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DOE OSTI2023

Mind the gap: the discrepancy between simulation and reality drives interpretations of the Galactic Center Excess

The Galactic Center Excess (GCE) in GeV gamma rays has been debated for over a decade, with the possibility that it might be due to dark matter annihilation or undetected point sources such as millisecond pulsars (MSPs). This study investigates how the gamma-ray emission model (γEM) used in Galactic center analyses affects the interpretation of the GCE's nature. To address this issue, we construct an ultra-fast and powerful inference pipeline based on convolutional Deep Ensemble Networks. We explore the two main competing hypotheses for the GCE using a set of γEMs with increasing parametric freedom. We calculate the fractional contribution (f src ) of a dim population of MSPs to the total luminosity of the GCE and analyze its dependence on the complexity of the γEM. For the simplest γEM, we obtain fsrc = 0.10 ± 0.07, while the most complex model yields f src = 0.79 ± 0.24. In conclusion, we find that the statement about the nature of the GCE (dark matter or not) strongly depends on the assumed γEM. The quoted results for f src do not account for the additional uncertainty arising from the fact that the observed gamma-ray sky is out-of-distribution concerning the investigated γEM iterations. We quantify the reality gap between our γEMs using deep-learning-based One-Class Deep Support Vector Data Description networks, revealing that all employed γEMs have gaps to reality. Finally, our study casts doubt on the validity of previous conclusions regarding the GCE and dark matter, and underscores the urgent need to account for the reality gap and consider previously overlooked "out of domain" uncertainties in future interpretations.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

Heterogeneous energetic material damage simulator (HEDS): A deep learning approach to simulate damage–sensitivity linkages

Damage in the microstructures of energetic materials (EMs), such as propellants and plastic bonded explosives (PBXs), can significantly alter their response to external loads. Both sensitization and desensitization can occur, causing concerns with safety and performance in the field; predictive models that connect damage and the sensitivity of EMs can enable design and provide confidence in their robustness and reliability. However, modeling of damage evolution is challenging for real microstructures of EMs; samples of damaged EMs are difficult to obtain, thereby hindering experiments and direct numerical simulations to determine the sensitivity of EMs at various stages of damage. Here, we develop an approach to generate synthetic, i.e., in silico produced, damaged microstructures for use in simulations to connect damage levels to sensitivity. The development of the present workflow to generate and impose varying levels of damage in microstructures, known as HEDS (Heterogeneous Energetic Material Damage Simulator), begins with a small set of images of damaged PBXs and combines a collection of deep neural network techniques to generate microstructures with varying levels of damage. By making the synthetic microstructures conform closely to those observed in available real, imaged microstructures, we develop an ensemble of damaged microstructures that can be used for in silico shock experiments. HEDS develops these microstructure ensembles as level set fields, which are directly employed in a sharp interface Eulerian hydrocode where shock simulations are performed to quantify the energy release rate from hotspot fields generated in the microstructure. These capabilities can be useful for the analysis and assessment of changes in the sensitivity of EMs and to design formulations that are less susceptible to damage-induced changes in sensitivity and performance.

Fang, Irene (ORCID:0009000844557122)↗

DOE OSTI2025

Improving Trustworthiness of Data-Driven Power Grid Contingency Analysis With Bayesian Residual Graph Neural Networks

The evolving energy landscape requires novel tools to efficiently perform contingency analysis and reliability assessment of power grids, potentially in real-time. The high computational cost of traditional power flow solvers limits their applicability in practice. Machine learning (ML) surrogates such as deep neural networks (NNs) accelerate power flow solvers computations, enabling high-order contingency analysis and real-time decision-making by learning highly nonlinear functions and integrating grid topology via graph architectures. However, (graph) NNs lack predictive power away from training data and do not provide predictive confidence estimates. Here, we present a Bayesian residual graph NN that integrates knowledge from low-fidelity data via residual training and embeds granular quantification of uncertainties, improving trustworthiness critical for high-consequence decision-making. Applying Bayesian concepts to NNs is challenging due to the high-dimensionality of both the parameter space, complicating derivation of a meaningful prior, and the output space in large grid systems, requiring enhanced techniques to assess the predicted high-dimensional uncertainties. Our contributions include: (1) Deriving a prior for fully connected and graph NNs that leverages low-fidelity data to guide mean predictions and appropriately control prior predictive uncertainty. (2) Integrating this prior within an ensembling with anchoring scheme for efficient approximate posterior inference. (3) Deriving enhanced metrics to assess accuracy of both the mean and uncertainty predictions in high dimensions, appropriately accounting for correlations propagated through graph layers. The resulting Bayesian residual graph NN is tested on a contingency analysis task for 14-bus and 118-bus grids.

24 - POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2022

Downscaling atmospheric chemistry simulations with physically consistent deep learning

Abstract. Recent advances in deep convolutional neural network (CNN)-based super resolution can be used to downscale atmospheric chemistry simulations with substantially higher accuracy than conventional downscaling methods. This work both demonstrates the downscaling capabilities of modern CNN-based single image super resolution and video super-resolution schemes and develops modifications to these schemes to ensure they are appropriate for use with physical science data. The CNN-based video super-resolution schemes in particular incur only 39 % to 54 % of the grid-cell-level error of interpolation schemes and generate outputs with extremely realistic small-scale variability based on multiple perceptual quality metrics while performing a large (8×10) increase in resolution in the spatial dimensions. Methods are introduced to strictly enforce physical conservation laws within CNNs, perform large and asymmetric resolution changes between common model grid resolutions, account for non-uniform grid-cell areas, super-resolve lognormally distributed datasets, and leverage additional inputs such as high-resolution climatologies and model state variables. High-resolution chemistry simulations are critical for modeling regional air quality and for understanding future climate, and CNN-based downscaling has the potential to generate these high-resolution simulations and ensembles at a fraction of the computational cost.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

Effective optimization of atomic decoration in giant and superstructurally ordered crystals with machine learning

Crystals with complicated geometry are often observed with mixed chemical occupancy among Wyckoff sites, presenting a unique challenge for accurate atomic modeling. Similar systems possessing exact occupancy on all the sites can exhibit superstructural ordering, dramatically inflating the unit cell size. In this work, a crystal graph convolutional neural network (CGCNN) is used to predict optimal atomic decorations on fixed crystalline geometries. This is achieved with a site permutation search (SPS) optimization algorithm based on Monte Carlo moves combined with simulated annealing and basin-hopping techniques. Our approach relies on the evidence that, for a given chemical composition, a CGCNN estimates the correct energetic ordering of different atomic decorations, as predicted by electronic structure calculations. This provides a suitable energy landscape that can be optimized according to site occupation, allowing the prediction of chemical decoration in crystals exhibiting mixed or disordered occupancy, or superstructural ordering. Verification of the procedure is carried out on several known compounds, including the superstructurally ordered clathrate compound Rb8Ga27Sb16 and vacancy-ordered perovskite Cs2SnI6, neither of which was previously seen during the neural network training. In addition, the critical temperature of an order–disorder phase transition in solid solution CuZn is probed with our SPS routines by sampling site configuration trajectories in the canonical ensemble. This strategy provides an accurate method for determining favorable decoration in complex crystals and analyzing site occupation at unprecedented speed and scale.

Chemistry↗

NASA NTRS2019

Exploring the Utility of Machine Learning-Based Passive Microwave Brightness Temperature Data Assimilation over Terrestrial Snow in High Mountain Asia

This study explores the use of a support vector machine (SVM) as the observation operator within a passive microwave brightness temperature data assimilation framework (herein SVM-DA) to enhance the characterization of snow water equivalent (SWE) over High Mountain Asia (HMA). A series of synthetic twin experiments were conducted with the NASA Land Information System (LIS) at a number of locations across HMA. Overall, the SVM-DA framework is effective at improving SWE estimates (~70% reduction in RMSE relative to the Open Loop) for SWE depths less than 200 mm during dry snowpack conditions. The SVM-DA framework also improves SWE estimates in deep, wet snow (~45% reduction in RMSE) when snow liquid water is well estimated by the land surface model, but can lead to model degradation when snow liquid water estimates diverge from values used during SVM training. In particular, two key challenges of using the SVM-DA framework were observed over deep, wet snowpacks. First, variations in snow liquid water content dominate the brightness temperature spectral difference (TB) signal associated with emission from a wet snowpack, which can lead to abrupt changes in SWE during the analysis update. Second, the ensemble of SVM-based predictions can collapse (i.e., yield a near-zero standard deviation across the ensemble) when prior estimates of snow are outside the range of snow inputs used during the SVM training procedure. Such a scenario can lead to the presence of spurious error correlations between SWE and TB, and as a consequence, can result in degraded SWE estimates from the analysis update. These degraded analysis updates can be largely mitigated by applying rule-based approaches. For example, restricting the SWE update when the standard deviation of the predicted TB is greater than 0.05 K helps prevent the occurrence of filter divergence. Similarly, adding a thin layer (i.e., 5 mm) of SWE when the synthetic TB is larger than 5 K can improve SVM-DA performance in the presence of a precipitation dry bias. The study demonstrates that a carefully constructed SVM-DA framework cognizant of the inherent limitations of passive microwave-based SWE estimation holds promise for snow mass data assimilation.

Kwon, Yonghwan↗

DOE OSTI2025

Leveraging AI and Spatial Data to Unlock Pipeline Integrity Insights: NETL’s Advanced Infrastructure Integrity Model (AIIM)

Maintaining the integrity of natural gas infrastructure plays a critical role in ensuring energy security. Robust, data-driven foundational AI models for pipeline integrity can help address risk management and mitigation issues. Trusted foundational models can help with industry adoption and accelerate innovation by enhancing integrity predictions, reduce costs, and informing infrastructure build-out. The AIIM dashboard was released in 2022 and utilizes multi-ML models for ensemble-type insights. It was expanded to include analytics on reported incidents. It was developed as an ESRI Dashboard to support data visualization & interrogation and contains pipeline data and model results.

Advanced Infrastructure Integrity Model (AIIM)↗

DOE OSTI2025

Uncertainty Quantification for Data-Driven Machine Learning Models in Nuclear Engineering Applications: Where We Are and What Do We Need?

Machine learning (ML) has been leveraged to tackle a diverse range of tasks in almost all branches of nuclear engineering. Many of the successes in ML applications can be attributed to the recent performance breakthroughs in deep learning, the growing availability of computational power, data, and easy-to-use ML libraries. However, these empirical successes have often outpaced our formal understanding of the ML algorithms. An important but under-rated area is uncertainty quantification (UQ) of ML. ML-based models are subject to approximation uncertainty when they are used to make predictions, due to sources including but not limited to, data noise, data coverage, extrapolation, imperfect model architecture and the stochastic training process. The goal of this paper is to clearly explain and illustrate the importance of UQ of ML. We will elucidate the differences in the basic concepts of UQ of physics-based models and data-driven ML models. Various sources of uncertainties in physical modeling and data-driven modeling will be discussed, demonstrated, and compared. We will also present and demonstrate a few techniques to quantify the ML prediction uncertainties, including Monte Carlo dropout, deep ensemble, Bayesian neural networks, Gaussian Processes and conformal prediction. Lastly, we will discuss the need for building a verification, validation and UQ framework to establish ML credibility.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2022

Entanglement features of random neural network quantum states

Restricted Boltzmann machines (RBMs) are a class of neural networks that have been successfully employed as a variational ansatz for quantum many-body wave functions. Here, we develop an analytic method to study quantum many-body spin states encoded by random RBMs with independent and identically distributed complex Gaussian weights. By mapping the computation of ensemble-averaged quantities to statistical mechanics models, we are able to investigate the parameter space of the RBM ensemble in the thermodynamic limit. We discover qualitatively distinct wave functions by varying RBM parameters, which correspond to distinct phases in the equivalent statistical mechanics model. Notably, there is a regime in which the typical RBM states have near-maximal entanglement entropy in the thermodynamic limit, similar to that of Haar-random states. However, these states generically exhibit nonergodic behavior in the Ising basis, and do not form quantum state designs, making them distinguishable from Haar-random states.

36 MATERIALS SCIENCE↗

DOE OSTI2024

PreMevE‐MEO: Predicting Ultra‐Relativistic Electrons Using Observations From GPS Satellites

Abstract Ultra‐relativistic electrons with energies greater than or equal to two megaelectron‐volt (MeV) pose a major radiation threat to spaceborne electronics, and thus specifying those highly energetic electrons has a significant meaning to space weather communities. Here we report the latest progress in developing our predictive model for MeV electrons in the outer radiation belt. The new version, primarily driven by electron measurements made along medium‐Earth‐orbits (MEO), is called PREdictive MEV Electron (PreMevE)‐MEO model that nowcasts ultra‐relativistic electron flux distributions across the whole outer belt. Model inputs include >2 MeV electron fluxes observed in MEOs by a fleet of GPS satellites as well as electrons measured by one Los Alamos satellite in the geosynchronous orbit. We developed an innovative Sparse Multi‐Inputs Latent Ensemble NETwork (SmileNet) which combines convolutional neural networks with transformers, and we used long‐term in situ electron data from NASA's Van Allen Probes mission to train, validate, optimize, and test the model. It is shown that PreMevE‐MEO can provide hourly nowcasts with high model performance efficiency and high correlation with observations. This prototype PreMevE‐MEO model demonstrates the feasibility of making high‐fidelity predictions driven by observations from longstanding space infrastructure in MEO, thus has great potential of growing into an invaluable space weather operational warning tool.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

Enhanced Boundary Layer Height Detection Using Ceilometer, Surface Meteorology, and Radiation Products With a Random Forest Ensemble Method

This study develops and evaluates a Random Forest (RF) model for estimating planetary boundary layer height (PBLH) using 9 years of data from the Atmospheric Radiation Measurement Southern Great Plains (ARM SGP) user facility, with potential application in the NOAA Surface Radiation (SURFRAD) Network. The model integrates ceilometer, surface meteorology, and radiation measurements, and is trained using thermodynamic PBLH estimates derived from radiosondes. This approach aims to bridge gaps between aerosol-based and thermodynamic-based PBLH estimates. The RF model outperformed traditional methods during daytime and better captured transition periods, demonstrating improved accuracy and robustness. At ARM SGP, it showed a substantial reduction in both bias and RMSE, with a bias near zero (−4.9 m) compared with traditional Haar Wavelet (HW) (70.9 m) and Vaisala BL-View software (124.1 m), and an RMSE of 303.2 m, lower than both BL-View (566.9 m) and HW (404.6 m). During daytime hours, RF consistently outperformed both alternatives, maintaining lower bias and RMSE across all periods. At a second evaluation site, RF achieved the lowest overall RMSE (323.7 m), similar to HW (326.4 m) and significantly better than BL-View (738.3 m). However, all models showed reduced accuracy under stable nighttime conditions, limiting the reliability of PBLH estimates. Key predictors for the model included the lifting condensation level height (LCLH), aerosol gradients, and month for seasonal variability. The study underscores the potential of integrating machine learning with multiple data sets such as surface energy and thermodynamic data to advance PBLH estimation.

boundary layer height↗

DOE OSTI2021

Unsupervised Power System Event Detection and Classification Using Unlabeled PMU Data

This paper proposes a novel data-driven power system event detection and classification method based on 5TB of actual PMU measurements collected from the US western interconnect. Firstly, a set of comprehensive power quality rules are proposed to pre-filter the raw data and extract the regions of interest (ROI). Six distinct event categories are defined and corresponding patterns are chosen as references. Meanwhile, detailed characteristics of patterns are summarized to enhance our understanding of the actual events. Then, the time-independent feature vectors are generated by extracting the statistical, temporal, and spectral features from the raw time-series data. Furthermore, an ensemble model is proposed to cluster the events by combining multiple K-means clustering models using a voting strategy. Besides, both system-level and PMU-level clustering models are developed. The accuracy and robustness of the event detection method are further improved through interactive evaluation of the two-level clustering results. This paper summarizes the actual characteristics of each event category and provides a reliable basis for accurate label generation. The experiments demonstrate the effectiveness of the proposed event detection and classification method.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2021

Unsupervised Power System Event Detection and Classification Using Unlabeled PMU Data

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2025

An efficient hybrid downscaling framework to estimate high-resolution river hydrodynamics

Flow depth and velocity are the most important hydrodynamic variables that govern various river functions, including water resources, navigation, sediment transport, and biogeochemical cycling. Existing high-resolution flow depth simulations rely on either computationally expensive river hydrodynamic models (RHMs) or data-driven models with formidable training costs, whereas data-driven modeling of flow velocity has rarely been explored. Here, using the hybrid Low-fidelity, Spatial analysis, and Gaussian process learning (LSG) model, we developed a downscaling approach to construct high-resolution flow depth and velocity from a two-dimensional (2-D) RHM simulation at coarse resolution. The LSG models were trained and tested in an urban watershed in Houston using two different hurricane-driven flood events. The high-resolution (as fine as 30 m resolution) and low-resolution (mostly 1000 m resolution) meshes include 664 724 and 14 536 grid cells, respectively. The results showed that through downscaling, the simulation errors were reduced to less than one-fourth and one-third of the errors of the low-resolution 2-D RHM for flow depth and velocity, respectively. Our analysis further revealed that the dominant uncertainty sources of the downscaled hydrodynamics are different, with flow velocity dominated by the dimensionality reduction error, which we reduced by using a regionalized training procedure. The downscaling approach achieves an 84-fold acceleration in computational time compared to the high-resolution 2-D RHM, making high-fidelity ensemble flood modeling feasible. More importantly, the developed method provides an opportunity to couple large-scale hydrodynamical processes with local physical, chemical, and biological processes in river models.

Tan, Zeli [Pacific Northwest National Laboratory (↗

DOE OSTI2023

Agilent AgileBioFoundry CRADA (Final Report)

The mission of this CRADA with Agilent was to couple powerful MS platforms (QQQ, IM-QTOF-MS) with Agilent’s novel Ultra-High-Performance Liquid Chromatography (UHPLC) fast metabolomic workflows and perform ABF Machine Learning (ML) to generated datasets. Agilent transferred UHPLC methods to PNNL and LBNL and methods were implemented and demonstrated in both labs, achieving total acquisition times of < 10 min. Metabolites analyzed using Agilent’s shared methods included metabolites from central carbon metabolism, common across hosts, and metabolites unique to engineered strains. Standards were acquired in an UHPLC-Drift Tube Ion Mobility Mass Spectrometer (DTIMS) system for the first time within the context of ABF and methods were optimized based on Agilent’s protocols. Samples from ABF hosts Pseudomonas putida, Aspergillus pseudoterreus, Aspergillus niger and Rhodosporidium toruloides were analyzed using the UHPLC-DTIMS platform for a total of 276 runs. A data analysis workflow compatible with the Experimental Data Depot (EDD) and completely shareable was developed for the acquired UHPLC-DTIMS data. Samples were analyzed using a Data Independent Acquisition Approach (DIA), which for most of the standards provided more transitions therefore increasing detection confidence. Using the data acquired by PNNL, LBNL, and Agilent’s specifications from previous ML projects, SNL applied an ensemble ML strategy to pick the best performing model for automated LC-method selection. Finally, with the contribution of the participant labs and Agilent, SNL developed an Automated Method Selection (AMS) software tool to predict the best liquid chromatography method for analysis of any new molecules of interest. Samples with novel pathways and new metabolite targets of interest are generated at a high pace in the ABF. Therefore, our accomplishment in this CRADA improved the efficiency and accuracy of strain testing by developing and implementing fast analytical methods, robust processing tools, and software for predicting the best methods for UHPLC analysis.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2010

Bird Migration Under Climate Change - A Mechanistic Approach Using Remote Sensing

The broad-scale reductions and shifts that may be expected under climate change in the availability and quality of stopover habitat for long-distance migrants is an area of increasing concern for conservation biologists. Researchers generally have taken two broad approaches to the modeling of migration behaviour to understand the impact of these changes on migratory bird populations. These include models based on causal processes and their response to environmental stimulation, "mechanistic models", or models that primarily are based on observed animal distribution patterns and the correlation of these patterns with environmental variables, i.e. "data driven" models. Investigators have applied the latter technique to forecast changes in migration patterns with changes in the environment, for example, as might be expected under climate change, by forecasting how the underlying environmental data layers upon which the relationships are built will change over time. The learned geostatstical correlations are then applied to the modified data layers.. However, this is problematic. Even if the projections of how the underlying data layers will change are correct, it is not evident that the statistical relationships will remain the same, i.e. that the animal organism may not adapt its' behaviour to the changing conditions. Mechanistic models that explicitly take into account the physical, biological, and behaviour responses of an organism as well as the underlying changes in the landscape offer an alternative to address these shortcomings. The availability of satellite remote sensing observations at multiple spatial and temporal scales, coupled with advances in climate modeling and information technologies enable the application of the mechanistic models to predict how continental bird migration patterns may change in response to environmental change. In earlier work, we simulated the impact of effects of wetland loss and inter-annual variability on the fitness of migratory shorebirds in the central fly ways of North America. We demonstrated the phenotypic plasticity of a migratory population of Pectoral sandpipers consisting of an ensemble of 10,000 individual birds in response to changes in stopover locations using an individual based migration model driven by remotely sensed land surface data, climate data and biological field data. With the advent of new computing capabilities enabled hy recent GPU-GP computing paradigms and commodity hardware, it now is possible to simulate both larger ensemble populations and to incorporate more realistic mechanistic factors into migration models. Here, we take our first steps use these tools to study the impact of long-term drought variability on shorebird survival.

Smith, James A.↗

NASA NTRS2023

The Statistical Emulators of GGCMI Phase 2: Responses of Year-to-Year Variation of Crop Yield to CO 2 , Temperature, Water and Nitrogen Perturbations

Understanding the impact of climate change on year-to-year variation of crop yield is critical to global food stability and security. While crop model emulators are believed to be lightweight tools to replace the models, few emulators have been developed to capture such interannual variation of crop yield in response to climate variability. In this study, we developed a statistical emulator with a machine learning algorithm to reproduce the response of year-to-year variation of four crop yields to CO 2 (C), temperature (T), water (W), and nitrogen (N) perturbations defined in the Global Gridded Crop Model Intercomparison Project (GGCMI) phase 2. The emulators were able to explain more than 52 % of the variance of simulated yield and performed well in capturing the year-to-year variation of global average and gridded crop yield over current croplands in the baseline. With the changes in CO 2 –temperature–water–nitrogen (CTWN) perturbations, the emulators could reproduce the year-to-year variation of crop yield well over most current cropland. The variation of R and the mean absolute error was small under the single CTWN perturbations and dual-factor perturbations. These emulators thus provide statistical response surfaces of yield, including both its mean and interannual variability, to climate factors. They could facilitate spatiotemporal downscaling of crop model simulation, projecting the changes in crop yield variability in the future and serving as a lightweight tool for multi-model ensemble simulation. The emulators enhanced the flexibility of crop yield estimates and expanded the application of large-ensemble simulations of crop yield under climate change.

Climate change↗

NASA NTRS2013

Forecasting Propagation and Evolution of CMEs in an Operational Setting: What Has Been Learned

One of the major types of solar eruption, coronal mass ejections (CMEs) not only impact space weather, but also can have significant societal consequences. CMEs cause intense geomagnetic storms and drive fast mode shocks that accelerate charged particles, potentially resulting in enhanced radiation levels both in ions and electrons. Human and technological assets in space can be endangered as a result. CMEs are also the major contributor to generating large amplitude Geomagnetically Induced Currents (GICs), which are a source of concern for power grid safety. Due to their space weather significance, forecasting the evolution and impacts of CMEs has become a much desired capability for space weather operations worldwide. Based on our operational experience at Space Weather Research Center at NASA Goddard Space Flight Center (http://swrc.gsfc.nasa.gov), we present here some of the insights gained about accurately predicting CME impacts, particularly in relation to space weather operations. These include: 1. The need to maximize information to get an accurate handle of three-dimensional (3-D) CME kinetic parameters and therefore improve CME forecast; 2. The potential use of CME simulation results for qualitative prediction of regions of space where solar energetic particles (SEPs) may be found; 3. The need to include all CMEs occurring within a ~24 h period for a better representation of the CME interactions; 4. Various other important parameters in forecasting CME evolution in interplanetary space, with special emphasis on the CME propagation direction. It is noted that a future direction for our CME forecasting is to employ the ensemble modeling approach.

forecasting↗