Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “classification models”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 901 records · Page 50
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Rapid Coal-Ash Characterization using Geophysical Methods & Machine Learning

Coal combustion products (CCP) are challenging to delineate in heterogeneous field settings. Conventional methods (test pits, coring, and laboratory analyses) are labor-intensive, slow, invasive, and provide sparse spatial coverage. This study evaluates whether rapid non-invasive geophysical screening methods—induced polarization (IP), magnetic susceptibility, and nuclear magnetic resonance (NMR) —combined with surface colorimetry (RGB_24), can discriminate CCP-soil mixtures and provide reliable estimates of CCP content. Laboratory measurements were collected on five CCP-soil mixtures (series) and modeled using (i) a linear baseline, (ii) a calibrated non-linear (power-mean) model, and (iii) a machine-learning (ML) Random Forest approach, with validation via leave-one-series-out and site-specific tests. Across the five series, individual signals—particularly IP and magnetic susceptibility—were strongly predictive of ash content but were consistently outperformed by combined models. The pooled calibrated non-linear and ML models captured the observed non-linearity and achieved high accuracy and precision, improving on linear fits. Colorimetry showed the weakest direct relationship with ash content for the tested samples but improved performance when included in multi-signal models. At pre-selected 3.5% decision threshold, calibrated and ML approaches yielded near-perfect classification (Matthews correlation coefficient ˜ 1), suggesting strong practical operability for field screening. Additionally, field-analog tests highlighted the role of endmembers—accuracy declined without access to end-member measurements but was largely recovered by collecting a minimal labeled pair for local recalibration. With end members, accuracy remained high. Globally trained models performed well on three operational unknowns; however, series-specific refits provided the most accurate predictions. Overall, these results highlight the potential of combining rapid geophysics and minimal local calibration for improved coal-ash delineation.

Peshtani, Klaudio↗
DOE OSTI2021

The Application of Convolutional Neural Networks (CNNs) to Recognize Defects in 3D-Printed Parts

Cracks and pores are two common defects in metallic additive manufacturing (AM) parts. In this paper, deep learning-based image analysis is performed for defect (cracks and pores) classification/detection based on SEM images of metallic AM parts. Three different levels of complexities, namely, defect classification, defect detection and defect image segmentation, are successfully achieved using a simple CNN model, the YOLOv4 model and the Detectron2 object detection library, respectively. The tuned CNN model can classify any single defect as either a crack or pore at almost 100% accuracy. The other two models can identify more than 90% of the cracks and pores in the testing images. In addition to the application of static image analysis, defect detection is also successfully applied on a video which mimics the AM process control images. The trained Detectron2 model can identify almost all the pores and cracks that exist in the original video. This study lays a foundation for future in situ process monitoring of the 3D printing process.

36 MATERIALS SCIENCE↗
NASA NTRS2021

Very High-Resolution Satellite-Derived Bathymetry and Habitat Mapping Using Pleiades-1 and ICESat-2

Accurate and reliable bathymetric data are needed for a wide diversity of marine research and management applications. Satellite-derived bathymetry represents a time saving method to map large shallow waters of remote regions compared to the current costly in situ measurement techniques. This study aims to create very high-resolution (VHR) bathymetry and habitat mapping in Mayotte island waters (Indian Ocean) by fusing 0.5 m Pleiades-1 passive multispectral imagery and active ICESat-2 LiDAR bathymetry. ICESat-2 georeferenced photons were filtered to remove noise and corrected for water column refraction. The bathymetric point clouds were validated using the French naval hydrographic and oceanographic service Litto3D® dataset and then used to calibrate the multispectral image to produce a digital depth model (DDM). The latter enabled the creation of a digital albedo model used to classify benthic habitats. ICESat-2 provided bathymetry down to 15 m depth with a vertical accuracy of bathymetry estimates reaching 0.89 m. The benthic habitats map produced using the maximum likelihood supervised classification provided an overall accuracy of 96.62%. This study successfully produced a VHR DDM solely from satellite data. Digital models of higher accuracy were further discussed in the light of the recent and near-future launch of higher spectral and spatial resolution satellites.

Bathymetry↗
NASA NTRS1993

Improvement and further development of SSM/I overland parameter algorithms using the WetNet workstation

Since the launch of the DMSP Special Sensor Microwave/Imager (SSM/I), several algorithms have been developed to retrieve overland parameters. These include the present operational algorithms resulting from the Navy calibration/validation effort such as land surface type (Neale et al. 1990), land surface temperature (McFarland et al. 1990), surface moisture (McFarland and Neale, 1991) and snow parameters (McFarland and Neale, 1991). In addition, other work has been done including the classification of snow cover and precipitation using the SSM/I (Grody, 1991). Due to the empirical nature of most of the above mentioned algorithms, further research is warranted and improvements can probably be obtained through a combination of radiative transfer modelling to study the physical processes governing the microwave emissions at the SSM/I frequencies, and the incorporation of additional ground truth data and special cases into the regression data sets. We have proposed specifically to improve the retrieval of surface moisture and snow parameters using the WetNet SSM/I data sets along with ground truth information namely climatic variables from the NOAA cooperative network of weather stations as well as imagery from other satellite sensors such as the AVHRR and Thematic Mapper. In the case of surface moisture retrievals the characterization of vegetation density is of primary concern. The higher spatial resolution satellite imagery collected at concurrent periods will be used to characterize vegetation types and amounts which, along with radiative transfer modelling should lead to more physically based retrievals. Snow parameter retrieval algorithm improvement will initially concentrate on the classification of snowpacks (dry snow, wet snow, refrozen snow) and later on specific products such as snow water equivalent. Significant accomplishments in the past year are presented.

Neale, Christopher M. U.↗
DOE OSTI2020

Identifying the nature of the QCD transition in heavy-ion collisions with deep learning

In this proceeding, we review our recent work using deep convolutional neural network (CNN) to identify the nature of the QCD transition in a hybrid modeling of heavy-ion collisions. Within this hybrid model, a viscous hydrodynamic model is coupled with a hadronic cascade “after-burner”. As a binary classification setup, we employ two different types of equations of state (EoS) of the hot medium in the hydrodynamic evolution. The resulting final-state pion spectra in the transverse momentum and azimuthal angle plane are fed to the neural network as the input data in order to distinguish different EoS. To probe the effects of the fluctuations in the event-by-event spectra, we explore different scenarios for the input data and make a comparison in a systematic way. We observe a clear hierarchy in the predictive power when the network is fed with the event-by-event, cascade-coarse-grained and event-fine-averaged spectra. The carefully-trained neural network can extract high-level features from pion spectra to identify the nature of the QCD transition in a realistic simulation scenario.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1990

Bias and design in software specifications

Implementation bias in a specification is an arbitrary constraint in the solution space. Presented here is a model of bias in software specifications. Bias is defined in terms of the specification process and a classification of the attributes of the software product. Our definition of bias provides insight into both the origin and the consequences of bias. It also shows that bias is relative and essentially unavoidable. Finally, we describe current work on defining a measure of bias, formalizing our model, and relating bias to software defects.

Straub, Pablo A.↗
NASA NTRS2000

BOREAS AFM-12 1-km AVHRR Seasonal Land Cover Classification

The Boreal Ecosystem-Atmosphere Study (BOREAS) Airborne Fluxes and Meteorology (AFM)-12 team's efforts focused on regional scale Surface Vegetation and Atmosphere (SVAT) modeling to improve parameterization of the heterogeneous BOREAS landscape for use in larger scale Global Circulation Models (GCMs). This regional land cover data set was developed as part of a multitemporal one-kilometer Advanced Very High Resolution Radiometer (AVHRR) land cover analysis approach that was used as the basis for regional land cover mapping, fire disturbance-regeneration, and multiresolution land cover scaling studies in the boreal forest ecosystem of central Canada. This land cover classification was derived by using regional field observations from ground and low-level aircraft transits to analyze spectral-temporal clusters that were derived from an unsupervised cluster analysis of monthly Normalized Difference Vegetation Index (NDVI) image composites (April-September 1992). This regional data set was developed for use by BOREAS investigators, especially those involved in simulation modeling, remote sensing algorithm development, and aircraft flux studies. Based on regional field data verification, this multitemporal one-kilometer AVHRR land cover mapping approach was effective in characterizing the biome-level land cover structure, embedded spatially heterogeneous landscape patterns, and other types of key land cover information of interest to BOREAS modelers.The land cover mosaics in this classification include: (1) wet conifer mosaic (low, medium, and high tree stand density), (2) mixed coniferous-deciduous forest (80% coniferous, codominant, and 80% deciduous), (3) recent visible bum, vegetation regeneration, or rock outcrops-bare ground-sparsely vegetated slow regeneration bum (four classes), (4) open water and grassland marshes, and (5) general agricultural land use/ grasslands (three classes). This land cover mapping approach did not detect small subpixel-scale landscape features such as fens, bogs, and small water bodies. Field observations and comparisons with Landsat Thematic Mapper (TM) suggest a minimum effective resolution of these land cover classes in the range of three to four kilometers, in part, because of the daily to monthly compositing process. In general, potential accuracy limitations are mitigated by the use of conservative parameterization rules such as aggregation of predominant land cover classes within minimum horizontal grid cell sizes of ten kilometers. The AFM-12 one-kilometer AVHRR seasonal land cover classification data are available from the Earth Observing System Data and Information System (EOSDIS) Oak Ridge National Laboratory (ORNL) Distributed Active Archive Center (DAAC). The data files are available on a CD-ROM (see document number 20010000884).

Steyaert, Lou↗
DOE OSTI2020

Automatic Classification of Biological Targets in a Tidal Channel Using a Multibeam Sonar

Multibeam sonars are widely used for environmental monitoring of fauna at marine renewable energy sites. However, they can rapidly accrue vast volumes of data, which poses a challenge for data processing. Here, using data from a deployment in a tidal channel with peak currents of 1–2 m s –1 , we demonstrate the data-reduction benefits of real-time automatic classification of targets detected and tracked in multibeam sonar data. First, we evaluate classification capabilities for three machine learning algorithms: random forests, support vector machines, and k-nearest neighbors. For each algorithm, a hill-climbing search optimizes a set of hand-engineered attributes that describe tracked targets. Here, the random forest algorithm is found to be most effective—in postprocessing, discriminating between biological and nonbiological targets with a recall rate of 0.97 and a precision of 0.60. In addition, 89% of biological targets are correctly classified as either seals, diving birds, fish schools, or small targets. Model dependence on the volume of training data is evaluated. Second, a real-time implementation of the model is shown to distinguish between biological targets and nonbiological targets with nearly the same performance as in postprocessing. From this, we make general recommendations for implementing real-time classification of biological targets in multibeam sonar data and the transferability of trained models.

16 TIDAL AND WAVE POWER↗
DOE OSTI2022

A Comparative Study of Machine Learning Algorithms for Industry-Specific Freight Generation Model

According to Bureau of Transportation Statistics, the U.S. transportation system handled 14,329 million ton-miles of freight per day in 2020. Understanding the generation of these freight shipments is crucial for transportation researchers, planners, and policymakers to design and plan for a more efficient and connected freight transportation system. Traditionally, the freight generation modeling has been based on Ordinary Least Square (OLS) regression, although more advanced Machine Learning (ML) algorithms have been evaluated and proven to have excellent performance in various transportation applications in recent years. Furthermore, one modeling approach applied for one industry might not always be applicable for another as their freight generation logics can be quite different. The objective of this study is to apply and evaluate alternative ML algorithms in the estimation of freight generation for each of 45 industry types. Seven alternative ML algorithms, along with the base OLS regression, were evaluated and compared. In addition, the study considered different combinations of variables in both the original and logarithmic form as well as hyperparameters of those ML algorithms in the model selection for each industry type. The results showed statistically significant improvements in the root mean square error reduction by the alternative ML algorithms over the OLS for over 80% of cases. The study suggests utilizing the alternative ML algorithms can reduce the root mean square error by about 30%, depending on industry types.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Feature‐shared adaptive‐boost deep learning for invasiveness classification of pulmonary subsolid nodules in CT images

Purpose In clinical practice, invasiveness is an important reference indicator for differentiating the malignant degree of subsolid pulmonary nodules. These nodules can be classified as atypical adenomatous hyperplasia (AAH), adenocarcinoma in situ (AIS), minimally invasive adenocarcinoma (MIA), or invasive adenocarcinoma (IAC). The automatic determination of a nodule's invasiveness based on chest CT scans can guide treatment planning. However, it is challenging, owing to the insufficiency of training data and their interclass similarity and intraclass variation. To address these challenges, we propose a two‐stage deep learning strategy for this task: prior‐feature learning followed by adaptive‐boost deep learning. Methods The adaptive‐boost deep learning is proposed to train a strong classifier for invasiveness classification of subsolid nodules in chest CT images, using multiple 3D convolutional neural network (CNN)‐based weak classifiers. Because ensembles of multiple deep 3D CNN models have a huge number of parameters and require large computing resources along with more training and testing time, the prior‐feature learning is proposed to reduce the computations by sharing the CNN layers between all weak classifiers. Using this strategy, all weak classifiers can be integrated into a single network. Results Tenfold cross validation of binary classification was conducted on a total of 1357 nodules, including 765 noninvasive (AAH and AIS) and 592 invasive nodules (MIA and IAC). Ablation experimental results indicated that the proposed binary classifier achieved an accuracy of with an AUC of 81.3 . These results are superior compared to those achieved by three experienced chest imaging specialists who achieved an accuracy of , , and , respectively. About 200 additional nodules were also collected. These nodules covered 50 cases for each category (AAH, AIS, MIA, and IAC, respectively). Both binary and multiple classifications were performed on these data and the results demonstrated that the proposed method definitely achieves better performance than the performance achieved by nonensemble deep learning methods. Conclusions It can be concluded that the proposed adaptive‐boost deep learning can significantly improve the performance of invasiveness classification of pulmonary subsolid nodules in CT images, while the prior‐feature learning can significantly reduce the total size of deep models. The promising results on clinical data show that the trained models can be used as an effective lung cancer screening tool in hospitals. Moreover, the proposed strategy can be easily extended to other similar classification tasks in 3D medical images.

Wang, Jun↗
NASA NTRS1990

Climate and atmospheric modeling studies. Climate applications of Earth and planetary observations. Chemistry of Earth and environment

The research conducted during the past year in the climate and atmospheric modeling programs concentrated on the development of appropriate atmospheric and upper ocean models, and preliminary applications of these models. Principal models are a one-dimensional radiative-convective model, a three-dimensional global climate model, and an upper ocean model. Principal applications have been the study of the impact of CO2, aerosols and the solar 'constant' on climate. Progress was made in the 3-D model development towards physically realistic treatment of these processes. In particular, a map of soil classifications on 1 degree x 1 degree resolution has been digitized, and soil properties have been assigned to each soil type. Using this information about soil properties, a method was developed to simulate the hydraulic behavior of soils of the world. This improved treatment of soil hydrology, together with the seasonally varying vegetation cover, will provide a more realistic study of the role of the terrestrial biota in climate change. A new version of the climate model was created which follows the isotopes of water and sources of water (or colored water) throughout the planet. Each isotope or colored water source is a fraction of the climate model's water. It participates in condensation and surface evaporation at different fractionation rates and is transported by the dynamics. A major benefit of this project has been to improve the programming techniques and physical simulation of the water vapor budget of the climate model.

Source record↗
NASA NTRS2017

A Model-Based, Bayesian Solution for Characterization of Complex Damage Scenarios in Aerospace Composite Structures

Ultrasonic damage detection and characterization is commonly used in nondestructive evaluation (NDE) of aerospace composite components. In recent years there has been an increased development of guided wave based methods. In real materials and structures, these dispersive waves result in complicated behavior in the presence of complex damage scenarios. Model-based characterization methods utilize accurate three dimensional finite element models (FEMs) of guided wave interaction with realistic damage scenarios to aid in defect identification and classification. This work describes an inverse solution for realistic composite damage characterization by comparing the wavenumber-frequency spectra of experimental and simulated ultrasonic inspections. The composite laminate material properties are first verified through a Bayesian solution (Markov chain Monte Carlo), enabling uncertainty quantification surrounding the characterization. A study is undertaken to assess the efficacy of the proposed damage model and comparative metrics between the experimental and simulated output. The FEM is then parameterized with a damage model capable of describing the typical complex damage created by impact events in composites. The damage is characterized through a transdimensional Markov chain Monte Carlo solution, enabling a flexible damage model capable of adapting to the complex damage geometry investigated here. The posterior probability distributions of the individual delamination petals as well as the overall envelope of the damage site are determined.

H. Reed↗
DOE OSTI2024

Yet Another Discriminant Analysis (YADA): A Probabilistic Model for Machine Learning Applications

This paper presents a probabilistic model for various machine learning (ML) applications. While deep learning (DL) has produced state-of-the-art results in many domains, DL models are complex and over-parameterized, which leads to high uncertainty about what the model has learned, as well as its decision process. Further, DL models are not probabilistic, making reasoning about their output challenging. In contrast, the proposed model, referred to as Yet Another Discriminate Analysis(YADA), is less complex than other methods, is based on a mathematically rigorous foundation, and can be utilized for a wide variety of ML tasks including classification, explainability, and uncertainty quantification. YADA is thus competitive in most cases with many state-of-the-art DL models. Ideally, a probabilistic model would represent the full joint probability distribution of its features, but doing so is often computationally expensive and intractable. Hence, many probabilistic models assume that the features are either normally distributed, mutually independent, or both, which can severely limit their performance. YADA is an intermediate model that (1) captures the marginal distributions of each variable and the pairwise correlations between variables and (2) explicitly maps features to the space of multivariate Gaussian variables. Numerous mathematical properties of the YADA model can be derived, thereby improving the theoretic underpinnings of ML. Validation of the model can be statistically verified on new or held-out data using native properties of YADA. However, there are some engineering and practical challenges that we enumerate to make YADA more useful.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1991

Semiannual progress report, April - September 1991

Research conducted during the past year in the climate and modeling programs has concentrated on the development of appropriate atmospheric and upper ocean models, and preliminary applications of these models. Principal models are a one-dimensional radiative-convective model, a three dimensional global climate model, and an upper ocean model. Principal applications have been the study of the impact of CO2, aerosols, and the solar constant on climate. Progress was made in the 3-D model development towards physically realistic treatment of these processes. In particular, a map of soil classifications on 1 degree by 1 degree resolution has now been digitized, and soil properties have been assigned to each soil type. Using this information about soil properties, a method has been developed to simulate the hydraulic behavior of the soils of the world. This improved treatment of soil hydrology, together with the seasonally varying vegetation cover, will provide a more realistic study of the role of the terrestrial biota in climate change. A new version of the climate model was created which follows the isotopes of water and sources of water throughout the planet.

Source record↗
DOE OSTI2023

Activation Analysis for the Inboard Region of FNSF Using SERPENT

This study describes an application of the SERPENT 2 code with the TENDL-2017 nuclear data library and the latest available model features of the Fusion Energy System Studies–Fusion Nuclear Science Facility (FNSF), to evaluate the activation of components after shutdown at 1, 10, and 100 years, assuming a plant lifetime of 8.5 full-power years. The primary parameters evaluated include the specific activity, decay heat, and waste disposal rating (WDR). The specific activity and decay heat are calculated with SERPENT 2 using a 360-deg model of the FNSF, while the WDR is calculated and classified based on the waste disposal limits established by the U.S. Nuclear Regulatory Commission under 10 CFR 61.55 as well as by using the Fetter approach. A python-based script developed for a previous high-level waste classification and analysis study was implemented and adapted to this research to calculate the WDR by comparing nuclide concentrations to the values established in 10 CFR 61.55 to generate a waste classification for each component surveyed. As only three short-lived isotopes have limitations for classifications beyond Class A, of which only 63Ni is present in appreciable quantities, there is a limit to the amount that short-lived isotopes contribute to the most significant waste analyzed here. In most cases, a handful of long-lived isotopes can be problematic, such as 59Ni and 94Nb, for example, which are solely responsible for multiple Class C classifications. The results herein reported heavily depend on the specific materials and mass/volume fractions in the specific model used in this study, which has changed and evolved since the inception of the FNSF concept and past studies. Furthermore, the more significant contributions of this study may be the development of a modeling and simulation toolkit and a strategy to perform these calculations, so to help evaluate and optimize future fusion facilities.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Feature-Based PMU Event Classification under Variable PMU Participation and Overlapping Events

Danovo Energy Solution's presented its paper named: Feature-Based PMU Event Classification under Variable PMU Participation and Overlapping Events at the 2026 Georgia Tech Fault & Disturbance Analysis Conference. The full paper can be found at OSTI ID# 3169150 Paper Abstract—Phasor Measurement Units (PMUs) stream time synchronized, high-resolution measurements from the grid, enabling data-driven techniques for event detection and classification. Accurate event classification improves grid reliability and stability. Events can be detected by varying numbers of PMUs and exhibit different durations depending on the event type. This variability challenges standard classifiers that require uniform input sizes. Moreover, multiple events may coincide, which increases classification complexity. Standard classifiers assign each instance to the class with the highest predicted probability, whereas overlapping events may exhibit comparable probabilities across multiple classes. In this study, to handle data size variability, we extract a wide range of time–frequency domain features from all available PMUs for each event into a fixed-length vector, facilitating the application of standard machine learning classifiers, including Random Forest, XGBoost, LightGBM, Support Vector Machine, and Multilayer Perceptron. To account for overlapping events, a probabilistic post-processing step is applied. For a given data instance, if multiple predicted class probabilities exceed 30% and the differences between them are less than 10%, the event is assigned to multiple classes. Experiments using real-world PMU data demonstrate that the Random Forest and XGBoost models achieve the highest accuracy, while the proposed post-processing method yields perfect classification performance on external unseen test sets.

Nematirad, Reza [Danova Energy Solutions]↗
DOE OSTI2026

Feature-Based PMU Event Classification under Variable PMU Participation and Overlapping Events

This paper is the basis for a presentation help at the 2026 Georgia Tech Fault & Disturbance Analysis Conference, which can be found at OSTI # 3168287 Paper Abstract—Phasor Measurement Units (PMUs) stream time synchronized, high-resolution measurements from the grid, enabling data-driven techniques for event detection and classification. Accurate event classification improves grid reliability and stability. Events can be detected by varying numbers of PMUs and exhibit different durations depending on the event type. This variability challenges standard classifiers that require uniform input sizes. Moreover, multiple events may coincide, which increases classification complexity. Standard classifiers assign each instance to the class with the highest predicted probability, whereas overlapping events may exhibit comparable probabilities across multiple classes. In this study, to handle data size variability, we extract a wide range of time–frequency domain features from all available PMUs for each event into a fixed-length vector, facilitating the application of standard machine learning classifiers, including Random Forest, XGBoost, LightGBM, Support Vector Machine, and Multilayer Perceptron. To account for overlapping events, a probabilistic post-processing step is applied. For a given data instance, if multiple predicted class probabilities exceed 30% and the differences between them are less than 10%, the event is assigned to multiple classes. Experiments using real-world PMU data demonstrate that the Random Forest and XGBoost models achieve the highest accuracy, while the proposed post-processing method yields perfect classification performance on external unseen test sets.

Nematirad, Reza [Danovo Energy Solutions]↗
DOE OSTI2023

Identification of mobile genetic elements with geNomad

Identifying and characterizing mobile genetic elements in sequencing data is essential for understanding their diversity, ecology, biotechnological applications and impact on public health. Here we introduce geNomad, a classification and annotation framework that combines information from gene content and a deep neural network to identify sequences of plasmids and viruses. geNomad uses a dataset of more than 200,000 marker protein profiles to provide functional gene annotation and taxonomic assignment of viral genomes. Using a conditional random field model, geNomad also detects proviruses integrated into host genomes with high precision. In benchmarks, geNomad achieved high classification performance for diverse plasmids and viruses (Matthews correlation coefficient of 77.8% and 95.3%, respectively), substantially outperforming other tools. Leveraging geNomad’s speed and scalability, we processed over 2.7 trillion base pairs of sequencing data, leading to the discovery of millions of viruses and plasmids that are available through the IMG/VR and IMG/PR databases. geNomad is available at https://portal.nersc.gov/genomad.

59 BASIC BIOLOGICAL SCIENCES↗