Search NASA⌕ Search

SEARCH · Search NASA

Results for “Large Scale Additive”

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 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Geometry-complete diffusion for 3D molecule generation and optimization

Abstract Generative deep learning methods have recently been proposed for generating 3D molecules using equivariant graph neural networks (GNNs) within a denoising diffusion framework. However, such methods are unable to learn important geometric properties of 3D molecules, as they adopt molecule-agnostic and non-geometric GNNs as their 3D graph denoising networks, which notably hinders their ability to generate valid large 3D molecules. In this work, we address these gaps by introducing the Geometry-Complete Diffusion Model (GCDM) for 3D molecule generation, which outperforms existing 3D molecular diffusion models by significant margins across conditional and unconditional settings for the QM9 dataset and the larger GEOM-Drugs dataset, respectively. Importantly, we demonstrate that GCDM’s generative denoising process enables the model to generate a significant proportion of valid and energetically-stable large molecules at the scale of GEOM-Drugs, whereas previous methods fail to do so with the features they learn. Additionally, we show that extensions of GCDM can not only effectively design 3D molecules for specific protein pockets but can be repurposed to consistently optimize the geometry and chemical composition of existing 3D molecules for molecular stability and property specificity, demonstrating new versatility of molecular diffusion models. Code and data are freely available on GitHub .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Holistic Small-Signal Stability Analysis for Large-Scale Inverter-Intensive Power Systems with Coupled and Full-Order Dynamics from Control Systems and Power Networks

The increasing penetration of inverter-based resources (IBRs) into the existing power systems introduces tremendous benefits for enhanced sustainability but also poses inevitable challenges in terms of insufficient inertia, potential instability, and complex network dynamics, among others. However, the additional coupling introduced by the interactions among gridfollowing (GFL) and grid-forming (GFM) IBRs and the other components (i.e., synchronous generators [SGs], loads, and network, etc.) has not been clearly explored. A holistic, scalable, and quantitative stability analysis framework with the control systems and power networks is still missing. Here, in this paper, to fill in the technical gaps, a holistic small-signal model of the entire system with both rotating generation units and IBRs is established. An extended power flow model with operation dynamics from both generator control schemes and power networks is proposed to provide the varying steady-state operating points for small-signal modeling. The proposed method is compared with MATLAB solvers, and the results show that the proposed approach has a minimum calculation time, which can be less than 12 seconds for a large-scale power system with up to 2,000 buses. Furthermore, a quantitative method is developed to identify the impacts of IBRs on system performance with emphases on the potential stability issues with GFL IBRs, additional benefits of employing GFM IBRs, the feasibility of replacing SGs with GFM IBRs, and the impact of penetration level of different kinds of generation units. Finally, a field island power system is used to verify the proposed approach, and hardware-in-the-loop (HIL) tests are provided to further demonstrate the effectiveness of the proposed analysis.

14 SOLAR ENERGY↗
DOE OSTI2024

Privacy-Preserving Federated Learning for Science: Challenges and Research Directions

This paper discusses the key challenges and future research directions for privacy-preserving federated learning (PPFL), with a focus on its application to large-scale scientific AI models, in particular, foundation models~(FMs). PPFL enables collaborative model training across distributed datasets while preserving privacy-- an important collaborative approach for science. We discuss the need for efficient and scalable algorithms to address the increasing complexity of FMs, particularly when dealing with heterogeneous clients. In addition, we underscore the need for developing advance privacy-preserving techniques, such as differential privacy, to balance privacy and utility in large FMs emphasizing fairness and incentive mechanisms to ensure equitable participation among heterogeneous clients. Finally, we emphasize the need for a robust software stack supporting scalable and secure PPFL deployments across multiple high-performance computing facilities. We envision that PPFL would play a crucial role to advance scientific discovery and enable large-scale, privacy-aware collaborations across science domains.

Kim, Kibaek [Argonne National Laboratory (ANL)]↗
DOE OSTI2025

A Chromosome-Scale Genome Assembly of the Flax Rust Fungus Reveals the Two Unusually Large Effector Proteins, AvrM3 and AvrN

Rust fungi comprise thousands of species, many of which cause disease on important crop plants. The flax rust fungus Melampsora lini has been a model species for the genetic dissection of plant immunity since the 1940s; however, the highly fragmented and incomplete reference genome has so far hindered progress in effector gene discovery. Here, we generated a fully phased, chromosome-scale assembly of the two nuclear genomes of M. lini strain CH5, resolving an additional 320 Mbp of the sequence. The 482-Mbp dikaryotic genome is at least 79% repetitive, with a large proportion (approximately 40%) of the genome comprising young, highly similar transposable elements. The assembly resolves the known effector gene loci, some of which carry complex duplications that were collapsed in the previous assembly. Using a genetic map followed by manual correction of gene models, we identified the AvrM3 and AvrN genes, which encode unusually large fungal effector proteins and trigger defense responses when co-expressed with the corresponding resistance genes. We located the genes linked to the tetrapolar mating system on chromosomes 4 and 9, but in contrast to the cereal rusts that have one pheromone receptor gene per haplotype, in flax rust, three pheromone receptor genes were found, with two of them closely linked on one haplotype. Taken together, we show that a high-quality assembly is crucial for resolving complex gene loci, and given the increasing number of fungal effectors of large size, the commonly applied criterion for effector candidates of being small proteins needs to be reconsidered.

Melampsora↗
DOE OSTI2025

Missing components in ΛCDM from DESI Y1 baryonic acoustic oscillation measurements: Insights from redshift remapping

We explore transformations of the Friedman-Lemaître-Robertson-Walker (FLRW) metric and cosmological parameters that align with observational data while aiming to gain insights into potential extensions of standard cosmological models. We modified the FLRW metric by introducing a scaling factor, e 2Θ(a) –the cosmological scaling function (CSF), which alters the standard relationship between cosmological redshift and the cosmic scale factor without affecting angular measurements or cosmic microwave background (CMB) anisotropies. Using data from DESI Year 1, Pantheon+ supernovae, and the Planck CMB temperature power spectrum, we constrained both the CSF and cosmological parameters through a Markov chain Monte Carlo approach. Our results indicate that the CSF model fits observational data with a lower Hubble constant (although it is compatible with the value given by Planck 2018 within 1σ) and is predominantly dark matter dominated. Additionally, the CSF model produces temperature and lensing power spectra similar to those predicted by the standard model, though with lower values in the CSF model at large scales. We also checked that when fitting a CSF model without dark energy to the data, we obtain a more negative conformal function. This suggests that the CSF model may offer hints about missing elements and opens up a new avenue for exploring physical interpretations of cosmic acceleration.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Scalable DAQ system operating the CHIPS-5 neutrino detector

The CHIPS R&D project focuses on development of low-cost water Cherenkov neutrino detectors through novel design strategies and resourceful engineering. This work presents an end-to-end DAQ solution intended for a recent 5 kt CHIPS prototype, which is largely based on affordable mass-produced components. Much like the detector itself, the presented instrumentation is composed of modular arrays that can be scaled up and easily serviced. A single such array can carry up to 30 photomultiplier tubes (PMTs) accompanied by electronics that generate high voltage in-situ and deliver time resolution of up to 0.69 ns. In addition, the technology is compatible with the White Rabbit timing system, which can synchronize its elements to within 100 ps. While deployment issues did not permit the presented DAQ system to operate beyond initial evaluation, the presented hardware and software successfully passed numerous commissioning tests that demonstrated their viability for use in a large-scale neutrino detector, instrumented with thousands of PMTs.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2026

Nondestructive ultrasonic characterization of a triple-weld-bead wire arc additively manufactured ER70S-6 S-curved wall

Understanding build-scale microstructural variation in wire arc additive manufacturing (WAAM) of low-carbon steels is essential for ensuring consistent structure–property relationships throughout large components. Conventional destructive characterization techniques, such as scanning electron microscopy (SEM) and electron backscatter diffraction (EBSD), are time-intensive and limited to localized regions, making comprehensive evaluation of large WAAM structures challenging. In this study, a nondestructive ultrasonic approach was employed to characterize a 252 mm tall ER70S-6 S-curved WAAM wall produced using a triple-bead deposition strategy. Optical and SEM analysis revealed a repeating dual-region microstructure consisting of uniform polygonal ferrite at melt pool centers and heterogeneous ferrite with coarse and fine grains near melt pool boundaries, attributed to cyclic thermal conditions. Longitudinal ultrasonic backscatter imaging was used to evaluate the continuity of this periodicity along the full build height. The ultrasonic response exhibited a consistent repeating pattern that correlated with the observed layer-wise microstructural variation. X-ray computed tomography confirmed the absence of detectable porosity, indicating that ultrasonic contrast is primarily governed by grain morphology. Overall, the results indicate that longitudinal backscatter ultrasound is a promising nondestructive characterization technique for validating microstructural variations along the s-curved WAAM wall, with significant potential for microstructure optimization and process control.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Coil optimization for quasi-helically symmetric stellarator configurations

Filament-based coil optimizations are performed for several quasi-helical stellarator configurations, beginning with the one from Landreman & Paul ( Phys. Rev. Lett. , vol. 128, 2022, 035001), demonstrating that precise quasi-helical symmetry can be achieved with realistic coils. Several constraints are placed on the shape and spacing of the coils, such as low curvature and sufficient plasma–coil distance for neutron shielding. The coils resulting from this optimization have a maximum curvature 0.8 times that of the coils of the Helically Symmetric eXperiment (HSX) and a mean squared curvature 0.4 times that of the HSX coils when scaled to the same plasma minor radius. When scaled up to reactor size and magnetic field strength, no fast particle losses were found in the free-boundary configuration when simulating 5000 alpha particles launched at $3.5\,\mathrm {MeV}$ on the flux surface with a normalized toroidal flux of $s=0.5$ . An analysis of the tolerance of the coils to manufacturing errors is performed using a Gaussian process model, and the coils are found to maintain low particle losses for smooth, large-scale errors up to amplitudes of approximately $0.15\,\mathrm {m}$ . Another coil optimization is performed for the Landreman–Paul configuration with the additional constraint that the coils are purely planar. Visual inspection of the Poincaré plot of the resulting magnetic field-lines reveal that the planar modular coils alone do a poor job of reproducing the target equilibrium. Additional non-planar coil optimizations are performed for the quasi-helical configuration with $5\,\%$ volume-averaged plasma beta from Landreman et al. ( Phys. Plasma , vol. 29, issue 8, 2022, 082501), and a similar configuration also optimized to satisfy the Mercier criterion. The finite beta configurations had larger fast-particle losses, with the free-boundary Mercier-optimized configuration performing the worst, losing approximately $5.5\,\%$ of alpha particles launched at $s=0.5$ .

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Strain-Based Assessment of Shale Caprock during Cyclic Underground Hydrogen Storage

Successful large-scale underground hydrogen storage (UHS) in depleted gas reservoirs depends on the integrity of the overlying caprock to prevent hydrogen loss during cyclic injection and depletion. Prior studies on crushed Marcellus shale, a potential caprock, indicate that cyclic hydrogen injection and depletion induces microstructural changes, increasing porosity and permeability. However, the extent of these changes in intact shale remains unclear. This study presents a strain-based experimental approach to quantify volumetric strain evolution in intact Marcellus shale matrix under unconstrained stress conditions. A quadrant-shaped shale sample without visible fractures underwent eight hydrostatic pore-pressure cycles (injection to 1500 psi and depletion to 500 psi in 250 psi steps). Linear strain gauges measured strain in three orthogonal directions. Results indicate progressive plastic strain accumulation, leading to an ∼12% increase in matrix porosity after eight cycles, with an estimated 19% increase after 30 cycles. This porosity increase follows a logarithmic trend, suggesting a diminishing effect in later cycles. Additionally, permeability and diffusive mass flux are projected to rise by ∼70% over 30 cycles, enhancing hydrogen migration risk. The shale matrix also exhibited mechanical stiffening over successive cycles, limiting large-scale deformation but not preventing porosity enhancement. A new parameter, α, was introduced to characterize shale sensitivity to cyclic loading, aiding UHS caprock assessments. These findings underscore the necessity of incorporating cyclic loading effects in UHS site selection and operational strategies to ensure long-term storage integrity.

08 HYDROGEN↗
DOE OSTI2024

The Realistic Potential of Soil Carbon Sequestration in U.S. Croplands for Climate Mitigation

Existing estimates of the climate mitigation potential from cropland carbon sequestration (C-sequestration) are limited because they tend to assume constant rates of soil organic carbon change over all available cropland area, use relatively coarse land delineations, and often fail to adequately consider the agronomic and socioeconomic dimensions of agricultural land use. This results in an inflated estimate of the C-sequestration potential. We address this gap by defining a more appropriate land base for cover cropping in the United States for C-sequestration purposes: stable croplands in annual production systems that can integrate cover cropping without irrigation. Our baseline estimate of this suitable stable cropland area is 32% of current U.S. cropland extent. Even an alternative, less restrictive definition of stability results in a large reduction in area (44% of current U.S. croplands). Focusing cover crop implementation to this constrained land base would increase durability of associated C-sequestration and limit soil carbon loss from land conversion to qualify for carbon-specific incentives. Applying spatially-variable C-sequestration rates from the literature to our baseline area yields a technical potential of 19.4 Tg CO 2 e yr –1 annually, about one-fifth of previous estimates. We also find the cost of realizing about half (10 Tg CO 2 e yr –1 ) of this potential could exceed 100 USD Mg CO 2 e –1 , an order of magnitude higher than previously thought. While our economic analyses suggest that financial incentives are necessary for large-scale adoption of cover cropping in the U.S., they also imply any C-sequestration realized under such incentives is likely to be additional.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Searching for heavy neutral leptons at a future muon collider

As the planning stages for a high energy muon collider enter a more concrete era, an important question arises as to what new physics could be uncovered. A TeV-scale muon collider is also a vector boson fusion (VBF) factory with a very clean background, and as such it is a promising environment to look for new physics that couples to the electroweak (EW) sector. In this paper, we explore the ability of a future TeV-scale muon collider to search for Majorana and Dirac heavy neutral leptons (HNLs) produced via EW bosons. Employing a model-independent, conservative approach, we present an estimation of the production and decay rate of HNLs over a mass range between 200 GeV and 9.5 TeV in two benchmark collider proposals with s = 3 , 10 TeV, as well as an estimation of the dominant Standard Model (SM) background. We find that exclusion limits for the mixing between the HNLs and SM neutrinos can be as low as O ( 10 − 6 ) . Additionally, we demonstrate that a TeV-scale muon collider allows for the ability to discriminate between Majorana and Dirac type HNLs for a large range of mixing values. Published by the American Physical Society 2024

Kwok, Tsz Hong↗
DOE OSTI2024

Molten flux growth of single crystals of quasi-1D hexagonal chalcogenide BaTiS3

Abstract BaTiS 3 , a quasi-1D complex chalcogenide, has gathered considerable scientific and technological interest due to its giant optical anisotropy and electronic phase transitions. However, the synthesis of high-quality BaTiS 3 crystals, particularly those featuring crystal sizes of millimeters or larger, remains a challenge. Here, we investigate the growth of BaTiS 3 crystals utilizing a molten salt flux of either potassium iodide, or a mixture of barium chloride and barium iodide. The crystals obtained through this method exhibit a substantial increase in volume compared to those synthesized via the chemical vapor transport method, while preserving their intrinsic optical and electronic properties. Our flux growth method provides a promising route toward the production of high-quality, large-scale single crystals of BaTiS 3 , which will greatly facilitate advanced characterizations of BaTiS 3 and its practical applications that require large crystal dimensions. Additionally, our approach offers an alternative synthetic route for other emerging complex chalcogenides. Graphical Abstract

Materials Science↗
DOE OSTI2026

Tula: Optimizing Time, Cost, and Generalization in Distributed Large-Batch Training

Distributed training increases the number of batches processed per iteration either by scaling-out (adding more nodes) or scaling-up (increasing the batch-size). However, the largest configuration does not necessarily yield the best performance. Horizontal scaling introduces additional communication overhead, while vertical scaling is constrained by computation cost and device memory limits. Thus, simply increasing the batch-size leads to diminishing returns: training time and cost decrease initially but eventually plateaus, creating a knee-point in the time/cost vs. batch-size pareto curve. The optimal batch-size therefore depends on the underlying model, data and available compute resources. Large batches also suffer from worse model quality due to the well-known “generalization gap”. In this paper, we present Tula, an online service that automatically optimizes time, cost, and convergence quality for large-batch training of convolutional models. It combines parallel-systems modeling with statistical performance prediction to identify the optimal batchsize. Tula predicts training time and cost within 7.5−14% error across multiple models, and achieves up to 20× overall speedup and improves test accuracy by ≈9% on average over standard large-batch training on various vision tasks, thus successfully mitigating the generalization gap and accelerating training at the same time.

Tyagi, Sahil [ORNL] (ORCID:0009000783144745)↗
DOE OSTI2026

Part-scale evolution of fine-scale microstructural heterogeneity in solid-state additive manufacturing

Current solid-state additive manufacturing methods, refined through costly and time-consuming trial and error, have spurred interest in computational models that replicate material behavior under typical thermomechanical conditions (e.g., strain-rate ~ 102 s−1). These models, however, struggle to capture time-dependent microstructural evolution. In this work, Additive Friction-Stir Deposition (AFSD) is used as a representative case study for part-scale quantification of microstructure evolution at a fine spatial resolution (200 μm) by examining a liquid-nitrogen-cooled stop-action build via energy-dispersive X-ray diffraction coupled with a multi-channel detector. These results inform modeling efforts by linking process asymmetry to stored plastic strain, residual elastic strain, and texture development, and unlike current state-of-the-art characterization methods (e.g., EBSD or neutron diffraction), this approach provides both the spatial resolution and collection efficiency necessary to quantify fine-scale microstructural heterogeneity over large component volumes. As such, this technique provides essential validation data for computational models, e.g., crystal plasticity, enabling future prediction of heterogeneous behavior in AFSD and other additive manufacturing processes.

Franz, Cole [ORNL] (ORCID:0000000213465881)↗
DOE OSTI2025

A GPU Accelerated Mixed‐Precision Finite Difference Informed Random Walker (FDiRW) Solver for Strongly Inhomogeneous Diffusion Problems

In nature, many complex multi‐physics coupling problems exhibit significant diffusivity inhomogeneity, where one process occurs several orders of magnitude faster than others temporally. Simulating rapid diffusion alongside slower processes demands intensive computational resources due to the necessity for small time steps. To address these computational challenges, we have developed an efficient numerical solver named Finite Difference informed Random Walker (FDiRW). In this study, we propose a GPU‐accelerated, mixed‐precision configuration for the FDiRW solver to maximize efficiency through GPU multi‐threaded parallel computation and lower precision computation. Numerical evaluation results reveal that the proposed GPU‐accelerated mixed‐precision FDiRW solver can achieve a 117× speedup over the CPU baseline, while an additional 1.75× speedup is achieved by employing lower precision GPU computation. Notably, for large model sizes, the GPU‐accelerated mixed‐precision FDiRW solver demonstrates strong scaling with the number of nodes used in simulation. When simulating radionuclide absorption processes by porous wasteform particles with a medium‐sized model of 192 × 192 × 192, this approach reduces the total computational time to 10 min, enabling the simulation of larger systems with strongly inhomogeneous diffusivity.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Subglacial Discharge Effects on Antarctic Ice‐Shelf Basal Melt and the Southern Ocean in a Global, Coupled Ocean—Sea‐Ice Model

Subglacial freshwater from beneath Antarctica enters the ocean at depth, enhancing ice-shelf melting and affecting Southern Ocean properties. To study these effects in an Antarctic-wide context, we use a continental-scale subglacial hydrology model that calculates grounding line freshwater flux for a global, coupled ocean—sea-ice model. We find that subglacial discharge impacts melt rates primarily through continental shelf temperature modification, contrasting with findings from regional studies that do not permit large-scale adjustments. The consequence is that Antarctic melt rates scale with subglacial discharge more strongly than inferred from regional studies. We also find that the addition of buoyancy at depth facilitates heat upwelling to the surface, resulting in higher sea ice volume downstream of cold ice shelves and lower sea ice volume downstream of warm ice shelves. This highlights the drawbacks of simplifications in previous global studies that deposit Antarctic meltwater at the ocean surface and find uniform ocean surface cooling and sea-ice growth. While the patterns we find are robust, we conclude that the addition of subglacial discharge at present-day rates has a small effect on basal melt rates, hydrography, and sea ice. However, stronger discharge can have significant effects and can even accelerate a shift from low to high melting for ice shelves close to such a tipping point. Finally, the importance of feedbacks between enhanced cavity overturning and continental shelf conditions poses a complication for parameterizing subglacial discharge effects on melting for ice-sheet projections that do not include a coupled ocean component.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Assessment of wafer scale MoS 2 atomic layers grown by metal–organic chemical vapor deposition using organo-metal, organo-sulfide, and H 2 S precursors

Transition Metal Dichalcogenides (TMDs) are a unique class of materials that exhibit attractive electrical and optical properties which have generated significant interest for applications in microelectronics, optoelectronics, energy storage, and sensing. Considering the potential of these materials to impact such applications, it is crucial to develop a reliable and scalable synthesis process that is compatible with modern industrial manufacturing methods. Metal–organic chemical vapor deposition (MOCVD) offers an ideal solution to produce TMDs, due to its compatibility with large-scale production, precise layer control, and high material purity. Optimization of MOCVD protocols is necessary for effective TMD synthesis and integration into mainstream technologies. Additionally, improvements in metrology are necessary to measure the quality of the fabricated samples more accurately. In this work, we study MOCVD of wafer-scale molybdenum disulfide (MoS 2 ) utilizing two common chalcogen precursors, H 2 S and DTBS. We then develop a metrology platform for wafer scale samples quality assessment. For this, the coalesced films were characterized using Raman spectroscopy, atomic force microscopy, transmission electron microscopy, X-ray photoelectron spectroscopy, and Kelvin probe force microscopy. We then correlate the structural analysis of these grown films with electrical performance by using aerosol jet printing to fabricate van der Pauw test structures and assess sheet resistance.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Deep Learning Super-Resolution X-Ray Computed Tomography Algorithms for Additive Manufacturing

Industrial X-ray computed tomography (XCT) is a nondestructive method for inspection and characterization of additively manufactured (AM) materials and parts. In practice, the resolution of XCT can be limited by factors such as detector binning, restricted field of view for large-scale objects, system blur, motion during scanning, and acquisition settings. These limitations can reduce the detectability of critical flaws such as pores, cracks, and lack of fusion. Super-resolution (SR) techniques offer a promising solution for improving the effective resolution and image quality of XCT reconstructions without the need for expensive hardware upgrades or laborious, time-consuming scans. In particular, deep learning-based SR methods have garnered attention in recent years as powerful tools for reconstructing high-resolution volumes from low-resolution inputs. In this work, a novel deep learning-based SR method is proposed for XCT scans of AM parts, and compared against several existing state-of-the-art (SOTA) methods. The proposed method, Simurgh-SR, is built on the pre-existing Simurgh framework and consists of a 2.5D U-Net trained to map low-quality inputs containing noise and artifacts to high-quality reconstructions characterized by higher flaw contrast, better noise texture, and reduced artifacts. The experimental results demonstrate superior performance of Simurgh-SR in performing 4× SR on real industrial XCT scans of thick 316L components, enhancing the structural similarity score and peak signal-to-noise ratio (>7dB) compared to the LR counterpart while improving the F1-score for flaw detection by more than 2.3× when compared to alternative SOTA SR methods. This improvement enables more accurate and significantly faster characterization of metal AM components. Additionally, Simurgh-SR was trained for both 2X and 4X SR and performs effectively at both levels, enabling the use of a single model for various SR factors.

Rahman, Obaid [ORNL] (ORCID:0000000277810840)↗