Predicting the tensor properties of crystalline materials is a fundamental task in materials science. Unlike single-value property prediction, which is inherently invariant, tensor property prediction requires maintaining O(3) group tensor equivariance. Such equivariance constraint often requires specialized architecture designs to achieve effective predictions, inevitably introducing tremendous computational costs. Canonicalization, a classical technique for geometry, has recently been explored for efficient learning with symmetry. In this work, we revisit the problem of crystal tensor property prediction through the lens of canonicalization. Specifically, we demonstrate how polar decomposition, a simple yet efficient algebraic method, can serve as a form of canonicalization and be leveraged to ensure equivariant tensor property prediction. Building upon this insight, we propose a general O(3)-equivariant framework for efficient crystal tensor property prediction, referred to as GoeCTP. By utilizing canonicalization, GoeCTP achieves high efficiency without requiring the explicit incorporation of equivariance constraints into the network architecture. Experimental results indicate that GoeCTP achieves the best prediction performance and runs at most 13 times faster compared to existing state-of-the-art methods in benchmarking datasets, underscoring its effectiveness and efficiency.

Crystal structures are defined by the periodic arrangement of atoms in 3D space, inherently making them equivariant to SO(3) group. A fundamental requirement for crystal property prediction is that the model's output should remain invariant to arbitrary rotational transformations of the input structure. One promising strategy to achieve this invariance is to align the given crystal structure into a canonical orientation with appropriately computed rotations, or called frames. However, existing work either only considers a global frame or solely relies on more advanced local frames based on atoms' local structure. A global frame is too coarse to capture the local structure heterogeneity of the crystal, while local frames may inadvertently disrupt crystal symmetry, limiting their expressivity. In this work, we revisit the frame design problem for crystalline materials and propose a novel approach to construct expressive {\bf S}ymmetry Preserving Frames, dubbed as SPFrame, for modeling crystal structures. Specifically, this local-global associative frame constructs invariant local frames rather than equivariant ones, thereby preserving the symmetry of the crystal. In parallel, it integrates global structural information to construct an equivariant global frame to enforce SO(3) invariance. Extensive experimental results demonstrate that SPFrame consistently outperforms traditional frame construction techniques and existing crystal property prediction baselines across multiple benchmark tasks.

Due to the non-Gaussian distribution of erratic noise, conventional Gaussian denoising methods often encounter substantial challenges and pressures when suppressing this kind of noise. To overcome this challenge, several state-of-the-art (SOTA) schemes, for instance, robust low-rank approximation (LRA) and deep learning (DL) methods, have been designed and achieved promising results in the treatment of erratic noise. However, these SOTA denoising methods focus mainly on matrix-based modeling representations and fail to fully reflect the correlations associated with erratic noise and valid signals in the spatial dimension and thus may display suboptimal performance. As an alternative, a robust tensor DL (RTDL) denoising method for unsupervised 3-D seismic erratic noise suppression that involves the use of a reasonable combination of tensor sparse representation (SR) and a tensor neural network (tNN) is proposed in this study. The key to RTDL is to introduce a robust tensor sparse norm for erratic noise to exhaustively exploit the spatial tubular sparse distribution properties in 3-D space; notably, adding a tensor sparse norm to the tNN model yields a new data-driven model with 3-D erratic noise reduction capabilities. To find the optimized parameters of the new model, an efficiency tensor optimization method is established on the basis of alternating minimization (Alt), the aim of which is to alternately solve two subproblems involving tensor SR and a tNN. This paper presents well-designed experiments and satisfactory results compared with those of SOTA methods based on both synthetic and real field datasets.

Due to the poorly coupled geophones present in boreholes, vertical seismic profiling (VSP) data are known to suffer from intense coupling noise, which causes severe VSP image deterioration and significantly hinders subsequent processing. Thus, diverse denoising approaches are indispensable preprocessing steps for suppressing this kind of noise to achieve good results. Among them, robust principal component analysis (RPCA) is a common signal and noise separation model that is generally considered a highly promising method for removing intense coupling noise; however, handcrafted priors have limited denoising ability, especially for the low-rank assumption of useful signals. As an alternative, following the RPCA framework, this article proposes an unsupervised iterative robust deep convolutional autoencoder (IRDCAE) model to suppress intense VSP coupling noise without any assumptions regarding valuable signals. The key to the IRDCAE approach is the use of weighted column sparsity (WCS) to characterize the behavior of the intense coupling noise, where the weight prior is derived from the pure noise component before the first break. By adding a WCS regularization term to the conventional deep convolutional autoencoder (DCAE), our IRDCAE method transforms the model from an entirely data-driven model to a model+data driven approach. Thus, the IRDCAE approach has the advantages of both RPCA and DCAE, resulting in the ability to separate intense coupling noise from useful signals in an unsupervised manner by optimizing the IRDCAE model via an alternating minimization algorithm. The exceptional performance of the IRDCAE model is exhibited with synthetic and field VSP data.

Seismic facies analysis (SFA) plays a pivotal role in the interpretation of subsurface structures, with a pressing need to develop automated techniques for analyzing 4-D prestack seismic data. Various automated SFA methods, encompassing both supervised and unsupervised paradigms, have shown encouraging potential in fulfilling this demand. Nonetheless, supervised methods heavily hinge upon precious labeled seismic datasets of high caliber, and unsupervised methods handle all seismic samples indiscriminately during training, resulting in pronounced biases toward the majority classes of seismic data. As an alternative, this letter proposes class-imbalanced deep embedding clustering (CDEC), an unsupervised deep clustering methodology devised to analyze seismic data with class-imbalanced facies distributions. Within CDEC, a focal loss meticulously tailored to address class imbalance challenges is seamlessly integrated into the classic deep convolutional embedding clustering (DCEC). By balancing weights between the minority and majority seismic samples during network training, this approach adeptly attenuates biases toward the majority classes while concurrently bolstering the efficacy of SFA. Experimental evaluations conducted on synthetic and real field datasets compellingly underscore the effectiveness and utility of the proposed CDEC method.