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Experimental study of the Si 30 ( He 3 , d ) P 31 reaction and thermonuclear reaction rate of Si 30 ( p , γ ) P 31

Background: Abundance anomalies in some globular clusters, such as the enhancement of potassium and the depletion of magnesium, can be explained in terms of an earlier generation of stars polluting the presently observed ones. It was shown that the potential range of temperatures and densities of the polluting sites depends on the strength of a few critical reaction rates. The 30 Si(p,γ) 31 P reaction has been identified as one of these important reactions. Purpose: The key ingredient for evaluating the thermonuclear 30 Si(p,γ) 31 P reaction rate is the strength of the resonances which, at low energy, are proportional to their proton width. Therefore, the goal of this work is to determine the proton widths of unbound 31 P states. Method: States in 31 P were studied at the Maier-Leibnitz-Laboratorium using the one-proton 30 Si( 3 He,d) 31 P transfer reaction. Deuterons were detected with the high resolution one quadrupole three dipoles (Q3D) magnetic spectrometer. Angular distribution and spectroscopic factors were extracted for 27 states, and proton widths and resonance strengths were calculated for the unbound states. Results: Several 31 P unbound states have been observed for the first time in a one-proton transfer reaction. Above 20 MK, the 30 Si(p,γ) 31 P reaction rate is now entirely estimated from the observed properties of 31 P states. The reaction rate uncertainty from all resonances other than the E$^{c.m.}_{r}$ = 149 keV resonance has been reduced down to less than a factor of 2 above that temperature. The unknown spin and parity of the E$^{c.m.}_{r}$ = 149 keV resonance dominates the uncertainty in the rate in the relevant temperature range. Conclusion: Here, the remaining source of uncertainty on the 30 Si(p,γ) 31 P reaction rate comes from the unknown spin and parity of the E$^{c.m.}_{r}$ = 149 keV resonance which can change the reaction rate by a factor of 10 in the temperature range of interest.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

MindSynchro

This report presents the developments and results of MindSynchro project as part of DOE OE FOA 1861. DOE and Pacific Northwest National Laboratory (PNNL) have made available to FOA awardees datasets containing years of real historical data recorded from various phasor measurement units (PMUs) which are installed in three large US interconnections: Texas (IC A), Western (IC B), and Eastern (IC C). The main goal of the project, which was successfully achieved, was to develop methods for detection and identification of events which are relevant for power grid operation. Tasks performed for achieving the project goals included data exploration and pre-processing, the development and application of physics-based features, data analysis and labeling based on unsupervised learning approaches, training and testing of DSSL models for classification of events which are relevant for power grid operation, and deployment of solutions to cloud environments. The methods developed in the project can potentially provide relevant benefits to power grid asset owners/operators in general in terms of situational awareness. Two main types of outcomes can be provided by these tools: Identification of specific relevant power grid event types: Semi-supervised ML methods developed in the project can adequately employ not only the relatively scarce labeled data but also the large amount of available unlabeled data to train models for detection of specific event types. Such methods enable the application of trained models for the detection of events in a population of PMUs much larger than that associated to the labeled events. Support in data labeling / label validation: Labels are critical for training of models for identification of specific types of events. However, labeling large amounts of data is a manual and tedious process. This means that such process is error prone and is not scalable. Methods developed in the project, based on ensembles of clustering models, have been successfully employed for turning manual labeling into a scalable process. Accurate identification of specific relevant events can provide the operators with immediate situational awareness that could otherwise require hours or days of analysis from domain experts. We envision that such methods could be initially employed in support of post-mortem analysis of events and, as confidence is gained, they could be employed for online/real-time support, providing, among other benefits, insights for avoiding major events which could happen due to a combination of smaller ones. On the longer term, related methods could potentially be employed to improve protection and control.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Weighted FFT estimators for 1D and 3D correlations of the Lyman- α forest

Correlations in the Lyman-α (Lyα) forest, both as a function of line of sight separation (1D) and 3D separation, provide a unique window to the distribution of matter at redshifts not accessible by current galaxy surveys. While optimal quadratic estimators have been used to measure 1D correlations, they are computationally expensive and difficult to extend to 3D analyses. On the other hand, estimators based on the Fast Fourier Transform (FFT) are significantly faster, but are affected by missing data in the spectra (masked pixels) and so far have not used pixel weights to reduce the uncertainties in the measurement. In this publication we describe how to compute the window matrix that enables forward-modelling the impact of masked pixels and weights on the FFT-based estimators. Here, we use Gaussian and hydrodynamical simulations with artificially masked pixels to validate the method on the measurement of 1D correlations. Finally, we show that the formalism can be extended to model the impact on 3D correlations, in particular on the cross-spectrum, the correlation of 1D Fourier modes as a function of transverse separation. This work will enable more precise clustering measurements with the Lyα forest dataset recently collected by the Dark Energy Spectroscopic Instrument (DESI).

Lokken, Martine [Univ. Autonoma de Barcelona (Spai↗

Transfer Learning Trained LSTM Models for Household Load Profile Forecasting

Grid edge renewable energy resources, such as rooftop solar photovoltaics, closely interact with consumer load profiles. Therefore, forecasting future electricity demand, ideally at the individual household level, is indispensable. In this paper, we present a transfer learning enhanced household load profile forecasting method. First, we tune a long short-term memory forecasting model to perform day-ahead prediction of household electricity load profiles. Then we improve these individualized models using transfer learning, and we use k-means clustering to create optimal source data sets. We find average improvements of 4.38% (largest improvement of 10.71%) when the entire data set was used to train the source model and 2.45% (largest improvement of 11.57%) in the mean absolute error when households were first clustered and used to train separate source models for each cluster. We find that transfer learning with clustered data can effectively boost the forecasting performance of the LSTM models. We use realistic household power measurements for 148 real residential households in Austin, Texas.

deep learning↗

High-resolution source imaging and moment tensor estimation of acoustic emissions during brittle creep of basalt undergoing carbonation

SUMMARY As the high-frequency analogue to field-scale earthquakes, acoustic emissions (AEs) provide a valuable complement to study rock deformation mechanisms. During the load-stepping creep experiments with CO2-saturated water injection into a basaltic sample from Carbfix site in Iceland, 8791 AE events are detected by at least one of the seven piezoelectric sensors. Here, we apply a cross-correlation-based source imaging method, called geometric-mean reverse-time migration (GmRTM) to locate those AE events. Besides the attractive picking-free feature shared with other waveform-based methods (e.g. time-reversal imaging), GmRTM is advantageous in generating high-resolution source images with reduced imaging artefacts, especially for experiments with relatively sparse receivers. In general, the imaged AE locations are found to be scattered across the sample, suggesting a complicated fracture network rather than a well-defined major shear fracture plane, in agreement with X-ray computed tomography imaging results after retrieval of samples from the deformation apparatus. Clustering the events in space and time using the nearest-neighbour approach revealed a group of ‘repeaters’, which are spatially co-located over an elongated period of time and likely indicate crack, or shear band growth. Furthermore, we select 2196 AE events with high signal-to-noise-ratio (SNR) and conduct moment tensor estimation using the adjoint (backpropagated) strain tensor fields at the locations of AE sources. The resulting AE locations and focal mechanisms support our previously assertion that creep of basalt at the experimental conditions is accommodated dominantly by distributed microcracking.

58 GEOSCIENCES↗

Flow annealed importance sampling bootstrap meets differentiable particle physics

High-energy physics requires the generation of large numbers of simulated data samples from complex but analytically tractable distributions called matrix elements. Surrogate models, such as normalizing flows, are gaining popularity for this task due to their computational efficiency. We adopt an approach based on flow annealed importance sampling bootstrap (FAB) that evaluates the differentiable target density during training and helps avoid the costly generation of training data in advance. We show that FAB reaches higher sampling efficiency with fewer target evaluations in high dimensions in comparison to other methods.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Boundary-Aware Adversarial Learning Domain Adaption and Active Learning for Cross-Sensor Building Extraction

The use of convolutional neural networks (CNNs) for building extraction from remote sensing images has been widely studied and many public datasets have been made available for accelerating development of these CNN models. Yet adapting pretrained models at scale in real-world scenarios remains a challenging task. The main barrier is that certain new labels are still needed to compensate for domain shifting between the labeled data and new images that potentially cover new geographic locations or that are from a different sensor. In this article, we propose to add informatively labeled samples from a new image pool under the paradigm of active learning. To select the most useful samples based on model uncertainty, we first tackle the problem of uncalibrated uncertainty estimation due to distribution shifting by adapting feature extractors with boundary-based adversarial learning. Calibrated uncertainty is used as the query criterion in the active learning process, where the most uncertain samples are selected for annotation and included for model retraining. The proposed workflow was tested with three data pairs in which each workflow represents a scenario often encountered in real-world applications, including adapting pretrained models to new images collected with different sensors or to new geographic areas where appearances and types of buildings are very different. Compared to several baselines, including random sampling, temperature scaling (a well-known uncertainty calibration technique), different query strategies, and active domain adaptation methods, the proposed workflow shows that strategically querying a smaller set of samples for labeling achieves comparable or better building extraction performance. The proposed method reduces the number of labeled samples required to achieve sufficient model accuracy, thus significantly reducing hundreds of person-hours for labeled data creation. In addition, we include a few considerations when deploying this workflow in a GPU cluster that can be easily adapted to achieve operational building extraction model retraining.

97 MATHEMATICS AND COMPUTING↗

Exploring HOD-dependent systematics for the DESI 2024 Full-Shape galaxy clustering analysis

We analyze the robustness of the DESI 2024 cosmological inference from the full shape of the galaxy power spectrum to uncertainties in the Halo Occupation Distribution (HOD) model of the galaxy-halo connection and the choice of priors on nuisance parameters. We assess variations in the recovered cosmological parameters across a range of mocks populated with different HOD models and find that shifts are often greater than 20% of the expected statistical uncertainties from the DESI data. We encapsulate the effect of such shifts in terms of a systematic covariance term, C HOD , and an additional diagonal contribution quantifying the impact of our choice of nuisance parameter priors on the ability of the effective field theory (EFT) model to correctly recover the cosmological parameters of the simulations. These two covariance contributions are designed to be added to the usual covariance term, C stat , describing the statistical uncertainty in the power spectrum measurement, in order to fairly represent these sources of systematic uncertainty. This novel approach should be more general and robust to the choice of model or additional external datasets used in cosmological fits than the alternative approach of adding systematic uncertainties to the recovered marginalised parameter posteriors. We compare the approaches within the context of a fixed ΛCDM model and demonstrate that our method gives conservative estimates of the systematic uncertainty that nevertheless have little impact on the final posteriors obtained from DESI data.

79 ASTRONOMY AND ASTROPHYSICS↗

Complications in the interpretation of the charge-asymmetry-dependent π flow for the chiral magnetic wave

The charge asymmetry ($A_ch$) dependence of the $π^₋$ and $π^+$ elliptic flow difference, $Δv_2(A_{\text{ch}})$, has been regarded as a sensitive observable for the possible chiral magnetic wave (CMW) in relativistic heavy ion collisions. In this work, we first demonstrate that, due to nonflow backgrounds, the flow measurements by the Q-cumulant method using all charged particles as reference introduce a trivial linear term to $Δv_2(A_{\text{ch}})$. The trivial contribution to the slope of triangle flow difference $Δv_3( A_{\text{ch}})$ can be negative if the nonflow is dominated by back-to-back pairs. After eliminating the trivial term, we find that the nonflow between like-sign pairs gives rise to an additional positive slope to $Δv_2(A_{\text{ch}})$ because of the larger multiplicity dilution to $π^+$ ($π^₋$) at positive (negative) $A_{\text{ch}}$. We further find that the competition between different π sources can introduce another nontrivial linear-$A_{\text{ch}}$ term due to their different multiplicity fluctuations and anisotropic flows. We then study the effect of neutral cluster (resonance) decays as a mechanism for local charge conservation on the slope parameter of $Δv_2(A_{\text{ch}})$. We find that the slope parameter is sensitive to the kinematics of those neutral clusters. Light resonances give positive slopes while heavy resonances give negative slopes. Local charge conservation from continuum cluster mass distribution can give a positive slope parameter comparable to experimental data. Our studies indicate that many non-CMW physics mechanisms can give rise to a $A_{\text{ch}}$-dependent $Δv_2(A_{\text{ch}})$ and the interpretation of $Δv_2(A_{\text{ch}})$ in terms of the CMW is delicate.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Charge radii of exotic neon and magnesium isotopes

We compute the charge radii and ground-state energies of even-mass neon and magnesium isotopes from neutron number N = 8 to the dripline. Our calculations are based on nucleon-nucleon and three-nucleon potentials from chiral effective field theory that include Δ isobars. These potentials yield an accurate saturation point and symmetry energy of nuclear matter. We use the coupled-cluster method and start from an axially symmetric reference state. Binding energies and two-neutron separation energies largely agree with data, and the dripline in neon is accurate. The computed charge radii are accurate for many isotopes where data exist. Finer details, such as isotope shifts, however, are not accurately reproduced. These chiral potentials indicate a subshell closure at N = 14 for the radii (but not for two-neutron separation energies) and a decrease in charge radii at N = 8 (observed in neon and predicted for magnesium). Furthermore, they yield a continued increase of charge radii as neutrons are added beyond N = 14 yet underestimate the large increase at N = 20 in magnesium.

20 ≤ A ≤ 38↗

A Hydrogen Load Modeling Method for Integrated Hydrogen Energy System Planning

The integrated hydrogen energy system incorporates hydrogen energy into the power grid, which has been recognized as a promising option for reaching a 100% renewable electricity supply. It can make a profit because the hydrogen produced can be sold as fuel or used to generate electricity for grid services. In this paper, we develop a planning model for the integrated hydrogen energy system that considers the uncertainty of the load demand, the renewable energy generation, and the market prices. To calculate the hydrogen load, we simulate the refueling operations at a hydrogen fueling station over the course of one day and generate representative load profiles with K-means clustering. Moreover, the long-term profitability of the integrated system under both current and future conditions is validated in 10-year planning results.

grid service↗

Determination of Sodium Abundance Ratio from Low-resolution Stellar Spectra and Its Applications

We present a method to determine sodium abundance ratios ([Na/Fe]) using the Na i D doublet lines in low-resolution (R ~ 2000) stellar spectra. As stellar Na i D lines are blended with those produced by the interstellar medium, we developed a technique for removing the interstellar Na I D lines using the relationship between extinction, which is proportional to E(B – V), and the equivalent width of the interstellar Na i D absorption lines. When measuring [Na/Fe], we also considered corrections for nonlocal thermodynamic equilibrium (NLTE) effects. Comparisons with data from high-resolution spectroscopic surveys suggest that the expected precision of [Na/Fe] from low-resolution spectra is better than 0.3 dex for stars with [Fe/H] > –3.0. We also present a simple application employing the estimated [Na/Fe] values for a large number of stellar spectra from the Sloan Digital Sky Survey (SDSS). After classifying the SDSS stars into Na-normal, Na-high, and Na-extreme, we explore their relation to stars in Galactic globular clusters (GCs). We find that while the Na-high SDSS stars exhibit a similar metallicity distribution function (MDF) to that of the GCs, indicating that the majority of such stars may have originated from GC debris, the MDF of the Na-normal SDSS stars follows that of typical disk and halo stars. As there is a high fraction of carbon-enhanced metal-poor stars among the Na-extreme stars, they may have a non-GC origin, perhaps due to mass-transfer events from evolved binary companions.

79 ASTRONOMY AND ASTROPHYSICS↗

The Intrinsic Shapes of Low Surface Brightness Galaxies (LSBGs): A Discriminant of LSBG Galaxy Formation Mechanisms

We use the low surface brightness galaxy (LSBG) samples created from the Hyper Suprime-Cam Subaru Strategic Program (781 galaxies), the Dark Energy Survey (20977 galaxies), and the Legacy Survey (selected via H ι detection in the Arecibo Legacy Fast ALFA Survey, 188 galaxies) to infer the intrinsic shape distribution of the LSBG population. To take into account the effect of the surface brightness cuts employed when constructing LSBG samples, we simultaneously model both the projected ellipticity and the apparent surface brightness in our shape inference. We find that the LSBG samples are well characterized by oblate spheroids, with no significant difference between red and blue LSBGs. This inferred shape distribution is in good agreement with similar inferences made for ultra-diffuse cluster galaxy samples, indicating that environment does not play a key role in determining the intrinsic shape of LSBGs. In this study, we also find some evidence that LSBGs are more thickened than similarly massive high surface brightness dwarfs. We compare our results to intrinsic shape measures from contemporary cosmological simulations, and find that the observed LSBG intrinsic shapes place considerable constraints on the formation path of such galaxies. In particular, LSBG production via the migration of star formation to large radii produces intrinsic shapes in good agreement with our observational findings.

79 ASTRONOMY AND ASTROPHYSICS↗

DeepAstroUDA: semi-supervised universal domain adaptation for cross-survey galaxy morphology classification and anomaly detection

Abstract Artificial intelligence methods show great promise in increasing the quality and speed of work with large astronomical datasets, but the high complexity of these methods leads to the extraction of dataset-specific, non-robust features. Therefore, such methods do not generalize well across multiple datasets. We present a universal domain adaptation method, DeepAstroUDA , as an approach to overcome this challenge. This algorithm performs semi-supervised domain adaptation (DA) and can be applied to datasets with different data distributions and class overlaps. Non-overlapping classes can be present in any of the two datasets (the labeled source domain, or the unlabeled target domain), and the method can even be used in the presence of unknown classes. We apply our method to three examples of galaxy morphology classification tasks of different complexities (three-class and ten-class problems), with anomaly detection: (1) datasets created after different numbers of observing years from a single survey (Legacy Survey of Space and Time mock data of one and ten years of observations); (2) data from different surveys (Sloan Digital Sky Survey (SDSS) and DECaLS); and (3) data from observing fields with different depths within one survey (wide field and Stripe 82 deep field of SDSS). For the first time, we demonstrate the successful use of DA between very discrepant observational datasets. DeepAstroUDA is capable of bridging the gap between two astronomical surveys, increasing classification accuracy in both domains (up to 40 % on the unlabeled data), and making model performance consistent across datasets. Furthermore, our method also performs well as an anomaly detection algorithm and successfully clusters unknown class samples even in the unlabeled target dataset.

79 ASTRONOMY AND ASTROPHYSICS↗

Profiling the BLAST bioinformatics application for load balancing on high-performance computing clusters

Abstract Background The Basic Local Alignment Search Tool (BLAST) is a suite of commonly used algorithms for identifying matches between biological sequences. The user supplies a database file and query file of sequences for BLAST to find identical sequences between the two. The typical millions of database and query sequences make BLAST computationally challenging but also well suited for parallelization on high-performance computing clusters. The efficacy of parallelization depends on the data partitioning, where the optimal data partitioning relies on an accurate performance model. In previous studies, a BLAST job was sped up by 27 times by partitioning the database and query among thousands of processor nodes. However, the optimality of the partitioning method was not studied. Unlike BLAST performance models proposed in the literature that usually have problem size and hardware configuration as the only variables, the execution time of a BLAST job is a function of database size, query size, and hardware capability. In this work, the nucleotide BLAST application BLASTN was profiled using three methods: shell-level profiling with the Unix “time” command, code-level profiling with the built-in “profiler” module, and system-level profiling with the Unix “gprof” program. The runtimes were measured for six node types, using six different database files and 15 query files, on a heterogeneous HPC cluster with 500+ nodes. The empirical measurement data were fitted with quadratic functions to develop performance models that were used to guide the data parallelization for BLASTN jobs. Results Profiling results showed that BLASTN contains more than 34,500 different functions, but a single function, RunMTBySplitDB, takes 99.12% of the total runtime. Among its 53 child functions, five core functions were identified to make up 92.12% of the overall BLASTN runtime. Based on the performance models, static load balancing algorithms can be applied to the BLASTN input data to minimize the runtime of the longest job on an HPC cluster. Four test cases being run on homogeneous and heterogeneous clusters were tested. Experiment results showed that the runtime can be reduced by 81% on a homogeneous cluster and by 20% on a heterogeneous cluster by re-distributing the workload. Discussion Optimal data partitioning can improve BLASTN’s overall runtime 5.4-fold in comparison with dividing the database and query into the same number of fragments. The proposed methodology can be used in the other applications in the BLAST+ suite or any other application as long as source code is available.

59 BASIC BIOLOGICAL SCIENCES↗

Remote Sensing-Informed Zonation for Understanding Snow, Plant and Soil Moisture Dynamics within a Mountain Ecosystem

In the headwater catchments of the Rocky Mountains, plant productivity and its dynamics are largely dependent upon water availability, which is influenced by changing snowmelt dynamics associated with climate change. Understanding and quantifying the interactions between snow, plants and soil moisture is challenging, since these interactions are highly heterogeneous in mountainous terrain, particularly as they are influenced by microtopography within a hillslope. Recent advances in satellite remote sensing have created an opportunity for monitoring snow and plant dynamics at high spatiotemporal resolutions that can capture microtopographic effects. In this study, we investigate the relationships among topography, snowmelt, soil moisture and plant dynamics in the East River watershed, Crested Butte, Colorado, based on a time series of 3-meter resolution PlanetScope normalized difference vegetation index (NDVI) images. To make use of a large volume of high-resolution time-lapse images (17 images total), we use unsupervised machine learning methods to reduce the dimensionality of the time lapse images by identifying spatial zones that have characteristic NDVI time series. We hypothesize that each zone represents a set of similar snowmelt and plant dynamics that differ from other identified zones and that these zones are associated with key topographic features, plant species and soil moisture. We compare different distance measures (Ward and complete linkage) to understand the effects of their influence on the zonation map. Results show that the identified zones are associated with particular microtopographic features; highly productive zones are associated with low slopes and high topographic wetness index, in contrast with zones of low productivity, which are associated with high slopes and low topographic wetness index. The zones also correspond to particular plant species distributions; higher forb coverage is associated with zones characterized by higher peak productivity combined with rapid senescence in low moisture conditions, while higher sagebrush coverage is associated with low productivity and similar senescence patterns between high and low moisture conditions. In addition, soil moisture probe and sensor data confirm that each zone has a unique soil moisture distribution. This cluster-based analysis can tractably analyze high-resolution time-lapse images to examine plant-soil-snow interactions, guide sampling and sensor placements and identify areas likely vulnerable to ecological change in the future.

54 ENVIRONMENTAL SCIENCES↗

AutoEnRichness: A hybrid empirical and analytical approach for estimating the richness of galaxy clusters

ABSTRACT We introduce AutoEnRichness, a hybrid approach that combines empirical and analytical strategies to determine the richness of galaxy clusters (in the redshift range of 0.1 ≤ z ≤ 0.35) using photometry data from the Sloan Digital Sky Survey Data Release 16, where cluster richness can be used as a proxy for cluster mass. In order to reliably estimate cluster richness, it is vital that the background subtraction is as accurate as possible when distinguishing cluster and field galaxies to mitigate severe contamination. AutoEnRichness is comprised of a multistage machine learning algorithm that performs background subtraction of interloping field galaxies along the cluster line of sight and a conventional luminosity distribution fitting approach that estimates cluster richness based only on the number of galaxies within a magnitude range and search area. In this proof-of-concept study, we obtain a balanced accuracy of 83.20 per cent when distinguishing between cluster and field galaxies as well as a median absolute percentage error of 33.50 per cent between our estimated cluster richnesses and known cluster richnesses within r200. In the future, we aim for AutoEnRichness to be applied on upcoming large-scale optical surveys, such as the Legacy Survey of Space and Time and Euclid, to estimate the richness of a large sample of galaxy groups and clusters from across the halo mass function. This would advance our overall understanding of galaxy evolution within overdense environments as well as enable cosmological parameters to be further constrained.

79 ASTRONOMY AND ASTROPHYSICS↗

Dynamic Shaping of Grid Response of Multi-Machine Multi-Inverter Systems Through Grid-Forming IBRs

We consider the problem of controlling the frequency response of weakly-coupled multi-machine multi-inverter low-inertia power systems via grid-forming inverter-based resources (IBRs). In contrast to existing methods, our approach relies on dividing the larger system into multiple strongly-coupled subsystems, without ignoring either the underlying network or approximating the subsystem response as an aggregate harmonic mean model. Rather, through a structured clustering and recursive dynamic shaping approach, the frequency response of the overall system to load perturbations is shaped appropriately. We demonstrate the proposed approach for a three-node triangular configuration and a small-scale radial network. Furthermore, previous synchronization analysis for heterogeneous systems requires the machines to satisfy certain proportionality property. In our approach, the effective transfer functions for each cluster can be tuned by the IBRs to satisfy such property, enabling us to apply the shaping control to systems with a wider range of heterogeneous machines.

frequency-shaping control↗