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Developing efficient numerical algorithms for the solution of high dimensional random Partial Differential Equations (PDEs) has been a challenging task due to the well-known curse of dimensionality. We present a new solution framework for…

Machine learning methods for solving nonlinear partial differential equations (PDEs) are hot topical issues, and different algorithms proposed in the literature show efficient numerical approximation in high dimension. In this paper, we…

High fidelity representation of shapes with arbitrary topology is an important problem for a variety of vision and graphics applications. Owing to their limited resolution, classical discrete shape representations using point clouds, voxels…

Generative thermal design for complex geometries is fundamental in many areas of engineering, yet it faces two main challenges: the high computational cost of high-fidelity simulations and the limitations of conventional generative models.…

Neural representations of 3D data have been widely adopted across various applications, particularly in recent work leveraging coordinate-based networks to model scalar or vector fields. However, these approaches face inherent challenges,…

This is a tutorial and survey paper on unification of spectral dimensionality reduction methods, kernel learning by Semidefinite Programming (SDP), Maximum Variance Unfolding (MVU) or Semidefinite Embedding (SDE), and its variants. We first…

Mathematical reasoning remains an ongoing challenge for AI models, especially for geometry problems that require both linguistic and visual signals. As the vision encoders of most MLLMs are trained on natural scenes, they often struggle to…

Very recently neural implicit rendering techniques have been rapidly evolved and shown great advantages in novel view synthesis and 3D scene reconstruction. However, existing neural rendering methods for editing purposes offer limited…

Large-scale multimodal contrastive learning has recently achieved impressive success in learning rich and transferable representations, yet it remains fundamentally limited by the uniform treatment of feature dimensions and the neglect of…

There has been an arising trend of adopting deep learning methods to study partial differential equations (PDEs). This article is to propose a Deep Learning Galerkin Method (DGM) for the closed-loop geothermal system, which is a new coupled…

Deep learning methods have played a more and more important role in hyperspectral image classification. However, the general deep learning methods mainly take advantage of the information of sample itself or the pairwise information between…

Enhancing neural networks with knowledge of physical equations has become an efficient way of solving various physics problems, from fluid flow to electromagnetism. Graph neural networks show promise in accurately representing irregularly…

When solving a segmentation task, shaped-base methods can be beneficial compared to pixelwise classification due to geometric understanding of the target object as shape, preventing the generation of anatomical implausible predictions in…

Hyperspectral unmixing (HU) is crucial for analyzing hyperspectral imagery, yet achieving accurate unmixing remains challenging. While traditional methods struggle to effectively model complex spectral-spatial features, deep learning…

Generative modeling aims to generate new data samples that resemble a given dataset, with diffusion models recently becoming the most popular generative model. One of the main challenges of diffusion models is solving the problem in the…

Partial differential equations (PDEs) are widely used across the physical and computational sciences. Decades of research and engineering went into designing fast iterative solution methods. Existing solvers are general purpose, but may be…

Diffusion geometry is a manifold learning framework that uses random walks defined by Markov transition matrices to characterize the geometry of a dataset at multiple scales. We use diffusion geometry for neural representations,…

In recent years, hyperspectral imaging, also known as imaging spectroscopy, has been paid an increasing interest in geoscience and remote sensing community. Hyperspectral imagery is characterized by very rich spectral information, which…

Spectral geometric methods have brought revolutionary changes to the field of geometry processing. Of particular interest is the study of the Laplacian spectrum as a compact, isometry and permutation-invariant representation of a shape.…

D shape generation is a fundamental operation in computer graphics. While significant progress has been made, especially with recent deep generative models, it remains a challenge to synthesize high-quality shapes with rich geometric…