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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 667 records · Page 37
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Uncertainty based Online Ensemble on Non-Stationary Data for Fusion Science

Machine Learning (ML) is poised to play a pivotal role in the development and operation of next-generation fusion devices. Fusion data shows non-stationary behavior due to drifts in the data. The drifts can arise from both experimental evolution and machine wear-and-tear. ML models assume stationary distribution and fail to maintain performance when encountered with non-stationary data streams.Online learning can be used to continuously adapt the models with new data as it is acquired. However, traditional online learning can suffer from short-term performance degradation, as ground truth are not available before making the prediction. To address this challenge, we propose uncertainty aware ensemble approach for online learning. We use Deep Gaussian Process Approximation (DGPA) technique for calibrated uncertainty estimation and use the uncertainty values to guide a meta-algorithm that produces predictions based on ensemble of learners. Moreover, DGPA also provides uncertainty estimation along with the predictions for decision makers. This paper demonstrates that the proposed method outperforms traditional online learning approach, and a naive ensemble without uncertainty guidance by about 7% and 6%, respectively, on B-coil deflection prediction at DIII-D Fusion Facility.

Rajput, Kishansingh [Thomas Jefferson National Acc↗
DOE OSTI2026

FY 2026 Midyear Report: Seismic Monitoring of Underground Vibration Sources Using Distributed Acoustic Sensing and Seismometers

Safeguards-relevant temporal changes in underground facilities can be observed using geophysical monitoring techniques. Seismic waves, in particular, provide valuable insights into subsurface activities and can serve as an important tool for detecting anomalous events that may indicate containment breaches at geological repositories. This midyear report summarizes ongoing efforts to automatically and rapidly detect and locate anomalous vibration signals that could be indicative of potential containment breaches. Previous work during FY25 focused on compiling continuous seismic datasets from two underground sites and developing a database of continuous waveforms and ground-truth event data derived from multiple sensing modalities. Building on this foundation, we are adapting anomaly detection and geolocation algorithms to explore methods for monitoring underground activities using two relatively low-maintenance sensing technologies: a dense surface geophone array deployed at the Pleasant Gap mine in Pennsylvania, and a three-dimensional fiber-optic cable array for distributed acoustic sensing (DAS) installed in the subsurface at the Sanford Underground Research Facility (SURF) in South Dakota. This report summarizes work conducted during the first two quarters of FY26, during which we refined a dynamic power spectral density (PSD)-based detector, applied it independently to each geophone station, and then combined the per‑station detections with density-based spatial clustering of applications with noise (DBSCAN) to cluster events and produce spatial maps over a nine‑day interval. In addition, we outline plans for a field trial at the Waste Isolation Pilot Plant (WIPP) in New Mexico to compare traditional seismic monitoring approaches with DAS techniques and to evaluate the benefits of combined data analysis. Activities during the past two quarters have included the preparation and submission of a Field Test Plan to WIPP for approval, as well as submission to headquarters for review and feedback.

58 GEOSCIENCES↗
DOE OSTI2026

PRACtical LLM Evaluation using Performance, Response, and Context

This project produced practical methods for evaluating Large Language Models (LLMs) based only on characteristics of LLM responses and without ground truth. Further development of these methods will enable the ability to rapidly identify and mitigate different failure types and supports the appropriate use of LLMs in mission applications.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Augmenting Molecular Graphs with Geometries via Machine Learning Interatomic Potentials

Accurate molecular property predictions require 3D geometries, which are typically obtained using expensive methods such as density functional theory (DFT). Here, we attempt to obtain molecular geometries by relying solely on machine learning interatomic potential (MLIP) models. To this end, we first curate a large-scale molecular relaxation dataset comprising 3.5 million molecules and 300 million snapshots. Then MLIP pre-trained models are trained with supervised learning to predict energy and forces given 3D molecular structures. Once trained, we show that the pre-trained models can be used in different ways to obtain geometries either explicitly or implicitly. First, it can be used to obtain approximate low-energy 3D geometries via geometry optimization. While these geometries do not consistently reach DFT-level chemical accuracy or convergence, they can still improve downstream performance compared to non-relaxed structures. To mitigate potential biases and enhance downstream predictions, we introduce geometry fine-tuning based on the relaxed 3D geometries. Second, the pre-trained models can be directly fine-tuned for property prediction when ground truth 3D geometries are available. Our results demonstrate that MLIP pre-trained models trained on relaxation data can learn transferable molecular representations to improve downstream molecular property prediction and can provide practically valuable but approximate molecular geometries that benefit property predictions. Our code is publicly available at: https://github.com/divelab/AIRS/.

Fu, Cong [Texas A & M Univ., College Station, TX (↗
DOE OSTI2026

Automated tape-target centering based on template matching for construction measurement tasks using robotic total station

Robotic total stations have transformed surveying and construction mapping through precise, efficient, and automated measurements. These instruments integrate a theodolite, which measures horizontal and vertical angles, with an electronic distance measurement (EDM) unit to determine distances, allowing accurate 3D measurement of observable points. Traditionally, users manually aimed the total station at a target. Recent advancements in robotic motor control and integration of cameras now enable automatic rotation and aiming, typically requiring only a single operator to position the target. Automated aiming is commonly performed using retroreflector prisms, which reflect light back to the source with minimal scattering, enabling high-precision measurements over long distances. However, retroreflectors, especially those designed for 360 degree, can be expensive and impractical for certain applications. This paper presents an algorithm for automating the center detection of low-cost disposable tape targets using the total station's onboard camera and a template matching algorithm. The algorithm identifies the target's center pixel in the image, and the instrument is commanded to aim at that location. We evaluated the performance of this template-matching-based centering method under various distances, angles, lighting conditions, and field environments, comparing its results to both manual aiming and conventional automated aiming of tape targets. Manual aiming was used as the baseline operational reference in the absence of an independent ground-truth measurement. The proposed approach achieves target centering results comparable to the manual baseline. This method provides a cost-effective alternative for high-precision applications where retroreflector targets are constrained by budget or logistics.

Harrington, Joshua [ORNL]↗
DOE OSTI2021

Methods and Comparisons Between Computer Vision and Radar Based Vehicle Location

Measuring vehicle locations relative to a driver's vehicle is a critical component in the analysis of driving data from both postanalysis (such as in naturalistic driving studies) or in autonomous vehicle navigation. In this work we describe a method to estimate vehicle positions from a forward-looking video camera using intrinsic camera calibration, estimates of extrinsic parameters, and a convolutional neural network trained to detect and locate vehicles in video data. We compare the measurements we achieve with this method with ground truth and with radar data available from a naturalistic driving study. We identify regions where video is preferred, where radar is preferred, and explore trade-offs between the two methods in regions where the preference is more ambiguous. We describe applications of these measurements for transportation analysis.

Aykac, Deniz↗
DOE OSTI2022

Cyber-Physical Secure Observer-Based Corrective Control under Compromised Sensor Measurements

In this paper we introduce the objectives and design principles of corrective control under cyber-physical attacks. We propose two types of observer-based corrective control for both the open-loop stable and the open-loop unstable LTI systems. The basic idea of our corrective control design is to use the observer as the ground-truth during the attack, making the plant dynamics follow the observer behavior. This is the opposite to the no-attack-detected period in which the observer is designed to follow the plant dynamics. We show stability of the proposed control under compromised sensor measurements, and quantify the effects of the discrepancy between the observer and the plant. Numerical examples, with illustrations using microgrid energy dynamics, are presented to show benefits of the proposed corrective control.

Wu, Dan↗
DOE OSTI2020

Aerodynamic Data Fusion Toward the Digital Twin Paradigm

This paper considers the fusion of two aerodynamic data sets originating from differing types of physical or computer experiments. This paper specifically addresses the fusion of 1) noisy and in-complete fields from wind-tunnel measurements and 2) deterministic but biased fields from numerical simulations. These two data sources are fused in order to estimate the true field that best matches measured quantities that serve as the ground truth. For example, two sources of pressure fields about an aircraft are fused based on measured forces and moments from a wind-tunnel experiment. A fundamental challenge in this problem is that the true field is unknown and cannot be estimated with 100% certainty. A Bayesian framework is employed to infer the true fields conditioned on measured quantities of interest; essentially a statistical correction to the data is performed. The fused data may then be used to construct more accurate surrogate models suitable for early stages of aerospace design. An extension of the proper orthogonal decomposition with constraints is also introduced to solve the same problem. In this work, both methods are demonstrated on fusing the pressure distributions for flow past the RAE2822 airfoil and the Common Research Model wing at transonic conditions. Comparison of both methods reveals that the Bayesian method is more robust when data are scarce and capable of also accounting for uncertainties in the data. Furthermore, given adequate data, the proper-orthogonal-decomposition-based and Bayesian approaches lead to surprisingly similar results.

42 ENGINEERING↗
DOE OSTI2025

Datasets for Custom-trained Machine-learning Interatomic Potentials: Nitric Acid Aqueous Solution

This dataset was generated using an iterative active learning strategy with the ArcaNN software package (https://github.com/arcann-chem/arcann_training) to train machine-learning interatomic potentials (MLIPs) for aqueous nitric acid. Each active-learning cycle consisted of three stages: (1) training, (2) exploration, and (3) labeling. The initial training set comprised approximately 800 randomly selected configurations from a previous study by Lewis et al. (https://doi.org/10.1021/jp205510q), which investigated nitric acid solutions at 2, 3, 4, and 5 mol/L. For all configurations, single-point calculations of atomic forces and total energies were performed at the quantum density functional theory BLYP-D2 and PBE-D3 levels of theory using the CP2K Quickstep module. Valence electrons were treated explicitly, while core electrons on all atoms were represented by norm-conserving Goedecker–Teter–Hutter (GTH) pseudopotentials. Long-range dispersion interactions were accounted for using Grimme dispersion corrections. Wave functions were expanded in a mixed Gaussian-and-plane-wave scheme using TZV2P-MOLOPT basis sets for all elements and an 800 Ry auxiliary plane-wave cutoff for the electron density. Self-consistent field convergence was accelerated using orbital transformation and Direct Inversion in the Iterative Subspace, with a convergence threshold of 10^{-6}. All single-point calculations were carried out in periodic orthorhombic cells whose dimensions match those of the molecular configurations sampled from earlier trajectories. The CELL_REF keyword in CP2K was used to define a fixed reference cell, ensuring consistency in the reference data used for MLIP training, particularly when cell fluctuations are present in NpT simulations. The resulting high-fidelity energies and forces constitute the ground-truth labels used to train the MLIPs contained in this dataset.

Dinpajooh, Mohammadhasan [Pacific Northwest Nation↗
DOE OSTI2026

Custom-trained Machine-learning Interatomic Potentials: ZnCl2 Aqueous Solution

This dataset was generated using an iterative active-learning strategy implemented in the ArcaNN software package (https://github.com/arcann-chem/arcann_training) to train machine-learning interatomic potentials for aqueous ZnCl2 solutions. Each active-learning cycle consisted of three stages: training, exploration, and labeling. The initial training set combined configurations generated in this work from enhanced-sampling ab initio molecular dynamics simulations with configurations from a previously reported neural-network-potential study of aqueous ZnCl2. The enhanced-sampling ab initio molecular dynamics simulations involved Zn–Cl separation and the chloride coordination number around Zn²? as collective variables. These configurations served as the seed dataset. Subsequent active-learning cycles expanded the training set by identifying and labeling configurations that were poorly represented by the current models, thereby improving coverage of ion-association states and changes in local coordination and charge-state environments relevant to the solution free-energy landscape. For all selected configurations, single-point calculations of the total energies and atomic forces were performed within density functional theory using the CP2K Quickstep module. Reference calculations employed the revPBE-D3 and r2SCAN exchange-correlation functionals. Motivated by recent work on aqueous Zn²?, the main revPBE calculations omitted D3 dispersion contributions involving Zn²?, while retaining the D3 correction for water and chloride. For comparison, fully dispersion-corrected revPBE-D3 reference calculations were also performed, with D3 applied to all species, including Zn²?. Valence electrons were treated explicitly, while core electrons were represented using norm-conserving Goedecker–Teter–Hutter pseudopotentials. The wave functions were expanded using the mixed Gaussian-and-plane-wave scheme with TZV2P-MOLOPT basis sets for all elements and a 600 Ry auxiliary plane-wave cutoff for the electron density. Self-consistent-field convergence was accelerated using the orbital-transformation and Direct Inversion in the Iterative Subspace algorithms, with a convergence threshold of 10?6. All single-point calculations were performed in periodic orthorhombic cells. The CELL_REF keyword in CP2K was used to define a fixed reference cell with a box length of 25 Å. This treatment ensured a consistent reference for configurations extracted from NpT trajectories with fluctuating cell dimensions. The resulting DFT energies and atomic forces constitute the ground-truth labels used to train the MLIPs. The resulting MLIP was trained for aqueous ZnCl2 solutions spanning concentrations from 0 to 30 molal and a broad pH range, from strongly acidic to strongly basic conditions. Representative examples of configurations included in the MLIP training dataset are provided below. These include 1) Representative configurations from the dataset labeled at the revPBE-D3 level, with D3 dispersion interactions involving Zn2+ excluded (revPBE-wo-D3). 2) Representative configurations from the dataset labeled at the fully dispersion-corrected revPBE-D3 level, with D3 interactions applied to all species, including Zn2+ (revPBE-D3). 3) Representative configurations from the dataset labeled at the r2SCAN level of theory (r2SCAN).

Dinpajooh, Mohammadhasan [Pacific Northwest Nation↗
DOE OSTI2025

Defect And Damage Characterization Of Additively Manufactured Titanium Alloy Ti-5553 Using Traditional Computed Tomography Volume Segmentation And Machine Learning Algorithms

The mechanical response of a component is affected by defects, such as porosity, arising from the laser powder bed fusion (LPBF) fabrication process. Thus, it is important to develop accurate and efficient inspection methods for identifying porosity. In this work, porosity identified in an X-ray computed tomography (XCT) volume of a Ti-5553 coupon was compared to pores identified in a serial sectioned volume that represented the ground truth. The porosity of the XCT scan was identified using contrast-based, ISO-based, and machine learning (ML) methods for segmentation. Large inherent porosity was easy to identify, but the ISO thresholding still struggled due to the intensity gradient resulting from both the beam hardening in XCT and the uneven lighting of the serial sectioning panels. Further, the results show that ML-based methods were better suited for identifying small pores and reducing the amount of false positives. Additionally, high strain-rate impact testing was done on some of the XCT samples as well as post-mortem XCT inspection, and the same suite of segmentation and quantification tools were used to identify the large spallation cavities. The comparison of porosity pre- and post-mortem provides insight on the influence of the LPBF porosity on the formation of spall cavities.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Online Machine Learning for Accelerating Molecular Dynamics Modeling of Cells

We developed a biomechanics-informed online learning framework to learn the dynamics with ground truth generated with multiscale modeling simulation. It was built on Summit-like supercomputers, which were also used to benchmark and validate our framework on one physiologically significant modeling of deformable biological cells. We generalized the century-old equation of Jeffery orbits to a new equation of motion with additional parameters to account for the flow conditions and the cell deformability. Using simulation data at particle-based resolutions for flowing cells and the learned parameters from our framework, we validated the new equation by the motions, mostly rotations, of a human platelet in shear blood flow at various shear stresses and platelet deformability. Our online framework, which surrogates redundant computations in the conventional multiscale modeling by solutions of our learned equation, accelerates the conventional modeling by three orders of magnitude without visible loss of accuracy.

multiscale modeling↗
DOE OSTI2022

Root system architecture and environmental flux analysis in mature crops using 3D root mesocosms

Current methods of root sampling typically only obtain small or incomplete sections of root systems and do not capture their true complexity. To facilitate the visualization and analysis of full-sized plant root systems in 3-dimensions, we developed customized mesocosm growth containers. While highly scalable, the design presented here uses an internal volume of 45 ft 3 (1.27 m 3 ), suitable for large crop and bioenergy grass root systems to grow largely unconstrained. Furthermore, they allow for the excavation and preservation of 3-dimensional root system architecture (RSA), and facilitate the collection of time-resolved subterranean environmental data. Sensor arrays monitoring matric potential, temperature and CO 2 levels are buried in a grid formation at various depths to assess environmental fluxes at regular intervals. Methods of 3D data visualization of fluxes were developed to allow for comparison with root system architectural traits. Following harvest, the recovered root system can be digitally reconstructed in 3D through photogrammetry, which is an inexpensive method requiring only an appropriate studio space and a digital camera. We developed a pipeline to extract features from the 3D point clouds, or from derived skeletons that include point cloud voxel number as a proxy for biomass, total root system length, volume, depth, convex hull volume and solidity as a function of depth. Ground-truthing these features with biomass measurements from manually dissected root systems showed a high correlation. We evaluated switchgrass, maize, and sorghum root systems to highlight the capability for species wide comparisons. We focused on two switchgrass ecotypes, upland (VS16) and lowland (WBC3), in identical environments to demonstrate widely different root system architectures that may be indicative of core differences in their rhizoeconomic foraging strategies. Finally, we imposed a strong physiological water stress and manipulated the growth medium to demonstrate whole root system plasticity in response to environmental stimuli. Hence, these new “3D Root Mesocosms” and accompanying computational analysis provides a new paradigm for study of mature crop systems and the environmental fluxes that shape them.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2022

Short-Term Rainfall Prediction Based on Radar Echo Using an Improved Self-Attention PredRNN Deep Learning Model

Accurate short-term precipitation forecast is extremely important for urban flood warning and natural disaster prevention. In this paper, we present an innovative deep learning model named ISA-PredRNN (improved self-attention PredRNN) for precipitation nowcasting based on radar echoes on the basis of the advanced PredRNN-V2. We introduce the self-attention mechanism and the long-term memory state into the model and design a new set of gating mechanisms. To better capture different intensities of precipitation, the loss function with weights was designed. We further train the model using a combination of reverse scheduled sampling and scheduled sampling to learn the long-term dynamics from the radar echo sequences. Experimental results show that the new model (ISA-PredRNN) can effectively extract the spatiotemporal features of radar echo maps and obtain radar echo prediction results with a small gap from the ground truths. From the comparison with the other six models, the new ISA-PredRNN model has the most accurate prediction results with a critical success index (CSI) of 0.7001, 0.5812 and 0.3052 under the radar echo thresholds of 10 dBZ, 20 dBZ and 30 dBZ, respectively.

Wu, Dali (ORCID:0000000231177074)↗
DOE OSTI2023

Updating and Evaluating Anthropogenic Emissions for NOAA’s Global Ensemble Forecast Systems for Aerosols (GEFS-Aerosols): Application of an SO 2 Bias-Scaling Method

We updated the anthropogenic emissions inventory in NOAA’s operational Global Ensemble Forecast for Aerosols (GEFS-Aerosols) to improve the model’s prediction of aerosol optical depth (AOD). We used a methodology to quickly update the pivotal global anthropogenic sulfur dioxide (SO 2 ) emissions using a speciated AOD bias-scaling method. The AOD bias-scaling method is based on the latest model predictions compared to NASA’s Modern-Era Retrospective analysis for Research and Applications, version 2 (MERRA2). The model bias was subsequently applied to the CEDS 2019 SO 2 emissions for adjustment. The monthly mean GEFS-Aerosols AOD predictions were evaluated against a suite of satellite observations (e.g., MISR, VIIRS, and MODIS), ground-based AERONET observations, and the International Cooperative for Aerosol Prediction (ICAP) ensemble results. The results show that transitioning from CEDS 2014 to CEDS 2019 emissions data led to a significant improvement in the operational GEFS-Aerosols model performance, and applying the bias-scaled SO 2 emissions could further improve global AOD distributions. The biases of the simulated AODs against the observed AODs varied with observation type and seasons by a factor of 3~13 and 2~10, respectively. The global AOD distributions showed that the differences in the simulations against ICAP, MISR, VIIRS, and MODIS were the largest in March–May (MAM) and the smallest in December–February (DJF). When evaluating against the ground-truth AERONET data, the bias-scaling methods improved the global seasonal correlation (r), Index of Agreement (IOA), and mean biases, except for the MAM season, when the negative regional biases were exacerbated compared to the positive regional biases. The effect of bias-scaling had the most beneficial impact on model performance in the regions dominated by anthropogenic emissions, such as East Asia. However, it showed less improvement in other areas impacted by the greater relative transport of natural emissions sources, such as India. The accuracies of the reference observation or assimilation data for the adjusted inputs and the model physics for outputs, and the selection of regions with less seasonal emissions of natural aerosols determine the success of the bias-scaling methods. A companion study on emission scaling of anthropogenic absorbing aerosols needs further improved aerosol prediction.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

A Gridded Solar Irradiance Ensemble Prediction System Based on WRF-Solar EPS and the Analog Ensemble

The WRF-Solar Ensemble Prediction System (WRF-Solar EPS) and a calibration method, the analog ensemble (AnEn), are used to generate calibrated gridded ensemble forecasts of solar irradiance over the contiguous United States (CONUS). Global horizontal irradiance (GHI) and direct normal irradiance (DNI) retrievals, based on geostationary satellites from the National Solar Radiation Database (NSRDB) are used for both calibrating and verifying the day-ahead GHI and DNI predictions (GDIP). A 10-member ensemble of WRF-Solar EPS is run in a re-forecast mode to generate day-ahead GDIP for three years. The AnEn is used to calibrate GDIP at each grid point independently using the NSRDB as the “ground truth”. Performance evaluations of deterministic and probabilistic attributes are carried out over the whole CONUS. The results demonstrate that using the AnEn calibrated ensemble forecast from WRF-Solar EPS contributes to improving the overall quality of the GHI predictions with respect to an AnEn calibrated system based only on the deterministic run of WRF-Solar. In fact, the calibrated WRF-Solar EPS’s mean exhibits a lower bias and RMSE than the calibrated deterministic WRF-Solar. Moreover, using the ensemble mean and spread as predictors for the AnEn allows a more effective calibration than using variables only from the deterministic runs. Finally, it has been shown that the recently introduced algorithm of correction for rare events is of paramount importance to obtain the lowest values of GHI from the calibrated ensemble (WRF-Solar EPS AnEn), qualitatively consistent with those observed from the NSRDB.

14 SOLAR ENERGY↗
DOE OSTI2024

Characterization of Crystal Properties and Defects in CdZnTe Radiation Detectors

CdZnTe-based detectors are highly valued because of their high spectral resolution, which is an essential feature for nuclear medical imaging. However, this resolution is compromised when there are substantial defects in the CdZnTe crystals. In this study, we present a learning-based approach to determine the spatially dependent bulk properties and defects in semiconductor detectors. This characterization allows us to mitigate and compensate for the undesired effects caused by crystal impurities. We tested our model with computer-generated noise-free input data, where it showed excellent accuracy, achieving an average RMSE of 0.43% between the predicted and the ground truth crystal properties. In addition, a sensitivity analysis was performed to determine the effect of noisy data on the accuracy of the model.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2022

Point Cloud Based Mapping of Understory Shrub Fuel Distribution, Estimation of Fuel Consumption and Relationship to Pyrolysis Gas Emissions on Experimental Prescribed Burns

Forest fires spread via production and combustion of pyrolysis gases in the understory. The goal of the present paper is to understand the spatial location, distribution, and fraction (relative to the overstory) of understory plants, in this case, sparkleberry shrub, namely its degree of understory consumption upon burn, and to search for correlations between the degree of shrub consumption to the composition of emitted pyrolysis gases. Data were collected in situ at seven small experimental prescribed burns at Ft. Jackson, an army base in South Carolina, USA. Using airborne laser scanning (ALS) to map overstory tree crowns and terrestrial laser scanning (TLS) to characterize understory shrub fuel density, both pre- and postburn estimates of sparkleberry coverage were obtained. Sparkleberry clump polygons were manually digitized from a UAV-derived orthoimage of the understory and intersected with the TLS point cloud-derived rasters of pre- and postburn shrub fuel bulk density; these were compared in relation to overstory crown cover as well as to ground truth. Shrub fuel consumption was estimated from the digitized images; sparkleberry clump distributions were generally found to not correlate well to the overstory tree crowns, suggesting it is shade-tolerant. Moreover, no relationship was found between the magnitude of the fuel consumption and the chemical composition of pyrolysis gases, even though mixing ratios of 25 individual gases were measured.

54 ENVIRONMENTAL SCIENCES↗