learning↗

NASA NTRS2024

Automatic Detection and Classification of Aurora in THEMIS All‐Sky Images

We report a novel machine-learning algorithm for automatically detecting and classifying aurora in all–sky images (ASI) that is largely trained without requiring ground–truth labels. By including a small number of labeled images, we are able to automatically label all of the approximately 700 million images in the Time History of Events and Macroscale Interactions during Substorms (THEMIS) ASI data set from 2008 to 2022. We use a two–stage approach. In the first stage, we adapt the Simple framework for Contrastive Learning of Representations (SimCLR) algorithm to learn latent representations of THEMIS all–sky images. We then finetune a classifier network on the latent representations our model learns of the manually labeled Oslo aurora THEMIS (OATH) data set. We demonstrate that this two–stage approach achieves excellent classification results on data for which there is no current ML classification benchmark. The outcome of this work will facilitate efficient information retrieval for researchers interested in specific categories of aurora and will enable large scale statistical studies and machine learning analyses of THEMIS all–sky images that have not previously been possible. To demonstrate possible ways to utilize this database, we performed a statistical analysis of the occurrence rates of auroral labels with respect to solar wind parameters, interplanetary magnetic field vector, and geomagnetic indices. We further investigate the occurrence rates of auroral phenomena in the annotated data set and their geoeffectiveness by utilizing the co–located THEMIS ground magnetometer data set.

Jeremiah W Johnson↗

NASA NTRS2018

Remote Sensing of CDOM, CDOM Spectral Slope, and Dissolved Organic Carbon in the Global Ocean

A Global Ocean Carbon Algorithm Database (GOCAD) has been developed from over 500 oceanographic field campaigns conducted worldwide over the past 30 years including in situ reflectances and coincident satellite imagery, multi- and hyperspectral Chromophoric Dissolved Organic Matter (CDOM) absorption coefficients from 245–715 nm, CDOM spectral slopes in eight visible and ultraviolet wavebands, dissolved and particulate organic carbon (DOC and POC, respectively), and inherent optical, physical, and biogeochemical properties. From field optical and radiometric data and satellite measurements, several semi-analytical, empirical, and machine learning algorithms for retrieving global DOC, CDOM, and CDOM slope were developed, optimized for global retrieval, and validated. Global climatologies of satellite-retrieved CDOM absorption coefficient and spectral slope based on the most robust of these algorithms lag seasonal patterns of phytoplankton biomass belying Case 1 assumptions, and track terrestrial runoff on ocean basin scales. Variability in satellite retrievals of CDOM absorption and spectral slope anomalies are tightly coupled to changes in atmospheric and oceanographic conditions associated with El Niño Southern Oscillation (ENSO), strongly covary with the multivariate ENSO index in a large region of the tropical Pacific, and provide insights into the potential evolution and feedbacks related to sea surface dissolved carbon in a warming climate. Further validation of the DOC algorithm developed here is warranted to better characterize its limitations, particularly in mid-ocean gyres and the southern oceans.

Dissolved organic carbon↗

NASA NTRSDate not supplied

Using Coordinated, Multi-Agent Platforms for Dynamic Ocean Worlds Science

Planetary science missions have the opportunity to enhance science return through deployment of autonomous capabilities designed to dynamically respond to new information. Future outer solar system missions to ocean worlds in particular would benefit from this technology - intelligent science payloads (ISP) - because it would allow for a coordinated, near real-time response to ephemeral ‘events’ such as plumes, tectonism, surface implantation, volatile releases, thermal and magnetic anomalies, or radiation, as well as increasing the cadence and coverage of data collection. Prioritization and decision-making frameworks from ISP could be deployed at various scales - from analysis onboard a spacecraft with multiple instruments – to coordinated analyses among separate spacecraft in an e.g., distributed systems mission (DSM) composed of multiple SmallSats. Goddard’s Intelligent Science Payload team is developing an agile autonomous architecture for an icy ocean worlds DSM concept. Our goals are to coordinate data collection and onboard data analysis, and to make autonomous decisions for new data collection and analysis based on science priorities between multiple spacecraft with variable instrumentation and orbits. We use a range of data analysis tools to coordinate the DSM response, spanning from observations of data over a specified threshold to more computationally intensive machine learning algorithms (ML). ML algorithms here currently focus on determining the composition of an ocean world using mass spectrometry, and specifically methods for understanding ‘novelties’ and potential biosignatures. These algorithms could be used to quickly process and analyze onboard data that would be significantly delayed in downlink due to long communication delays for outer solar system missions in order to make dynamic science observations. Our ocean worlds case study ISP architecture is intended as an ‘agile’ and modular framework that could be used as a whole or as particular modules based on mission needs.

Distributed Systems↗

DOE OSTI2024

Anomaly Detection and Mitigation for Dynamic Frequency Regulation in Hydropower-Battery Systems

Hydropower operators and energy storage providers are increasingly interested in participating in frequency regulation services, driven by the incentives offered by independent system operators, such as the PJM Interconnection. This transition, however, unfolds against the backdrop of a modernizing and rapidly digitizing power grid, exposing the integrated legacy infrastructure to a multitude of cybersecurity threats. This work presents an approach for developing an anomaly detection and mitigation system to address cybersecurity challenges during the participation of a hydropower-integrated battery energy storage system (BESS) in a frequency regulation market. The applied anomaly detector utilizes machine learning algorithms to provide detailed classification of cyber-physical events. Later, the applied mitigation system triggers predefined corrective actions to minimize the impact of data integrity attacks on the regulation market and system stability. We evaluated the proposed approach on a hydropower-integrated BESS topology, specifically analyzing the slow regulation signal (Reg A) coming from the PJM market. Our simulation results demonstrate that the proposed approach performs well in detecting data integrity attacks within the allocated time frame and also minimizes the system's transient instability during the participation of hydropower and BESS in the regulation market.

battery energy storage system↗

NASA NTRS2021

Machine Learning the COSMO Model for Predicting Thermodynamics of Electrolyte Mixtures

Bottom-up design of electrolyte mixtures for battery systems requires predicting macro thermodynamic properties from molecular constituents. For instance, molten salt electrolyte batteries require conditions far above room temperature to operate. Therefore, discovering mixtures with increasingly lower eutectic melting points is desirable. A model that can approximate chemical activity is a valuable tool to search through the vast compositional design space. Machine learning can predict properties of materials such as vibrational free energies, electronic energy gaps, and thermal conductivities. Moreover, they can learn physical models such as interatomic potentials. The COSMO-SAC model uses theory and empirical parameterization to predict liquid-vapor and liquid-solid properties using first-principles calculations. However, obtaining activity coefficients required for parameterizing the COSMO-SAC model is costly and limited to a select chemical space. In this work, we explored if machine learning methods could improve the COSMO-SAC model and bridge density functional theory calculations to liquid phase thermodynamic properties. Our data-driven approach uses existing databases for sigma-profiles of organic solvents and reconciles their methodological differences via ensemble averaging. First, an optimal machine learning model is constructed for each dataset. Our machine learning algorithms use the sigma-profile as an input feature to predict binary mixtures' activity coefficients using multi-output regression. Each dataset uses different choices of functionals, methods, and basis sets. Therefore, our ensemble model attempts to predict corrected activity coefficients given the combination of all the model outputs. The activity coefficients used for training are generated using the COSMO-SAC model. This approach enables the extraction of meaningful information from the existing datasets to improve the COSMO-SAC model for obtaining thermodynamic properties of electrolyte mixtures. With the liquid phase activities, we can identify electrolyte mixtures that meet desired phase equilibria conditions.

Thermodynamics↗

NASA NTRSDate not supplied

NASA GPM Status and Future Activities

Global Precipitation Measuremen↗

NASA NTRS2017

Educational and Scientific Applications of Climate Model Diagnostic Analyzer

Climate Model Diagnostic Analyzer (CMDA) is a web-based information system designed for the climate modeling and model analysis community to analyze climate data from models and observations. CMDA provides tools to diagnostically analyze climate data for model validation and improvement, and to systematically manage analysis provenance for sharing results with other investigators. CMDA utilizes cloud computing resources, multi-threading computing, machine-learning algorithms, web service technologies, and provenance-supporting technologies to address technical challenges that the Earth science modeling and model analysis community faces in evaluating and diagnosing climate models. As CMDA technology and infrastructure have matured, we have developed the educational and scientific applications of CMDA. Educationally, CMDA supported the summer school of the JPL Center for Climate Sciences in 2014, 2015, and 2016. In the summer school, the students work on group research projects where CMDA provide datasets, analysis tools, and provenance support utility tools. Each student is assigned to a virtual machine with CMDA installed in Amazon Web Services. Scientifically, we have developed several science use cases of CMDA covering various topics, datasets, and analysis types. Each of the science use cases is described in terms of a scientific goal, datasets used, the analysis tools used, scientific results discovered, an analysis result such as output plots and data files, and a link to the corresponding analysis service call with all the input arguments filled.

Bao, Qihao↗

NASA NTRSDate not supplied

Extracting Lessons of Resilience Using Machine Mining of the ASRS Database

NASA’s Aviation Safety Reporting System (ASRS) database is the world's largest repository of voluntary, confidential safety information provided by aviation's frontline personnel, including pilots, air traffic controllers, mechanics, flight attendants, dispatchers, and other members of the aviation community and the public. The database contains close to 2 million narratives, many of which describe everyday situations in which people saved the day. In these situations, people’s resilient behavior solved a problem, dealt with a malfunction, and maintained a safe operation despite a serious perturbation. To be able to extract lessons of such resilience from this large database, the use of machine learning algorithms is being explored. In this report, we describe a comparison between two such algorithms: Perilog and Word2Vec. An identical search using both programs was done on a database containing approximately 470,000 ASRS reports submitted between 1988 and 2022. The comparison reveals some of the strength and weaknesses of each algorithm as well as the challenges inherent in using such algorithms to extract lessons of resilience from the ASRS database.

resilience↗

DOE OSTI2024

Characterization of Fuel Cladding Chemical Interaction on a High Burnup U-10Zr Metallic Fuel via Electron Energy Loss Spectroscopy Enhanced by Machine Learning

Fuel cladding chemical interaction (FCCI) is one of the main performance limiting factors for metallic nuclear fuels. The interaction destabilizes the martensitic microstructure and deteriorates mechanical properties of HT-9 cladding. The detection of low atomic number elements (Z<10) and overlapping of elemental peaks can be problematic in interpreting energy dispersive X-ray spectroscopy (EDS) data. Electron energy loss spectroscopy (EELS) provides precise elemental edge energy values and can detect elements with a low atomic number. This work utilizes EELS to study the distribution of lanthanides and light elements at the interaction region. The sample was prepared from the FCCI region of a U-10Zr (wt.%) solid fuel with HT-9 cladding, irradiated to a burnup of 13.2 at.%. Processing the EELS data included three major steps: 1) enhance the signal to noise ratio by denoising the spectrum with principal component analysis (PCA) method, removing background and performing deconvolution; 2) identify chemical elements with core energy loss edges; 3) confirm different phases using a popular machine learning method, K-means. This work presents qualitative assessment of lanthanides and light elements like carbon (C) and oxygen (O) enhanced by the application of machine learning algorithms. By comparing with EDS elemental maps, EELS provides higher resolution chemical maps, reveals the distribution of carbon at the interaction region supporting the formation of zirconium carbide, a rind-like microstructure feature that was proposed to mitigate the chemical interaction. Furthermore, the plasmon peak map was also found to indicate an energy shift associated with the formation of phases/compounds. K-means clustering method was used on the processed electron energy loss (EEL) spectrum to automatically reveal different phases. The resulting clustered maps from K-means clustering align well with elemental maps confirming certain phases, especially Fe-Ce and Zr-C, in the FCCI region.

EELS↗

DOE OSTI2025

Baseflow Identification via Explainable AI With Kolmogorov‐Arnold Networks

Abstract Hydrological models often involve constitutive laws that may not be optimal in every application. We propose to replace such laws with the Kolmogorov‐Arnold networks (KANs), a class of neural networks designed to identify symbolic expressions. We demonstrate KAN's potential on the problem of baseflow identification, a notoriously challenging task plagued by significant uncertainty. KAN‐derived functional dependencies of the baseflow components on the aridity index outperform their original counterparts; they demonstrate that water availability, rather than potential evapotranspiration, drives baseflow by constraining actual evapotranspiration under arid conditions. On a test set, they increase the Nash‐Sutcliffe efficiency (NSE) by 65%, decrease the root mean squared error by 29%, and increase the Kling‐Gupta efficiency by 34%. This superior performance is achieved while reducing the number of fitting parameters from three to two. Next, we use data from 378 catchments across the continental United States to refine the water‐balance equation at the mean‐annual scale. The KAN‐derived equations based on the refined water balance outperform both the current aridity index model, with up to a 105% increase in NSE, and the KAN‐derived equations based on the original water balance. While the performance of our model and tree‐based machine learning methods is similar, KANs offer the advantage of simplicity and transparency and require no specific software or computational tools. This case study focuses on the aridity index formulation, but the approach is flexible and transferable to other hydrological processes. Plain Language Summary Equations used in hydrologic model are often suboptimal, resulting in reduced prediction accuracy and efficiency. We implemented Kolmogorov‐Arnold networks (KAN), a machine learning algorithm for deriving symbolic formulations, to estimate groundwater recharge and showed that it outperforms an existing state‐of‐the‐art semi‐empirical formulation. In hydrology, Nash‐Sutcliffe efficiency (NSE), root mean squared error (RMSE), and Kling‐Gupta efficiency (KGE) are commonly used to evaluate model performance. Higher NSE and KGE values indicate better performance, while lower RMSE values are preferable. Our results show that NSE increased by 71%, RMSE decreased by 32%, and KGE improved by 25%. In addition, KAN identifies an optimal functional form and can be used to derive new analytical formulas using the prior knowledge. The KAN‐inspired equation outperformed the original formulation and reduced the fitting parameters. Furthermore, we refined the water‐balance equation at the mean‐annual scale and showed that, based on the new water‐balance equation, KAN can derive new formulations that are superior to the original aridity index formulations (up to 105% increase in NSE) and KAN‐derived equations based on the original water balance. These findings highlight the significant potential of KAN to advance the scientific understanding of a wide range of hydrologic processes. Key Points Kolmogorov‐Arnold networks (KANs) enhance interpretability of machine‐learned hydrological models KAN‐derived symbolic formulations outperform state‐of‐the‐art semi‐empirical aridity indices KAN‐identified functional form yields an analytical index with fewer fitting parameters and improved performance

baseflow↗

NASA NTRSDate not supplied

NASA GPM Status and Future Activities

The joint U.S.-Japan Global Precipitation Measurement (GPM) mission is approaching a decade of operations, and continues to pursue research, dataset production, and outreach related to precipitation. Key activities over the last year were the release of an improved “Version 07” of all GPM precipitation and latent heating products, boosting the orbit of the GPM Core Observatory (GPM CO) to 435 km, and improving quality control on precipitation retrievals from the GPM constellation of passive microwave satellites. This presentation summarizes key improvements to the GPM products and provides some examples of the changes between Versions 06 and 07 in algorithm performance. One important operational change that affected Version 07 is that the scanning strategy for the Ka-band radar channel changed in May 2018; all products that depend on Ka were revised to accommodate this change. For example, in Version 07 the Goddard Profiling (GPROF) algorithm has implemented improvements in regions where orographic enhancement and suppression take place and where the surface is snowy/icy, and again covers radiometers reaching back to 1987. The Combined Radar Radiometer Algorithm (CORRA) now incorporates modified drop-size distribution constraints that substantially reduce bias. Revisions to the Convective-Stratiform Heating (CSH) algorithm employ new radiative transfer retrievals as well as accounting for terrain in the vertical coordinates. Each algorithm was adjusted to ensure continuity for each product across the boundary in 2014 between the predecessor Tropical Rainfall Measuring Mission (TRMM) and the GPM CO. The U.S. Science Team’s Integrated Multi-satellitE Retrievals for GPM (IMERG) was upgraded to account for distortions in the probability density function of regional precipitation rates due to weighted averaging in the Kalman filter used for “morphing” the passive microwave data. Maintaining the GPM CO orbital altitude in the the current very active solar cycle has been forcing the use of more fuel than planned and consequently shortening the forecasted life of the mission from the early 2030's to the late 2020's. It was considered vital to regain some of this lifetime to ensure overlap with the upcoming Atmosphere Observing System mission to provide crosscalibration of instruments. To accomplish this, the orbital altitude was raised from 400 to 435 km on 7-8 November 2023. Thereafter, the primary GPM CO algorithms had to be revised to account for the change in observing parameters. By meeting time this action should be complete. Recently, a screening algorithm based on auto-encoding was developed that uncovered 162 orbits (out of the many thousands of orbits across all years and all satellites) of passive microwave retrievals that had highly anomalous values. Removing these defective retrievals has improved the integrity of both the GPROF and IMERG records. However, the nature of the IMERG processing interacted sufficiently badly with the now-discovered anomalous orbits that it was necessary to completely reprocess the IMERG Final Run record, now labeled Version 07B. The presentation also considers major issues that require continued attention, including the use of machine learning algorithms and the operational challenge of swarms of “small”, perhaps short-lived satellites.

GPM↗

NASA NTRS2010

Understanding the Scalability of Bayesian Network Inference Using Clique Tree Growth Curves

One of the main approaches to performing computation in Bayesian networks (BNs) is clique tree clustering and propagation. The clique tree approach consists of propagation in a clique tree compiled from a Bayesian network, and while it was introduced in the 1980s, there is still a lack of understanding of how clique tree computation time depends on variations in BN size and structure. In this article, we improve this understanding by developing an approach to characterizing clique tree growth as a function of parameters that can be computed in polynomial time from BNs, specifically: (i) the ratio of the number of a BN s non-root nodes to the number of root nodes, and (ii) the expected number of moral edges in their moral graphs. Analytically, we partition the set of cliques in a clique tree into different sets, and introduce a growth curve for the total size of each set. For the special case of bipartite BNs, there are two sets and two growth curves, a mixed clique growth curve and a root clique growth curve. In experiments, where random bipartite BNs generated using the BPART algorithm are studied, we systematically increase the out-degree of the root nodes in bipartite Bayesian networks, by increasing the number of leaf nodes. Surprisingly, root clique growth is well-approximated by Gompertz growth curves, an S-shaped family of curves that has previously been used to describe growth processes in biology, medicine, and neuroscience. We believe that this research improves the understanding of the scaling behavior of clique tree clustering for a certain class of Bayesian networks; presents an aid for trade-off studies of clique tree clustering using growth curves; and ultimately provides a foundation for benchmarking and developing improved BN inference and machine learning algorithms.

Mengshoel, Ole J.↗