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DOE OSTI2022

Representing Socio‐Economic Uncertainty in Human System Models

Abstract Socio‐economic development pathways and their implications for the environment are highly uncertain, and energy transitions will involve complex interactions among sectors. Here, traditional Monte Carlo analysis is paired with scenario discovery techniques to provide a richer portrait of these complexities. Modeled uncertain input variables include costs of advanced energy technologies, energy efficiency trends, fossil fuel resource availability, elasticities of substitution for labor, capital, and energy across economic sectors, population growth, and labor and capital productivity. The sampled values are simulated through a multi‐sector, multi‐region, recursively dynamic model of the world economy to explore a range of possible future outcomes. We find that many patterns of energy and technology development are possible for various long‐term environmental pathways and that sectoral output for most sectors is little affected through 2050 by the long‐term temperature target, but with tight constraints on emissions, emission intensities must fall much more rapidly. Scenario discovery techniques are applied to the large uncertainty ensembles to explore if there are prevailing storylines behind outcomes of interest. An illustrative investigation focused on different levels of economic growth shows many combinations of pathways and no single storyline emerging for a given economic outcome. This method can be extended to other outcomes of interest, exploring the nature of scenarios with both tail and median outcomes. Sampling from a Monte Carlo generated ensemble provides a rich set of scenarios to investigate, and potentially aids in avoiding heuristic biases in less structured scenario approaches.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2022

The DOE E3SM Model Version 2: Overview of the Physical Model and Initial Model Evaluation

Abstract This work documents version two of the Department of Energy's Energy Exascale Earth System Model (E3SM). E3SMv2 is a significant evolution from its predecessor E3SMv1, resulting in a model that is nearly twice as fast and with a simulated climate that is improved in many metrics. We describe the physical climate model in its lower horizontal resolution configuration consisting of 110 km atmosphere, 165 km land, 0.5° river routing model, and an ocean and sea ice with mesh spacing varying between 60 km in the mid‐latitudes and 30 km at the equator and poles. The model performance is evaluated with Coupled Model Intercomparison Project Phase 6 Diagnosis, Evaluation, and Characterization of Klima simulations augmented with historical simulations as well as simulations to evaluate impacts of different forcing agents. The simulated climate has many realistic features of the climate system, with notable improvements in clouds and precipitation compared to E3SMv1. E3SMv1 suffered from an excessively high equilibrium climate sensitivity (ECS) of 5.3 K. In E3SMv2, ECS is reduced to 4.0 K which is now within the plausible range based on a recent World Climate Research Program assessment. However, a number of important biases remain including a weak Atlantic Meridional Overturning Circulation, deficiencies in the characteristics and spectral distribution of tropical atmospheric variability, and a significant underestimation of the observed warming in the second half of the historical period. An analysis of single‐forcing simulations indicates that correcting the historical temperature bias would require a substantial reduction in the magnitude of the aerosol‐related forcing.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2023

An Ensemble of Neural Networks for Moist Physics Processes, Its Generalizability and Stable Integration

Abstract With the recent advances in data science, machine learning has been increasingly applied to convection and cloud parameterizations in global climate models (GCMs). This study extends the work of Han et al. (2020, https://doi.org/10.1029/2020MS002076 ) and uses an ensemble of 32‐layer deep convolutional residual neural networks, referred to as ResCu‐en, to emulate convection and cloud processes simulated by a superparameterized GCM, SPCAM. ResCu‐en predicts GCM grid‐scale temperature and moisture tendencies, and cloud liquid and ice water contents from moist physics processes. The surface rainfall is derived from the column‐integrated moisture tendency. The prediction uncertainty inherent in deep learning algorithms in emulating the moist physics is reduced by ensemble averaging. Results in 1‐year independent offline validation show that ResCu‐en has high prediction accuracy for all output variables, both in the current climate and in a warmer climate with +4K sea surface temperature. The analysis of different neural net configurations shows that the success to generalize in a warmer climate is attributed to convective memory and the 1‐dimensional convolution layers incorporated into ResCu‐en. We further implement a member of ResCu‐en into CAM5 with real world geography and run the neural‐network‐enabled CAM5 (NCAM) for 5 years without encountering any numerical integration instability. The simulation generally captures the global distribution of the mean precipitation, with a better simulation of precipitation intensity and diurnal cycle. However, there are large biases in temperature and moisture in high latitudes. These results highlight the importance of convective memory and demonstrate the potential for machine learning to enhance climate modeling.

Meteorology & Atmospheric Sciences↗

DOE OSTI2025

ZTF SN Ia DR2: Improved SN Ia colors through expanded dimensionality with SALT3+

Context. Type Ia supernovae (SNe Ia) are a key probe in modern cosmology, as they can be used to measure luminosity distances at gigaparsec scales. Models of their light curves are used to project heterogeneous observed data onto a common basis for analysis. Aims. The SALT model currently used for SN Ia cosmology describes SNe as having two sources of variability, accounted for by a color parameter c , and a “stretch” parameter x 1 . We extend the model to include an additional parameter we label x 2 , to investigate the cosmological impact of currently unaddressed light-curve variability. Methods. We constructed a new SALT model, that we dub “SALT3+”. This model was trained by an improved version of the SALTshaker code, using training data combining a selection of the second data release of cosmological SNe Ia from the Zwicky Transient Facility and the existing SALT3 training compilation. Results. We find additional, coherent variability in supernova light curves beyond SALT3. Most of this variation can be described as phase-dependent variation in g − r and r − i color curves, correlated with a boost in the height of the secondary maximum in i -band. These behaviors correlate with spectral differences, particularly in line velocity. We find that fits with the existing SALT3 model tend to address this excess variation with the color parameter, leading to less informative measurements of supernova color. We find that neglecting the new parameter in light-curve fits leads to a trend in Hubble residuals with x 2 of 0.039 ± 0.005 mag, representing a potential systematic uncertainty. However, we find no evidence of a bias in current cosmological measurements. Conclusions. We conclude that extended SN Ia light-curve models promise mild improvement in the accuracy of color measurements, and corresponding cosmological precision. However, models with more parameters are unlikely to substantially affect current cosmological results.

Kenworthy, W. D. (ORCID:0000000251535983)↗

DOE OSTI2025

Parameterized anomalous transport model for current-carrying collisionless plasmas in pulsed power inertial confinement fusion

Current delivery in pulsed power inertial confinement fusion is influenced by collisionless current-carrying microturbulent plasmas, which are sourced from electrode surfaces. In this setting, the lower hybrid drift instability—triggered by plasma acceleration—is a leading candidate driver of difficult-to-predict momentum and energy transport. To characterize the nonlinear state of the microturbulent plasma, a parameterized anomalous transport model is developed for the instability, with analytic formulas for anomalous collision frequency, resistivity, and species heating rates. The formulas are expressed in terms of linear-theory variables and four dimensionless parameters that characterize the macroscopic plasma state. The model is built on linear theory analysis, power law analysis, and quasilinear theory analysis, and is validated using a series of nonlinear continuum kinetic Vlasov–Poisson simulations. The theoretical and computational investigation demonstrates that the anomalous collision frequency associated with the instability can be reliably approximated, within about a factor of five or better, by the unscaled linear theory growth rate of the fastest-growing wavenumber mode. This finding enables efficient calculation of anomalous resistivity and species heating rates over a wide range of plasma conditions, resulting in improved predictive capabilities.

Complex functions↗

DOE OSTI2023

Quantification of spatial and seasonal trends in the atmosphere and construction of statistical models for infrasonic propagation

SUMMARY Infrasonic waves are influenced by variations in the density, pressure and temperature as well as the ambient winds. Modelling infrasonic propagation can be challenging due to the dynamic nature of the atmosphere as well as the sparseness of measurements which result in variability and notable uncertainty. A framework is presented to quantify spatial and seasonal trends in atmospheric structure via analysis of the effective sound speed profile and identification of temporal trends in the middle atmospheric waveguide produced by the circumpolar vortex winds. Seasonal definitions identifying typical atmospheric structures during the summer, winter and spring/fall transition periods are identified using atmospheric data from 2010 through 2020. Seasonal trend analysis is conducted for a number of locations across the contiguous United States to quantify spatial variations in atmospheric structure that impact infrasonic propagation. For each season and location, empirical orthogonal function analysis is used to reduce the historical archive of atmospheric data into a smaller representative set that can be analysed using numerical tools more efficiently. Infrasonic ray tracing and finite-frequency modal propagation analyses are applied to construct propagation path geometry and transmission loss statistics which are useful in localization and yield estimation for infrasonic sources, respectively. An example application is detailed in which transmission loss statistics are combined with an explosive source model and noise statistics to quantify the capability of a network to detect nearby sources.

58 GEOSCIENCES↗

DOE OSTI2024

Data-Efficient Dimensionality Reduction and Surrogate Modeling of High-Dimensional Stress Fields

Tensor datatypes representing field variables like stress, displacement, velocity, etc., have increasingly become a common occurrence in data-driven modeling and analysis of simulations. Numerous methods [such as convolutional neural networks (CNNs)] exist to address the meta-modeling of field data from simulations. As the complexity of the simulation increases, so does the cost of acquisition, leading to limited data scenarios. Modeling of tensor datatypes under limited data scenarios remains a hindrance for engineering applications. Here, in this article, we introduce a direct image-to-image modeling framework of convolutional autoencoders enhanced by information bottleneck loss function to tackle the tensor data types with limited data. The information bottleneck method penalizes the nuisance information in the latent space while maximizing relevant information making it robust for limited data scenarios. The entire neural network framework is further combined with robust hyperparameter optimization. We perform numerical studies to compare the predictive performance of the proposed method with a dimensionality reduction-based surrogate modeling framework on a representative linear elastic ellipsoidal void problem with uniaxial loading. The data structure focuses on the low-data regime (fewer than 100 data points) and includes the parameterized geometry of the ellipsoidal void as the input and the predicted stress field as the output. The results of the numerical studies show that the information bottleneck approach yields improved overall accuracy and more precise prediction of the extremes of the stress field. Additionally, an in-depth analysis is carried out to elucidate the information compression behavior of the proposed framework.

artificial intelligence↗

DOE OSTI2020

Measurement of the transverse momentum distribution of Drell–Yan lepton pairs in proton–proton collisions at √s=13 TeV with the ATLAS detector

This paper describes precision measurements of the transverse momentum $p_\mathrm {T}^{\ell \ell }$ ($\ell =e,\mu $) and of the angular variable $\phi ^{*}_{\eta }$ distributions of Drell–Yan lepton pairs in a mass range of 66–116 GeV. The analysis uses data from 36.1 fb$^{-1}$ of proton–proton collisions at a centre-of-mass energy of $\sqrt{s}=13\,$TeV collected by the ATLAS experiment at the LHC in 2015 and 2016. Measurements in electron-pair and muon-pair final states are performed in the same fiducial volumes, corrected for detector effects, and combined. Compared to previous measurements in proton–proton collisions at $\sqrt{s}=7$ and $8\,$TeV, these new measurements probe perturbative QCD at a higher centre-of-mass energy with a different composition of initial states. They reach a precision of 0.2$\%$ for the normalized spectra at low values of $p_\mathrm {T}^{\ell \ell }$. The data are compared with different QCD predictions, where it is found that predictions based on resummation approaches can describe the full spectrum within uncertainties.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2026

Did You Win the GPU Cloud Lottery? Benchmarking from TFLOPS to Tokens/$

Cloud GPUs are commonly assumed to deliver consistent performance for a given GPU model. This assumption does not always hold: cloud providers employ diverse system configurations and virtualization mechanisms, and GPUs themselves exhibit non-negligible manufacturing variability (the silicon lottery). In this work, we present a large-scale measurement study of GPU performance variability across 11 cloud providers, covering over 3,500 physical GPUs and 6,800 benchmark runs. Our hierarchical analysis shows that while execution-level variation stays below 9%, performance varies by up to 38% across devices and providers for the same GPU model. Regression analysis indicates that driver- and OS-related software factors contribute less than 1% of the variance; instead, silicon lottery effects dominate observed performance variation, and cloud providers further amplify them through persistent, systematic second-order effects.

Slynko, Platon [Silicon Data, New York, USA] (ORCI↗

DOE OSTI2025

Evaluation of the 2022 West Nile virus forecasting challenge, USA

Abstract Background West Nile virus (WNV) is the most common cause of mosquito-borne disease in the continental USA, with an average of ~1200 severe, neuroinvasive cases reported annually from 2005 to 2021 (range 386–2873). Despite this burden, efforts to forecast WNV disease to inform public health measures to reduce disease incidence have had limited success. Here, we analyze forecasts submitted to the 2022 WNV Forecasting Challenge, a follow-up to the 2020 WNV Forecasting Challenge. Methods Forecasting teams submitted probabilistic forecasts of annual West Nile virus neuroinvasive disease (WNND) cases for each county in the continental USA for the 2022 WNV season. We assessed the skill of team-specific forecasts, baseline forecasts, and an ensemble created from team-specific forecasts. We then characterized the impact of model characteristics and county-specific contextual factors (e.g., population) on forecast skill. Results Ensemble forecasts for 2022 anticipated a season at or below median long-term WNND incidence for nearly all (> 99%) counties. More counties reported higher case numbers than anticipated by the ensemble forecast median, but national caseload (826) was well below the 10-year median (1386). Forecast skill was highest for the ensemble forecast, though the historical negative binomial baseline model and several team-submitted forecasts had similar forecast skill. Forecasts utilizing regression-based frameworks tended to have more skill than those that did not and models using climate, mosquito surveillance, demographic, or avian data had less skill than those that did not, potentially due to overfitting. County-contextual analysis showed strong relationships with the number of years that WNND had been reported and permutation entropy (historical variability). Evaluations based on weighted interval score and logarithmic scoring metrics produced similar results. Conclusions The relative success of the ensemble forecast, the best forecast for 2022, suggests potential gains in community ability to forecast WNV, an improvement from the 2020 Challenge. Similar to the previous challenge, however, our results indicate that skill was still limited with general underprediction despite a relative low incidence year. Potential opportunities for improvement include refining mechanistic approaches, integrating additional data sources, and considering different approaches for areas with and without previous cases. Graphical Abstract

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Opportunities for Hybrid Wind and Solar PV Plants in India

The share of variable renewable energy (VRE) on India's grid has surpassed 100 GW, and the government has ambitious plans reach 450 GW by 2030. One strategy to increase wind and solar PV deployment is through the co-location of wind and solar PV plants to form a single hybrid power plant. Hybrid plants have the potential to reduce transmission infrastructure costs and variability in the output power profile compared to a standalone plant with a single technology, and this resource analysis aims to take a first step towards quantifying the potential savings from hybridizing wind and solar PV plants in India and the size of this opportunity. We utilize a brute-force optimization to minimize the levelized cost of energy (LCOE) for standalone wind, standalone solar PV, and hybrid wind/solar PV plants across all of India. By comparing these LCOEs, we determine that locations where hybrid plants exhibit potential cost savings and grid benefits exhibit both; a high interconnection cost and; a wind capacity factor between roughly 34% and 38%. However, because our work does not capture the value of the electricity generated by looking at energy prices, nor does it quantify the potential of hybrids to provide other value streams such as firm capacity and reserves. Further, because the work does not compare solar PV and wind hybrids to alternative generation technologies or storage systems, it cannot be considered a holistic cost-benefit analysis.

14 SOLAR ENERGY↗

DOE OSTI2024

Tracking the Sun: Pricing and Design Trends for Distributed Photovoltaic Systems in the United States, 2024 Edition [Slides]

Berkeley Lab’s annual Tracking the Sun report describes trends among grid-connected, distributed solar photovoltaic (PV) and paired PV+storage systems in the United States. For the purpose of this report, distributed solar includes residential systems, roof-mounted non-residential systems, and ground-mounted systems up to 5 MW-AC. Ground-mounted systems larger than 5 MW-AC are covered in Berkeley Lab’s companion annual report, Utility-Scale Solar. The latest edition of the report is based on 3.7 million systems installed through year-end 2023, representing close to 80% of systems installed to date. The report describes and discusses key trends related to: -Project characteristics, including system size, module efficiencies, roof-coverage ratios, prevalence of paired PV with storage, use of module-level power electronics, third-party ownership, mounting configurations, panel orientation, and customer segmentation -Median installed-price trends, both nationally and by state -Variability in pricing according to system size, state, installer, equipment type, and other factors, relying on both descriptive analysis and a multi-variate regression to estimate the effects of key pricing drivers for residential systems installed in 2023.

14 SOLAR ENERGY↗

DOE OSTI2025

Real-time neutron multiplicity and source localization for criticality safety during fuel debris removal

Advancing neutron detection and analysis techniques for complex radiation environments is an ongoing focus in nuclear instrumentation and monitoring. This proposal presents research and development of a generalized real-time neutron monitoring and analysis system, applicable to any detector capable of producing time-tagged neutron count data. While the work is demonstrated using the Neutron Multiplication Analysis Detector (NoMAD), a modular 15-tube helium-3 (He-3) array, due to its availability, spatial resolution, and flexible deployment, the methods developed are extensible to other systems, including organic scintillators and fast digital detectors. This research investigates two complementary analytical techniques for real-time characterization of neutron emitting sources: neutron multiplicity estimation based on the Hage-Cifarelli formalism and spatial localization using supervised machine learning applied to spatial count rate patterns. These methods are designed to operate under dynamic, evolving conditions such as fuel debris retrieval or reactor startup, where neutron-emitting material geometries may be partially unknown or changing over time. By integrating statistical neutron emission data with spatial localization, this research aims to develop and evaluate methods for real time neutron monitoring, source characterization, and material verification. Key contributions include implementation of a low-latency data pipeline for continuous neutron multiplicity analysis, development and validation of machine learning models for spatial inference, and experimental evaluation of system performance under variable measurement conditions. The outcomes are intended to support applications in nuclear safeguards, verification, emergency response, and reactor startup.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2025

Benchmark Tracking System for Performance Monitoring

Benchmarking is essential for high-performance software development, particularly for monitoring performance across code iterations. This project focused on enhancing the benchmarking process for Lamellar, an asynchronous runtime for High-Performance Computing (HPC) systems developed at Pacific Northwest National Laboratory. Prior to this work, benchmark results were difficult to track and compare across code versions, presenting significant challenges in identifying performance regressions and long-term trends. The primary objective was to establish a systematic, reproducible approach for measuring performance and detecting regressions following code commits. Our methodology involved three key components: standardizing benchmark outputs, implementing data versioning, and developing analysis tools. We standardized the benchmark output format to JSON Line records containing specific fields (execution time, hardware specifications, and environmental variables). To address data management challenges, we evaluated several options and eventually chose a git repository dedicated to benchmark data. We developed a suite of Python tools that processed benchmark results, enriched them with metadata, and facilitated search in the repository. The resulting system enables more efficient filtering and comparison of performance metrics across commit histories, hardware configurations, and benchmark variants through a unified query interface. Our implementation reduces computational overhead by first checking for existing results through configuration matching before initiating new benchmark runs, thereby conserving resources. The system has been validated by Lamellar developers. It organizes results by benchmark type and build configurations for efficient retrieval. Future developments include a planned Large Language Model interface for predicting benchmark performance, incorporating the criterion package for statistical analysis, which will enable automated detection of statistically significant performance changes, and integration with continuous integration pipelines. Despite these enhancements being reserved for future work, this project has successfully provided the Lamellar development team with a framework for maintaining consistent performance standards and identifying optimization opportunities across workloads and hardware environments.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Sensitivity analysis of homogenized cross section in AP1000 lattices

The two-step method for light water reactor simulation consists of performing lattice-level calculations to determine homogenized properties of the lattice for a variety of configurations and burnups then performing a core-level calculation which relies on those pre-calculated lattice properties. Calculating the homogenized lattice properties for the specific conditions needed in the core-level calculation relies on interpolating from the pre-calculated lattice properties. Although many studies have explored different models that can be used for this interpolation, there is a need to explore how to appropriately parameterize the lattice for those interpolation models. The present study uses linear sensitivity methods to determine the sensitivity of homogenized cross sections to both instantaneous and historical values of state variables. The results from this study can be used to inform parameterizations which more appropriately capture history effects in homogenized cross section interpolation. Two different lattices are used for this analysis from the AP1000 reactor, one includes burnable absorbers. It was found that early in the cycle, the historical values of state variables have little effect on the instantaneous value of the homogenized cross sections explored here - especially in the case of the lattice containing burnable absorbers. However, it was found that later in the cycle, the thermal fission homogenized cross section was sensitive to the historic states of the lattice. In fact, using the average of a state variable as a predictor for interpolation models may be insufficient for capturing historic effects due to more recent states having larger sensitivity measures than less recent states. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2020

Analysis of thermal response of new diagnostic probe in TCV

Thermal response of the new multi-purpose diagnostic probe inside the TCV (Tokamak à Configuration Variable) tokamak is studied. The New Probe Head (NPH) was constructed at the University of Innsbruck and developed in collaboration with various European laboratories within EUROfusion program. The NPH can be used in different MST devices by applying corresponding adapters. Its design, followed by the prototype, has to go through a number of tests (numerical and experimental), before it can be used in the tokamak environment, where it has to withstand repeated exposure to the Scrape-Off-Layer (SOL) plasma. Presented numerical analyses of the NPH thermal response inside the TCV tokamak are performed by the Jožef Stefan Institute.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

A robust clustering algorithm for analysis of composition-dependent organic aerosol thermal desorption measurements

Abstract. One of the challenges of understanding atmospheric organic aerosol (OA) particles stems from its complex composition. Mass spectrometry is commonly used to characterize the compositional variability of OA. Clustering of a mass spectral dataset helps identify components that exhibit similar behavior or have similar properties, facilitating understanding of sources and processes that govern compositional variability. Here, we developed an algorithm for clustering mass spectra, the noise-sorted scanning clustering (NSSC), appropriate for application to thermal desorption measurements of collected OA particles from the Filter Inlet for Gases and AEROsols coupled to a chemical ionization mass spectrometer (FIGAERO-CIMS). NSSC, which extends the common density-based special clustering of applications with noise (DBSCAN) algorithm, provides a robust, reproducible analysis of the FIGAERO temperature-dependent mass spectral data. The NSSC allows for the determination of thermal profiles for compositionally distinct clusters of mass spectra, increasing the accessibility and enhancing the interpretation of FIGAERO data. Applications of NSSC to several laboratory biogenic secondary organic aerosol (BSOA) systems demonstrate the ability of NSSC to distinguish different types of thermal behaviors for the components comprising the particles along with the relative mass contributions and chemical properties (e.g., average molecular formula) of each mass spectral cluster. For each of the systems examined, more than 80 % of the total mass is clustered into 9–13 mass spectral clusters. Comparison of the average thermograms of the mass spectral clusters between systems indicates some commonality in terms of the thermal properties of different BSOA, although with some system-specific behavior. Application of NSSC to sets of experiments in which one experimental parameter, such as the concentration of NO, is varied demonstrates the potential for mass spectral clustering to elucidate the chemical factors that drive changes in the thermal properties of OA particles. Further quantitative interpretation of the thermograms of the mass spectral clusters will allow for a more comprehensive understanding of the thermochemical properties of OA particles.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

Screening candidate supplementary cementitious materials under standard and accelerated curing through time-series surface resistivity measurements and change-point detection

Time-series surface resistivity (SR) measurements are evaluated as an indicator of pozzolanicity in concretes containing 13 materials of both known and unknown pozzolanicity, under standard and accelerated curing conditions, and the results were validated against portlandite consumption obtained through thermogravimetric analysis. Change-point detection (CPD) analysis is applied to the data to provide a rigorous indicator of hydration age of the onset and rate of the pozzolanic reaction, if occurring. The SR measurements were able to capture the onset of the pozzolanic reactions in concretes curing at elevated temperature regimes, which allows determination of pozzolanicity weeks earlier than at standard curing temperatures. Using CPD along with slope analysis allows a comprehensive analysis of a material's reactivity and determination of pozzolanicity in as quickly as two days. Time-series SR measurements at elevated curing conditions, along with limits on material composition, are recommended for determination of pozzolanic reactivity in novel or variable materials.

36 MATERIALS SCIENCE↗