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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Multiscale characterization and comparison of historical and modern nuclear graphite grades

Beginning with Chicago Pile I, graphite has been used as a moderator material in nuclear power stations and is considered a potential material for use in future Generation IV advanced reactors. The microstructure of graphite is responsible for much of its mechanical and thermo-physical properties, and how it responds to irradiation. To understand graphite microstructure, it is necessary to understand its porosity at the macro- and micro-scales; and to understand its porosity, it is necessary to characterize the morphological connectivity of the void content and the two main phases of graphite: filler and binder. Here, using several microscopy and analytical techniques, a detailed examination of the heterogeneity, microstructure and pore structure of different graphite grades and their binder and filler phases is presented. Significant differences were found between coarser and finer nuclear grades. Coarse grades have a more diverse range of filler particles, pores and thermal cracks. Finer grades have a more well-defined pore size distribution, fewer variations of filler particles sizes and do not contain as many large thermal cracks. Fine grades tend to have a well-connected network of pores whereas coarser grades contain a larger content of closed porosity. The framework developed within this work can be applied and used to assess the various graphite grades that would down-select materials for specific use in graphite moderated reactor designs.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2025

SAGIPS: a physics-inspired scalable asynchronous generative inverse-problem solver

Abstract Solving large-scale inverse problems using deep-learning algorithms have become an essential part of modern research and industrial applications. The complexity of the underlying inverse problem may require the utilization of high performance computing systems which poses a challenge on the algorithmic design of the inverse problem solver. Most deep learning algorithms require, due to their design, custom parallelization techniques in order to be resource efficient while showing a reasonable convergence. In this paper we introduce a S calable A synchronous G enerative I nverse P roblem S olver (SAGIPS) on high-performance computing systems. We present a workflow that utilizes an asynchronous ring-allreduce algorithm to transfer the gradients of the generator network across multiple GPUs. Experiments with a scientific proxy application demonstrate that SAGIPS shows near linear weak scaling, together with a convergence quality that is comparable to traditional methods. The approach presented here allows leveraging Generative Adverserial Network across multiple GPUs, promising advancements in solving complex inverse problems at scale.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Constraining Galaxy-Halo connection using machine learning

We investigate the potential of machine learning (ML) methods to model small-scale galaxy clustering for constraining Halo Occupation Distribution (HOD) parameters. Our analysis reveals that while many ML algorithms report good statistical fits, they often yield likelihood contours that are significantly biased in both mean values and variances relative to the true model parameters. This highlights the importance of careful data processing and algorithm selection in ML applications for galaxy clustering, as even seemingly robust methods can lead to biased results if not applied correctly. ML tools offer a promising approach to exploring the HOD parameter space with significantly reduced computational costs compared to traditional brute-force methods if their robustness is established. Using our ANN-based pipeline, we successfully recreate some standard results from recent literature. Properly restricting the HOD parameter space, transforming the training data, and carefully selecting ML algorithms are essential for achieving unbiased and robust predictions. Among the methods tested, artificial neural networks (ANNs) outperform random forests (RF) and ridge regression in predicting clustering statistics, when the HOD prior space is appropriately restricted. We demonstrate these findings using the projected two-point correlation function (w p (r p )), angular multipoles of the correlation function (ξ ℓ (r)), and the void probability function (VPF) of Luminous Red Galaxies from Dark Energy Spectroscopic Instrument mocks. Our results show that while combining w p (r p ) and VPF improves parameter constraints, adding the multipoles ξ 0 , ξ 2 , and ξ 4 to w p (r p ) does not significantly improve the constraints.

cosmology↗
DOE OSTI2022

Automatic Detection and Classification of Radio Galaxy Images by Deep Learning

Abstract Surveys conducted by radio astronomy observatories, such as SKA, MeerKAT, Very Large Array, and ASKAP, have generated massive astronomical images containing radio galaxies (RGs). This generation of massive RG images has imposed strict requirements on the detection and classification of RGs and makes manual classification and detection increasingly difficult, even impossible. Rapid classification and detection of images of different types of RGs help astronomers make full use of the observed astronomical image data for further processing and analysis. The classification of FRI and FRII is relatively easy, and there are more studies and literature on them at present, but FR0 and FRI are similar, so it is difficult to distinguish them. It poses a greater challenge to image processing. At present, deep learning has made breakthrough progress in the field of image analysis and processing and has preliminary applications in astronomical data processing. Compared with classification algorithms that can only classify galaxies, object detection algorithms that can locate and classify RGs simultaneously are preferred. In target detection algorithms, YOLOv5 has outstanding advantages in the classification and positioning of small targets. Therefore, we propose a deep-learning method based on an improved YOLOv5 object detection model that makes full use of multisource data, combining FIRST radio with SDSS optical image data, and realizes the automatic detection of FR0, FRI, and FRII RGs. The innovation of our work is that on the basis of the original YOLOv5 object detection model, we introduce the SE Net attention mechanism, increase the number of preset anchors, adjust the network structure of the feature pyramid, and modify the network structure, thereby allowing our model to demonstrate galaxy classification and position detection effects. Our improved model produces satisfactory results, as evidenced by experiments. Overall, the mean average precision (mAP@0.5) of our improved model on the test set reaches 89.4%, which can determine the position (R.A. and decl.) and automatically detect and classify FR0s, FRIs, and FRIIs. Our work contributes to astronomy because it allows astronomers to locate FR0, FRI, and FRII galaxies in a relatively short time and can be further combined with other astronomically generated data to study the properties of these galaxies. The target detection model can also help astronomers find FR0s, FRIs, and FRIIs in future surveys and build a large-scale star RG catalog. Moreover, our work is also useful for the detection of other types of galaxies.

Astronomy & Astrophysics↗
DOE OSTI2023

Solving Seismic Wave Equations on Variable Velocity Models With Fourier Neural Operator

Here, in the study of subsurface seismic imaging, solving the acoustic wave equation is a pivotal component in existing models. The advancement of deep learning (DL) enables solving partial differential equations (PDEs), including wave equations, by applying neural networks to identify the mapping between the inputs and the solution. This approach can be faster than traditional numerical methods when numerous instances are to be solved. Previous works that concentrate on solving the wave equation by neural networks consider either a single velocity model or multiple simple velocity models, which is restricted in practice. Instead, inspired by the idea of operator learning, this work leverages the Fourier neural operator (FNO) to effectively learn the frequency domain seismic wavefields under the context of variable velocity models. We also propose a new framework paralleled FNO (PFNO) for efficiently training the FNO-based solver given multiple source locations and frequencies. Numerical experiments demonstrate the high accuracy of both FNO and PFNO with complicated velocity models in the OpenFWI datasets. Furthermore, the cross-dataset generalization test verifies that PFNO adapts to out-of-distribution velocity models. Finally, PFNO admits higher computational efficiency on large-scale testing datasets than the traditional finite-difference method. The aforementioned advantages endow the FNO-based solver with the potential to build powerful models for research on seismic waves.

58 GEOSCIENCES↗
DOE OSTI2024

Atmospheric H 2 observations from the NOAA Cooperative Global Air Sampling Network

Abstract. The NOAA Global Monitoring Laboratory (GML) measures atmospheric hydrogen (H2) in grab samples collected weekly as flask pairs at over 50 sites in the Cooperative Global Air Sampling Network. Measurements representative of background air sampling show higher H2 in recent years at all latitudes. The marine boundary layer (MBL) global mean H2 was 552.8 ppb in 2021, 20.2 ± 0.2 ppb higher compared to 2010. A 10 ppb or more increase over the 2010–2021 average annual cycle was detected in 2016 for MBL zonal means in the tropics and in the Southern Hemisphere. Carbon monoxide measurements in the same-air samples suggest large biomass burning events in different regions likely contributed to the observed interannual variability at different latitudes. The NOAA H2 measurements from 2009 to 2021 are now based on the World Meteorological Organization Global Atmospheric Watch (WMO GAW) H2 mole fraction calibration scale, developed and maintained by the Max Planck Institute for Biogeochemistry (MPI-BGC), Jena, Germany. GML maintains eight H2 primary calibration standards to propagate the WMO scale. These are gravimetric hydrogen-in-air mixtures in electropolished stainless steel cylinders (Essex Industries, St. Louis, MO), which are stable for H2. These mixtures were calibrated at the MPI-BGC, the WMO Central Calibration Laboratory (CCL) for H2, in late 2020 and span the range 250–700 ppb. We have used the CCL assignments to propagate the WMO H2 calibration scale to NOAA air measurements performed using gas chromatography and helium pulse discharge detector instruments since 2009. To propagate the scale, NOAA uses a hierarchy of secondary and tertiary standards, which consist of high-pressure whole-air mixtures in aluminum cylinders, calibrated against the primary and secondary standards, respectively. Hydrogen at the parts per billion level has a tendency to increase in aluminum cylinders over time. We fit the calibration histories of these standards with zero-, first-, or second-order polynomial functions of time and use the time-dependent mole fraction assignments on the WMO scale to reprocess all tank air and flask air H2 measurement records. The robustness of the scale propagation over multiple years is evaluated with the regular analysis of target air cylinders and with long-term same-air measurement comparison efforts with WMO GAW partner laboratories. Long-term calibrated, globally distributed, and freely accessible measurements of H2 and other gases and isotopes continue to be essential to track and interpret regional and global changes in the atmosphere composition. The adoption of the WMO H2 calibration scale and subsequent reprocessing of NOAA atmospheric data constitute a significant improvement in the NOAA H2 measurement records.

Pétron, Gabrielle↗
DOE OSTI2022

Organizational Principles of Hyporheic Exchange Flow and Biogeochemical Cycling in River Networks Across Scales

Hyporheic zones increase freshwater ecosystem resilience to hydrological extremes and global environmental change. However, current conceptualizations of hyporheic exchange, residence time distributions, and the associated biogeochemical cycling in streambed sediments do not always accurately explain the hydrological and biogeochemical complexity observed in streams and rivers. Specifically, existing conceptual models insufficiently represent the coupled transport and reactivity along groundwater and surface water flow paths, the role of autochthonous organic matter in streambed biogeochemical functioning, and the feedbacks between surface-subsurface ecological processes, both within and across spatial and temporal scales. While simplified approaches to these issues are justifiable and necessary for transferability, the exclusion of important hyporheic processes from our conceptualizations can lead to erroneous conclusions and inadequate understanding and management of interconnected surface water and groundwater environments. This is particularly true at the landscape scale, where the organizational principles of spatio-temporal dynamics of hyporheic exchange flow (HEF) and biogeochemical processes remain largely uncharacterized. This article seeks to identify the most important drivers and controls of HEF and biogeochemical cycling based on a comprehensive synthesis of findings from a wide range of river systems. We use these observations to test current paradigms and conceptual models, discussing the interactions of local-to-regional hydrological, geomorphological, and ecological controls of hyporheic zone functioning. This improved conceptualization of the landscape organizational principles of drivers of HEF and biogeochemical processes from reach to catchment scales will inform future river research directions and watershed management strategies.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Joint routing of conventional and range-extended electric vehicles in a large metropolitan network

Range-extended electric vehicles combine the higher efficiency and environmental benefits of battery-powered electric motors with the longer mileage and autonomy of conventional internal combustion engines. This combination is particularly advantageous for time-constrained delivery routing in dense urban areas, where battery recharging along routes can be too time-consuming to economically justify the use of all-electric vehicles. However, switching from electric to conventional fossil fuel modes also results in higher costs and emissions and lower efficiency. This paper analyzes this heterogeneous vehicle routing problem and describes two solution methods: an exact branch-price-and-cut algorithm and an iterated tabu search metaheuristic. From a methodological perspective, we find that the exact algorithm consistently obtains tight lower bounds that also serve to certify the metaheuristic solutions as near-optimal. From a policy standpoint, we examine a large-scale real-world case study concerning parcel deliveries in the Chicago metropolitan area and quantify various operational metrics including energy costs and vehicle miles traveled. We find that by deploying roughly 20% of range -extended vehicles with a modest all-electric range of 33 miles, parcel distributors can save energy costs by up to 17% while incurring less than 0.5% increase in vehicle miles traveled. Increasing the range to 60 miles further reduces costs by only 4%, which can alternatively be achieved by decreasing the average service time by 1 minute or increasing driver working time by 1 hour. In conclusion, our study reveals several key areas of improvement on which vehicle manufacturers, distributors, and policy makers can focus their attention.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2024

GraMeR: Gra ph Me ta R einforcement learning for multi-objective influence maximization

Influence maximization (IM) is a combinatorial problem of identifying a subset of seed nodes in a network (graph), which when activated, provide a maximal spread of influence in the network for a given diffusion model and a budget for seed set size. IM has numerous applications such as viral marketing, epidemic control, sensor placement and other network-related tasks. However, its practical uses are limited due to the computational complexity of current algorithms. Recently, deep reinforcement learning has been leveraged to solve IM in order to ease the computational burden. However, there are serious limitations in current approaches, including narrow IM formulation that only consider influence via spread and ignore self-activation, low scalability to large graphs, and lack of generalizability across graph families leading to a large running time for every test network. In this work, we address these limitations through a unique approach that involves: (1) Formulating a generic IM problem as a Markov decision process that handles both intrinsic and influence activations; (2)incorporating generalizability via meta-learning across graph families. There are previous works that combine deep reinforcement learning with graph neural network, but this work solves a more realistic IM problem and incorporates generalizability across graphs via meta reinforcement learning. Extensive experiments are carried out in various standard networks to validate performance of the proposed Graph Meta Reinforcement learning (GraMeR) framework. Finally, the results indicate that GraMeR is multiple orders faster and generic than conventional approaches when applied on small to medium scale graphs.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Generative adversarial networks (GAN) based efficient sampling of chemical composition space for inverse design of inorganic materials

A major challenge in materials design is how to efficiently search the vast chemical design space to find the materials with desired properties. One effective strategy is to develop sampling algorithms that can exploit both explicit chemical knowledge and implicit composition rules embodied in the large materials database. Here, we propose a generative machine learning model (MatGAN) based on a generative adversarial network (GAN) for efficient generation of new hypothetical inorganic materials. Trained with materials from the ICSD database, our GAN model can generate hypothetical materials not existing in the training dataset, reaching a novelty of 92.53% when generating 2 million samples. The percentage of chemically valid (charge-neutral and electronegativity-balanced) samples out of all generated ones reaches 84.5% when generated by our GAN trained with such samples screened from ICSD, even though no such chemical rules are explicitly enforced in our GAN model, indicating its capability to learn implicit chemical composition rules to form compounds. Our algorithm is expected to be used to greatly expand the range of the design space for inverse design and large-scale computational screening of inorganic materials.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Accelerating Scientific Workflows on HPC Platforms with In Situ Processing

Scientific workflows drive most modern large-scale science breakthroughs by allowing scientists to define their computations as a set of jobs executed in a given order based on their data dependencies. Workflow management systems (WMSs) have become key to automating scientific workflows-executing computational jobs and orchestrating data transfers between those jobs running on complex high-performance computing (HPC) platforms. Traditionally, WMSs use files to communicate between jobs: a job writes out files that are read by other jobs. However, HPC machines face a growing gap between their storage and compute capabilities. To address that concern, the scientific community has adopted a new approach called in situ, which bypasses costly parallel filesystem I/O operations with faster in-memory or in-network communications. When using in situ approaches, communication and computations can be interleaved. In this work, we leverage the Decaf in situ dataflow framework to accelerate task-based scientific workflows managed by the Pegasus WMS, by replacing file communications with faster MPI messaging. We propose a new execution engine that uses Decaf to manage communications within a sub-workflow (i.e., set of jobs) to optimize inter-job communications. We consider two workflows in this study: (i) a synthetic workflow that benchmarks and compares file- and MPI-based communication; and (ii) a realistic bioinformatics workflow that computes mu-tational overlaps in the human genome. Experiments show that in situ communication can improve the bioinformatics workflow execution time by 22% to 30% compared with file communication. Our results motivate further opportunities and challenges for bridging traditional WMSs with in situ frameworks.

Decaf↗
DOE OSTI2024

Factorized visual representations in the primate visual system and deep neural networks

Object classification has been proposed as a principal objective of the primate ventral visual stream and has been used as an optimization target for deep neural network models (DNNs) of the visual system. However, visual brain areas represent many different types of information, and optimizing for classification of object identity alone does not constrain how other information may be encoded in visual representations. Information about different scene parameters may be discarded altogether (‘invariance’), represented in non-interfering subspaces of population activity (‘factorization’) or encoded in an entangled fashion. In this work, we provide evidence that factorization is a normative principle of biological visual representations. In the monkey ventral visual hierarchy, we found that factorization of object pose and background information from object identity increased in higher-level regions and strongly contributed to improving object identity decoding performance. We then conducted a large-scale analysis of factorization of individual scene parameters – lighting, background, camera viewpoint, and object pose – in a diverse library of DNN models of the visual system. Models which best matched neural, fMRI, and behavioral data from both monkeys and humans across 12 datasets tended to be those which factorized scene parameters most strongly. Notably, invariance to these parameters was not as consistently associated with matches to neural and behavioral data, suggesting that maintaining non-class information in factorized activity subspaces is often preferred to dropping it altogether. Thus, we propose that factorization of visual scene information is a widely used strategy in brains and DNN models thereof.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2023

Stable isotopes contain substantial additive information about terrestrial carbon and water cycling

Abstract Stable isotope ratios of H ( δ 2 H ), O ( δ 18 O), and C ( δ 13 C) are linked to key biogeochemical processes of the water and carbon cycles; however, the degree to which isotope-associated processes are reflected in macroscale ecosystem flux observations remains unquantified. Here through formal information assessment, new measurements of δ 13 C of net ecosystem exchange ( NEE ) as well as δ 2 H and δ 18 O of latent heat ( LH ) fluxes across the United States National Ecological Observation Network (NEON) are used to determine conditions under which isotope measurements are informative of environmental exchanges. We find all three isotopic datasets individually contain comparable amounts of information about NEE and LH fluxes as wind speed observations. Such information from isotope measurements, however, is largely unique. Generally, δ 13 C provides more information about LH as aridity increases or mean annual precipitation decreases. δ 2 H provides more information about LH as temperatures or mean annual precipitation decreases, and also provides more information about NEE as temperatures decrease. Overall, we show that the stable isotope datasets collected by NEON contribute non-trivial amounts of new information about bulk environmental fluxes useful for interpreting biogeochemical and ecohydrological processes at landscape scales. However, the utility of this new information varies with environmental conditions at continental scales. This study provides an approach for quantifying the value adding non-traditional sensing approaches to environmental monitoring sites and the patterns identified here are expected to aid in modeling and data interpretation efforts focused on constraining carbon and water cycles’ mechanisms.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Foliar functional traits from imaging spectroscopy across biomes in eastern North America

Summary Foliar functional traits are widely used to characterize leaf and canopy properties that drive ecosystem processes and to infer physiological processes in Earth system models. Imaging spectroscopy provides great potential to map foliar traits to characterize continuous functional variation and diversity, but few studies have demonstrated consistent methods for mapping multiple traits across biomes. With airborne imaging spectroscopy data and field data from 19 sites, we developed trait models using partial least squares regression, and mapped 26 foliar traits in seven NEON (National Ecological Observatory Network) ecoregions (domains) including temperate and subtropical forests and grasslands of eastern North America. Model validation accuracy varied among traits (normalized root mean squared error, 9.1–19.4%; coefficient of determination, 0.28–0.82), with phenolic concentration, leaf mass per area and equivalent water thickness performing best across domains. Across all trait maps, 90% of vegetated pixels had reasonable values for one trait, and 28–81% provided high confidence for multiple traits concurrently. Maps of 26 traits and their uncertainties for eastern US NEON sites are available for download, and are being expanded to the western United States and tundra/boreal zone. These data enable better understanding of trait variations and relationships over large areas, calibration of ecosystem models, and assessment of continental‐scale functional diversity.

Wang, Zhihui↗
DOE OSTI2024

SUNBIRD : a simulation-based model for full-shape density-split clustering

Combining galaxy clustering information from regions of different environmental densities can help break cosmological parameter degeneracies and access non-Gaussian information from the density field that is not readily captured by the standard two-point correlation function (2PCF) analyses. However, modelling these density-dependent statistics down to the non-linear regime has so far remained challenging. We present a simulation-based model that is able to capture the cosmological dependence of the full shape of the density-split clustering (DSC) statistics down to intra-halo scales. Our models are based on neural-network emulators that are trained on high-fidelity mock galaxy catalogues within an extended-ΛCDM framework, incorporating the effects of redshift-space, Alcock–Paczynski distortions, and models of the halo–galaxy connection. Our models reach sub-percent level accuracy down to $1 \, h^{-1}\text{Mpc}$ and are robust against different choices of galaxy–halo connection modelling. When combined with the galaxy 2PCF, DSC can tighten the constraints on ω cdm , σ 8 , and n s by factors of 2.9, 1.9, and 2.1, respectively, compared to a 2PCF-only analysis. DSC additionally puts strong constraints on environment-based assembly bias parameters.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

OpenCRUMS USA: An Open Machine Learning Framework for Characterizing Variability in Aerosol Reanalysis Data

Advances in artificial intelligence (AI) have called for exploring how these techniques can be used for exploring patterns in large climate datasets. To that regard, the U.S. Department of Energy AI for Earth System Predictability (AI4ESP) supported a pilot initiative called the Open Classification of Regimes in the Southeast USA (OpenCRUMS USA) project to explore how AI can be used to characterize modes of spatial variability in large climate datasets. For this study, we focus on comparing two methods for characterizing the modes of spatial variability of surface aerosol concentration over the Houston region: empirical orthogonal functions (EOFs) and layerwise relevance propagation (LRP) applied to a convolutional neural network (CNN) classifier. We show that EOF analysis typically attributes spatial variability modes that span all of southeast Texas, prohibiting the attribution of spatial variability to localized regions. However, using LRP on the CNN classifier resolves the explanatory parameters at a finer spatial resolution than EOFs. This allows for the attribution of the spatial variability of surface aerosols to local regions of organic carbon which was not possible using EOFs. In addition, the LRP analysis also suggests that synoptic-scale transport of dust is most prevalent during anticyclonic and pretrough synoptic conditions as categorized by self-organizing maps.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

A 1 km soil moisture dataset over eastern CONUS generated by assimilating SMAP data into the Noah-MP land surface model

An improved fine-scale soil moisture (SM) dataset at 1 km grid spacing, covering much of the eastern continental US, was generated by assimilating 9 km Soil Moisture Active Passive (SMAP) SM data into the v4.0.1 Noah-MP land surface model. With 12 ensemble members, the assimilation was carried out using the ensemble Kalman filter algorithm within NASA's Land Information System. The SM analysis for 2016 was fully validated against in situ observations from four different networks and compared with four other existing datasets. Results indicate that this SM analysis surpasses other datasets in top-layer SM distribution, including a machine-learning-based product, despite all SM estimates being less heterogeneous than observed. The analysis of anomalous errors suggests that large similarity in intrinsic errors is likely due to overlapping data sources among the selected SM datasets. More detailed evaluations were performed over two geographic areas. The observations collected by the Atmospheric Radiation Measurement facility in Oklahoma suggest that soil temperature and surface heat fluxes are concurrently simulated with good accuracy. Investigation into the 2016 southeastern US drought response further indicates drier conditions and higher evapotranspiration estimates compared to GLEAMv4.1. Notably, large errors are associated with grids having clay soil textures, underscoring the need for refined model treatments for specific soil types to further improve SM estimates. The dataset is publicly available on Zenodo at https://doi.org/10.5281/zenodo.14370563 (Tai et al., 2024).

Tai, Sheng-Lun [Pacific Northwest National Laborat↗
DOE OSTI2020

Computationally Efficient Learning of Large Scale Dynamical Systems: A Koopman Theoretic Approach

In recent years there has been a considerable drive towards data-driven analysis, discovery and control of dynamical systems. To this end, operator theoretic methods, namely, Koopman operator methods have gained a lot of interest. In general, the Koopman operator is obtained as a solution to a least-squares problem, and as such, the Koopman operator can be expressed as a closed-form solution that involves the computation of Moore-Penrose inverse of a matrix. For high dimensional systems and also if the size of the obtained data-set is large, the computation of the Moore-Penrose inverse becomes computationally challenging. In this paper, we provide an algorithm for computing the Koopman operator for high dimensional systems in a time-efficient manner. We further demonstrate the efficacy of the proposed approach on two different systems, namely a network of coupled oscillators (with state-space dimension up to 2500) and IEEE 68 bus system (with state-space dimension 204 and up to 24,000 time-points).

Sinha, Subhrajit↗