Rotational Invariance Research Articles

Toward viewing behavior for aerial scene categorization

Previous work has demonstrated similarities and differences between aerial and terrestrial image viewing. Aerial scene categorization, a pivotal visual processing task for gathering geoinformation, heavily depends on rotation-invariant information. Aerial image-centered research has revealed effects of low-level features on performance of various aerial image interpretation tasks. However, there are fewer studies of viewing behavior for aerial scene categorization and of higher-level factors that might influence that categorization. In this paper, experienced subjects’ eye movements were recorded while they were asked to categorize aerial scenes. A typical viewing center bias was observed. Eye movement patterns varied among categories. We explored the relationship of nine image statistics to observers’ eye movements. Results showed that if the images were less homogeneous, and/or if they contained fewer or no salient diagnostic objects, viewing behavior became more exploratory. Higher- and object-level image statistics were predictive at both the image and scene category levels. Scanpaths were generally organized and small differences in scanpath randomness could be roughly captured by critical object saliency. Participants tended to fixate on critical objects. Image statistics included in this study showed rotational invariance. The results supported our hypothesis that the availability of diagnostic objects strongly influences eye movements in this task. In addition, this study provides supporting evidence for Loschky et al.’s (Journal of Vision, 15(6), 11, 2015) speculation that aerial scenes are categorized on the basis of image parts and individual objects. The findings were discussed in relation to theories of scene perception and their implications for automation development.

A Diffusion-Based Pre-training Framework for Crystal Property Prediction

Many significant problems involving crystal property prediction from 3D structures have limited labeled data due to expensive and time-consuming physical simulations or lab experiments. To overcome this challenge, we propose a pretrain-finetune framework for the crystal property prediction task named CrysDiff based on diffusion models. In the pre-training phase, CrysDiff learns the latent marginal distribution of crystal structures via the reconstruction task. Subsequently, CrysDiff can be fine-tuned under the guidance of the new sparse labeled data, fitting the conditional distribution of the target property given the crystal structures. To better model the crystal geometry, CrysDiff notably captures the full symmetric properties of the crystals, including the invariance of reflection, rotation, and periodic translation. Extensive experiments demonstrate that CrysDiff can significantly improve the performance of the downstream crystal property prediction task on multiple target properties, outperforming all the SOTA pre-training models for crystals with good margins on the popular JARVIS-DFT dataset.

SphereDiffusion: Spherical Geometry-Aware Distortion Resilient Diffusion Model

Controllable spherical panoramic image generation holds substantial applicative potential across a variety of domains. However, it remains a challenging task due to the inherent spherical distortion and geometry characteristics, resulting in low-quality content generation. In this paper, we introduce a novel framework of SphereDiffusion to address these unique challenges, for better generating high-quality and precisely controllable spherical panoramic images. For the spherical distortion characteristic, we embed the semantics of the distorted object with text encoding, then explicitly construct the relationship with text-object correspondence to better use the pre-trained knowledge of the planar images. Meanwhile, we employ a deformable technique to mitigate the semantic deviation in latent space caused by spherical distortion. For the spherical geometry characteristic, in virtue of spherical rotation invariance, we improve the data diversity and optimization objectives in the training process, enabling the model to better learn the spherical geometry characteristic. Furthermore, we enhance the denoising process of the diffusion model, enabling it to effectively use the learned geometric characteristic to ensure the boundary continuity of the generated images. With these specific techniques, experiments on Structured3D dataset show that SphereDiffusion significantly improves the quality of controllable spherical image generation and relatively reduces around 35% FID on average.

REPS: Rotation equivariant Siamese network enhanced by probability segmentation for satellite video tracking

Satellite video is an emerging surface observation data that has drawn increasing interest due to its potential in spatiotemporal dynamic analysis. Single object tracking of satellite videos allows the continuous acquisition of the positions and ranges of objects and establishes the correspondences in the video sequence. However, small-sized objects are vulnerable to rotation and non-rigid deformation. Moreover, the horizontal bounding box of most trackers has difficulty in providing accurate semantic representations such as object position, orientation, and spatial distribution. In this article, we propose a unified framework, named rotation equivariant Siamese network enhanced by probability segmentation (REPS), to enhance the tracking accuracy and semantic representations simultaneously. First, to deal with the inconsistency of representations, we design a rotation equivariant (RE) Siamese network architecture to detect the rotation variations of objects right from the start frame, achieving the RE tracking. Second, a pixel-level (PL) refinement is proposed to refine the spatial distribution of objects. In addition, we proposed an adaptive Gaussian fusion that synergizes tracking and segmentation results to obtain compact outputs for satellite object representations. Extensive experiments on satellite videos demonstrate the superiority of the proposed approach. The code will be available at https://github.com/YZCU/REPS

Revisiting Tensor Basis Neural Network for Reynolds stress modeling: Application to plane channel and square duct flows

Recent advances in computing power devoted to Computational Fluid Dynamics (CFD) have opened up a new avenue for addressing the turbulence closure problem through Machine Learning (ML). Several Tensor Basis Neural Network (TBNN) frameworks aimed at enhancing turbulence Reynolds-Averaged Navier–Stokes (RANS) modeling have recently been proposed in the literature as data-driven constitutive models for systems with known invariance properties. However, persistent ambiguities remain regarding the physical adequacy of applying the General Eddy Viscosity Model (GEVM) within these frameworks. This work aims at investigating this aspect in an a priori stage for better predictions of the Reynolds stress anisotropy tensor, while preserving the Galilean and rotational invariances. In particular, we propose a general framework providing optimal tensor basis models for two types of canonical flows with increasing complexity: Plane Channel Flow (PCF) and Square Duct Flow (SDF). Subsequently, deep neural networks based on these optimal models are trained using state-of-the-art strategies to achieve a balanced and physically sound prediction of the full anisotropy tensor. A priori results obtained by the proposed framework are in very good agreement with the reference Direct Numerical Simulations (DNS) data. Notably, our shallow network with three layers excels in providing accurate predictions of the anisotropy tensor for PCF at unobserved friction Reynolds numbers, both in interpolation and extrapolation scenarios. The learning of the SDF case is more challenging because of its physical nature but also due to a lack of training data at various regimes. We propose a numerical strategy to alleviate this problem based on Transfer Learning (TL). In order to more efficiently generalize to an unseen intermediate Reτ regime, we take advantage of our prior knowledge acquired from a training with a larger and wider dataset. Our results indicate the potential of the developed network model, and demonstrate the feasibility and efficiency of the TL process in terms of training data size and training time. Based on these results, we believe there is a promising future by integrating these neural networks into an adapted in-house RANS solver.

A workflow for single-particle structure determination via iterative phasing of rotational invariants in fluctuation X-ray scattering.

Fluctuation X-ray scattering (FXS) offers a complementary approach for nano- and bioparticle imaging with an X-ray free-electron laser (XFEL), by extracting structural information from correlations in scattered XFEL pulses. Here a workflow is presented for single-particle structure determination using FXS. The workflow includes procedures for extracting the rotational invariants from FXS patterns, performing structure reconstructions via iterative phasing of the invariants, and aligning and averaging multiple reconstructions. The reconstruction pipeline is implemented in the open-source software xFrame and its functionality is demonstrated on several simulated structures.

Spherical convolutional neural networks can improve brain microstructure estimation from diffusion MRI data.

Diffusion magnetic resonance imaging is sensitive to the microstructural properties of brain tissue. However, estimating clinically and scientifically relevant microstructural properties from the measured signals remains a highly challenging inverse problem that machine learning may help solve. This study investigated if recently developed rotationally invariant spherical convolutional neural networks can improve microstructural parameter estimation. We trained a spherical convolutional neural network to predict the ground-truth parameter values from efficiently simulated noisy data and applied the trained network to imaging data acquired in a clinical setting to generate microstructural parameter maps. Our network performed better than the spherical mean technique and multi-layer perceptron, achieving higher prediction accuracy than the spherical mean technique with less rotational variance than the multi-layer perceptron. Although we focused on a constrained two-compartment model of neuronal tissue, the network and training pipeline are generalizable and can be used to estimate the parameters of any Gaussian compartment model. To highlight this, we also trained the network to predict the parameters of a three-compartment model that enables the estimation of apparent neural soma density using tensor-valued diffusion encoding.

Geometric Algebra based 2D-DOA Estimation for Non-circular Signals with an Electromagnetic Vector Array

This paper presents two novel methods based on geometric algebra (GA) to estimate two-dimensional (2D) direction-of-arrival (DOA) of non-circular (NC) signals for uniform rectangular array (URA). Traditional methods treat the received NC signals as a long vector which will inevitably lose orthogonality inside each electromagnetic vector sensor (EMVS) and thus miss some information of second-order statistical properties. Furthermore, the computational complexity will also increase. By contrast, the GA-based estimating signal parameter via rotational invariance techniques (ESPRIT) and propagation method (PM) algorithms are proposed to estimation DOA of NC signals. Taking advantage of GA, the relationship among multidimensional signals can be maintained. First, the six components of the EMVS are represented as a multivector in GA space. Then, we construct the GA-based extended covariance matrix to utilize the signal information more completely. The DOA parameters can be estimated through the ESPRIT and PM principle. The proposed GA-based estimation of signal parameter via rotational invariance techniques for NC signals processing (GANC-ESPRIT) can estimate DOA with high estimation accuracy. The proposed GA-based propagation method for NC signals estimation (GANC-PM) uses linear transformation to calculate angle parameters. Our model has much lower memory requirements and less computational burden compared with long vector models. Simulation results demonstrate the robustness and superiority of the proposed GANC-ESPRIT algorithm in terms of angular resolution. Complexity analysis shows that the proposed GANC-PM algorithm performances better with less computations.

Motorizing the buckled blister for rotary actuation.

Snap-through bistability was widely exploited for rapid hopping in micro-electro-mechanical systems and soft robots. However, considerable energy input was required to trigger the transition between discrete buckling states blocked by potential wells. Here a dynamic buckling mechanism of a buckled blister constrained inside an outer ring is explored for eliciting rotary actuation via a localized change of curvature in the blister. Due to rotational invariance of the buckled blister, lower energy supply is required to initiate the snap-through of buckling compared to conventional bistable mechanism. The controllability in rotational speed and output torque of the bimetallic blister-based rotator inside a rigid stator is exhibited, and the locomotion is demonstrated with two elastic rings via localized pneumatic actuators. With broad choices of stimulus and material for rings, the findings illustrate the promising potential of two nested rings to create active motions for diverse applications including gearless motors, peristaltic pumps, and locomotive robots.

Heavy-ion collisions, Gubser flow, and Carroll hydrodynamics

Gubser flow provides an analytic model for describing the spacetime dynamics of the quark-gluon plasma produced in heavy-ion collisions. Along with boost and rotation invariance along the beam axis, the model assumes invariance under a combination of translations and special conformal transformations in the transverse plane, leading to a flow profile which evolves not just along the beam axis, but also radially. We argue that Gubser flow and its associated symmetry assumptions arise naturally as a consequence of Carrollian symmetries for a conformal Carroll fluid, thereby providing a dual geometric picture for the flow. Given the inherent ultrarelativistic nature of the flow, this duality with Carroll hydrodynamics which arises in the c→0 limit of relativistic hydrodynamics, is natural. We provide a precise map between Gubser flow and the conformal Carroll fluid, appropriate to capture the duality between the two, not just at the ideal level, but also with the inclusion of hydrodynamic derivative corrections. Published by the American Physical Society 2024

연속 최적화를 위한 개선된 MAP-Elites 알고리즘

In this paper, we propose a new approach that enhances the continuous optimization performance of the MAP-Elites algorithm. The existing self-referencing MAP-Elites algorithm employed the “DE/rand/1/bin” operator from the differential evolution algorithm, which, due to its lack of rotational invariance, led to a degradation in optimization performance when there were high correlations among variables. The proposed algorithm replaces the “DE/rand/1/bin” operator with the “DE/current-to-rand/1” operator. This operator, possessing rotational invariance, ensures robust performance even in cases where there are high correlations among variables. Experimental results confirm that the proposed algorithm performs better than the comparison algorithms.

Meteoroid rotation and quasi-periodic brightness variation of meteor light curves

Meteor light curves are sometimes known to display flickering: rapid, quasi-periodic variations in brightness. This effect is generally attributed to the rotational modulation of the ablation rate, which is caused by the time-varying cross section area presented by a nonspherical rotating meteoroid to the oncoming airflow. In this work we investigate the effects that the rotation of a meteoroid of given shape (spherical, cubic, or cylindrical) has on the meteor’s light curve, given state-of-the-art experimental laboratory estimates of the drag and lift coefficients of hypersonic flow (Mach number > 5) around various shaped objects. The meteoroid’s shape is important in determining these two forces, due to the different response of the drag and lift coefficients according to the angle of attack. As a case study, the model was applied to a fireball observed on 2018 April 17 by the PRISMA network, a system of all-sky cameras that achieves a systematic monitoring of meteors and fireballs in the skies over the Italian territory. The results show that this methodology is potentially able to yield a powerful diagnostic of the rotation rate of meteoroids prior to their encounter with the atmosphere, while also providing essential information on their pre-fall actual shapes.

Towards in-field assessment of humeral and scapular kinematics: a comparison between laboratory and field settings using inertial sensors.

Inertial measurement units allow for quantitative assessment of body motion in many environments. Determining the ability to measure upper limb motion with inertial measurement units, leveraging procedures traditionally used in the lab such as scapular calibration procedures and humeral axial rotation calculation, would expand the opportunities to assess upper limb function in externally valid environments. This study examined if humeral and scapular motion measured in different field settings is consistent with motion measured in a lab setting in similar tasks. Twenty-eight adults participated in the study (14 field setting, 14 lab setting). Three different types of field settings were included: home (n = 5), work (n = 4), and sports (n = 5). Field participants were matched to lab participants based on sex and body height. All participants were equipped with five inertial and magnetic measurement units (Xsens Awinda, Xsens Technlogies, NL, Fs = 100 Hz) on the torso, humeri, and scapulae. Humeral and scapular angles were measured during a functional task protocol consisting of seven tasks. Data from all three field settings were combined. Statistical parametric mapping (α = .05) was used to assess differences in waveforms between the lab and field data. Five out of seven tasks displayed no differences for humeral elevation and humeral axial rotation, while scapular upward rotation and tilt were not statistically different for any tasks. Scapular internal rotation variability was very high for the field setting, but not for the lab setting. Task-based differences in humeral elevation and humeral axial rotation may be related to equipment modifications for the field protocol and between subjects' variability in task performance. Data indicate that humeral elevation, humeral axial rotation, and scapular upward rotation can be measured in externally valid field settings, which is promising for the evaluation of upper limb movement in natural environments.

DCCN: A dual-cross contrastive neural network for 3D point cloud representation learning

The proliferation of depth cameras and LiDAR sensors in actual industrial environments has fueled the pursuit of an effective and efficient 3D point cloud model that enables us to perceive and interact with the physical world. However, the intrinsic complexity of 3D semantic information poses significant challenges to model design, including spatial rotation invariance and irregular point cloud structure, which fundamentally impact the representation and behavior of 3D point cloud systems. Existing have either heavily relied on labeling information in a supervised learning setting or failed to effectively capture the inherent patterns of the 3D point clouds within a self-supervised learning framework, leading to poor performance in specific downstream tasks. To address these limitations, this paper introduces a self-supervised framework, Dual-Cross Contrastive Neural Network (DCCN) for 3D point cloud self-supervised representation learning. DCCN leverages cross-view, cross-network, and domain-specific knowledge distillation to enhance the extraction of hidden features from point clouds and fully exploit the capabilities of the encoder. Our DCCN employs a pseudo-Siamese network consisting of an online network and a target network, facilitating knowledge interaction and distillation. The method extracts internal states from augmented 3D point cloud by learning cross-view relationships and optimizes model parameters through intra-modal cross-network learning. We incorporate a momentum-updating mechanism without shared weights in the Siamese network architecture to distill knowledge and enhance the role differentiation the online and target networks. Experimental results demonstrate that our approach outperforms a range of supervised and self-supervised learning methods across a series of downstream tasks consisting of four tasks in three representative datasets. Ablation studies validate the component-wise effectiveness of cross-view, cross-network, and moment-updating learning objectives in achieving superior point cloud representation. The overall findings establish our method, DCCN, as an effective solution for 3D point cloud representation learning in real-world applications.

A hidden population of massive white dwarfs: two spotted K+WD binaries

Abstract The identification and characterization of massive (≳ 0.8 M⊙) white dwarfs is challenging in part due to their low luminosity. Here we present two candidate single-lined spectroscopic binaries, Gaia DR3 4014708864481651840 and 5811237403155163520, with K-dwarf primaries and optically dark companions. Both have orbital periods of P ∼ 0.45 days and show rotational variability, ellipsoidal modulations, and high-amplitude radial velocity variations. Using light curves from the Transiting Exoplanet Survey Satellite (TESS), radial velocities from ground-based spectrographs, and spectral energy distributions, we characterize these binaries to describe the nature of the unseen companion. We find that both systems are consistent with a massive white dwarf companion. Unlike simple ellipsoidal variables, star spots cause the light curve morphology to change between TESS sectors. We attempt to constrain the orbital inclination using PHOEBE binary light curve models, but degeneracies in the light curves of spotted stars prevent a precise determination. Finally, we search for similar objects using Gaia DR3 and TESS, and comment on these systems in the context of recently claimed compact object binaries.

QSAR modelling to predict structural features of certain sulfonamide as Urokinase-type Plasminogen Activator inhibitors

The serine hydrolase family includes serine proteases. It is essential for hydrolyzing protein peptide bonds and breaking them. The urokinase-type plasminogen activator (uPA) selectively binds to the uPAR on numerous cell types, including cancer cells. Pericellular proteolysis of cell-bound proteins requires this interaction. High uPA and uPAR levels regularly worsen cancer prognoses. Thus, small chemical active-site inhibitors that block uPA may diminish cancer cell invasion and metastasis. In compliance with Organization for Economic Corporation and Development guidelines, this research performed a complete Quantitative structure activity relationship analysis of sulfonamide compounds as Urokinase-type Plasminogen Activator inhibitors. Py-Descriptors were used for this investigation. PyDescriptor uses PyMOL standards and idioms to calculate 11,145 simple molecular descriptors. This plugin calculates molecular descriptors irrespective of molecular representation properties like atom numbering or labelling, spatial reference frame, translational and rotational invariance, etc. The investigation sought to find essential and hidden structural characteristics that regulate sulfonamide-type drugs' Urokinase-type Plasminogen Activator Inhibitory action. Twenty-eight sulfonamide chemicals are used in the Quantitative structure activity relationship study to generate statistically robust and highly predictive univariate and multivariate models. All models were thoroughly evaluated and meet several statistical parameter thresholds (e.g., R2 =0.9259–0.9280, Q2Loo= 0.8579–0.8558, Q2LMO= 0.8013–0.7865). The analysis reveal that occurance of ring carbon atoms exactly at 3 A0 from carbon atom, number of negatively charged atoms from sulphur atoms within 5 bonds, presence of hydrogen atom exactly at 3 bonds from donar atoms, presence of carbon atom exactly at 4 A0 from donar atom, presence of acceptor atom exactly at 5 A0 from sulphur atom and sum of partial charges of lipo atoms within 6 bonds from sulphur atom are important pharmacophoric features for Urokinase-type Plasminogen Activator Inhibition binding affinity. Thus, the developed Quantitative structure activity relationship study has an equilibrium of quantitative and qualitative tactics. The results could be useful for future optimizations of sulfonamide analogues.

Model-free low-power observer based robust trajectory tracking control of UAV quadrotor with unknown disturbances

PurposeThe purpose of this paper is to design an output-feedback algorithm based on low-power observer (LPO), robust chattering-free controller and nonlinear disturbance observer (DO) to achieve trajectory tracking of quadrotor in the Cartesian plane.Design/methodology/approachTo achieve trajectory tracking control, firstly the decoupled rotational and translational model of quadrotor are modified by introducing backstepped state-space variables. In the second step, robust integral sliding mode control is designed based on the proportional-integral-derivative (PID) technique. In the third step, a DO is constructed. In next step, the measurable outputs, i.e. rotational and translational state variables, are used to design the LPO. Finally, in the control algorithm all state variables and its rates are replaced with its estimates obtained using the state-observer.FindingsThe finding includes output-feedback control (OFC) algorithm designed by using a LPO. A modified backstepping model for rotational and rotational systems is developed prior to the design of integral sliding mode control based on PID technique. Unlike traditional high-gain observers (HGO), this paper used the LPO for state estimation of quadrotor systems to solve the problem of peaking phenomenon in HGO. Furthermore, a nonlinear DO is designed such that it attenuates disturbance with unknown magnitude and frequency. Moreover, a chattering reduction criterion has been introduced to solve the inherited chattering issue of controllers based on sliding mode technique.Practical implicationsThis paper presents input and output data-driven model-free control algorithm. That is, only input and output of the quadrotor model are required to achieve the trajectory tracking control. Therefore, for practical implementation, the number of on-board sensor is reduced.Originality/valueAlthough extensive research has been done for designing OFC algorithms for quadrotor, LPO has never been implemented for the rotational and translational state estimations of quadrotor. Furthermore, the mathematical model of rotational and translational systems is modified by using backstepped variables followed by the controller designed using PID and integral sliding mode control technique. Moreover, a DO is developed for attenuation of disturbance with unknown bound, magnitude and frequency.

Evaluation of Scapular Dynamics in Sports Trainees

Background: The scapula provides stability and mobility for efficient upper-limb movement. Optimal scapular kinematics are essential for efficient force generation and injury prevention. Sports trainees, particularly those involved in sports requiring repetitive or high-intensity shoulder movements, are susceptible to injuries and performance limitations if associated with aberrant scapular mechanics. Understanding the intricacies of scapular dynamics is essential for designing tailored training interventions that enhance athletic performance. Rationale and objectives: Previous research has emphasized the need for sports-specific training protocols. The measurement of scapular rotation has gained significant attention. Evaluating asymmetries in scapular dynamics across various sports trainee populations is a step forward for the need for tailored interventions and injury prevention strategies in preventing injury and planning better exercise programs. The study uses a PALM meter for the measurement of scapular rotation. Methodology: 40 Subjects 19 to 24 years old from the sports authority of Andhra Pradesh, India, were studied after obtaining written informed consent. Scapular rotation measured in a neutral and with hands on the hip position. Root of the scapula (RSS), inferior angle of the scapula (IAS), and spinous processes (Sp) of C7 to T8 are taken as the anatomical landmarks. Measurements of scapular position taken in two arm positions: shoulder neutral, hands on hip. A right-angle triangle created by dropping a perpendicular line from the scapula's root to intersect the horizontal line between the scapula's inferior angle and the thoracic spine's closest spinous process (IAS-Sp). The hypotenuse represents the distance IAS to RSS, while the side opposite the angle θ is the distance IAS-Sp minus RSS-Sp. A positive result indicates upward scapular rotation, while a negative result indicates downward scapular rotation. Results and Conclusion: This cross-sectional study revealed variations in scapular rotation and the distances from spinous processes in the scapular position in neutral and hands-on Hip positions from right to left and male to female. Further studies are required to understand scapular rotation variations concerning various sports involving overhead activity, heavy weight lifting, endurance sports and anatomical variations, muscle activation patterns, or task demands. KEYWORDS: Scapular Rotation, Sports Trainees, Shoulder Movements, Scapular Mechanics, Athletic Performance.

Mesh-based GNN surrogates for time-independent PDEs

Physics-based deep learning frameworks have shown to be effective in accurately modeling the dynamics of complex physical systems with generalization capability across problem inputs. However, time-independent problems pose the challenge of requiring long-range exchange of information across the computational domain for obtaining accurate predictions. In the context of graph neural networks (GNNs), this calls for deeper networks, which, in turn, may compromise or slow down the training process. In this work, we present two GNN architectures to overcome this challenge—the edge augmented GNN and the multi-GNN. We show that both these networks perform significantly better than baseline methods, such as MeshGraphNets, when applied to time-independent solid mechanics problems. Furthermore, the proposed architectures generalize well to unseen domains, boundary conditions, and materials. Here, the treatment of variable domains is facilitated by a novel coordinate transformation that enables rotation and translation invariance. By broadening the range of problems that neural operators based on graph neural networks can tackle, this paper provides the groundwork for their application to complex scientific and industrial settings.

Highly Accurate Prediction of NMR Chemical Shifts from Low-Level Quantum Mechanics Calculations Using Machine Learning.

Theoretical predictions of NMR chemical shifts from first-principles can greatly facilitate experimental interpretation and structure identification of molecules in gas, solution, and solid-state phases. However, accurate prediction of chemical shifts using the gold-standard coupled cluster with singles, doubles, and perturbative triple excitations [CCSD(T)] method with a complete basis set (CBS) can be prohibitively expensive. By contrast, machine learning (ML) methods offer inexpensive alternatives for chemical shift predictions but are hampered by generalization to molecules outside the original training set. Here, we propose several new ideas in ML of the chemical shift prediction for H, C, N, and O that first introduce a novel feature representation, based on the atomic chemical shielding tensors within a molecular environment using an inexpensive quantum mechanics (QM) method, and train it to predict NMR chemical shieldings of a high-level composite theory that approaches the accuracy of CCSD(T)/CBS. In addition, we train the ML model through a new progressive active learning workflow that reduces the total number of expensive high-level composite calculations required while allowing the model to continuously improve on unseen data. Furthermore, the algorithm provides an error estimation, signaling potential unreliability in predictions if the error is large. Finally, we introduce a novel approach to keep the rotational invariance of the features using tensor environment vectors (TEVs) that yields a ML model with the highest accuracy compared to a similar model using data augmentation. We illustrate the predictive capacity of the resulting inexpensive shift machine learning (iShiftML) models across several benchmarks, including unseen molecules in the NS372 data set, gas-phase experimental chemical shifts for small organic molecules, and much larger and more complex natural products in which we can accurately differentiate between subtle diastereomers based on chemical shift assignments.