Solving time-dependent Partial Differential Equations (PDEs) using a densely discretized spatial domain is a fundamental problem in various scientific and engineering disciplines, including modeling climate phenomena and fluid dynamics.

We propose a novel regularization loss that enforces standard Gaussianity, encouraging samples to align with a standard Gaussian distribution.

Solving time-dependent Partial Differential Equations (PDEs) using a densely discretized spatial domain is a fundamental problem in various scientific and engineering disciplines, including modeling climate phenomena and fluid dynamics.

Determining the 3D orientations of an object in an image, known as single-image pose estimation, is a crucial task in 3D vision applications. Existing methods typically learn 3D rotations parametrized in the spatial domain using Euler angles or quaternions, but these representations often introduce discontinuities and singularities. SO(3)-equivariant networks enable the structured capture of pose patterns with data-efficient learning, but the parametrizations in spatial domain are incompatible with their architecture, particularly spherical CNNs, which operate in the frequency domain to enhance computational efficiency. To overcome these issues, we propose a frequency-domain approach that directly predicts Wigner-D coefficients for 3D rotation regression, aligning with the operations of spherical CNNs. Our SO(3)-equivariant pose harmonics predictor overcomes the limitations of spatial parameterizations, ensuring consistent pose estimation under arbitrary rotations. Trained with a frequency-domain regression loss, our method achieves state-of-the-art results on benchmarks such as ModelNet10-SO(3) and PASCAL3D+, with significant improvements in accuracy, robustness, and data efficiency.

Vanilla pixel-level classifiers for semantic segmentation are based on a certain paradigm, involving the inner product of fixed prototypes obtained from the training set and pixel features in the test image. This approach, however, encounters significant limitations, i.e., feature deviation in the semantic domain and information loss in the spatial domain. The former struggles with large intra-class variance among pixel features from different images, while the latter fails to utilize the structured information of semantic objects effectively. This leads to blurred mask boundaries as well as a deficiency of fine-grained recognition capability. In this paper, we propose a novel Semantic and Spatial Adaptive Classifier (SSA-Seg) to address the above challenges. Specifically, we employ the coarse masks obtained from the fixed prototypes as a guide to adjust the fixed prototype towards the center of the semantic and spatial domains in the test image. The adapted prototypes in semantic and spatial domains are then simultaneously considered to accomplish classification decisions. In addition, we propose an online multi-domain distillation learning strategy to improve the adaption process. Experimental results on three publicly available benchmarks show that the proposed SSA-Seg significantly improves the segmentation performance of the baseline models with only a minimal increase in computational cost.

The OSSE NADIR and SWOT are pseudo-observations generated from the NEMO simulation.