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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…

In recent years, there has been a growing interest in leveraging deep learning and neural networks to address scientific problems, particularly in solving partial differential equations (PDEs). However, many neural network-based methods…

In light of the inherent entailment relations between images and text, hyperbolic point vector embeddings, leveraging the hierarchical modeling advantages of hyperbolic space, have been utilized for visual semantic representation learning.…

Finite element methods typically require a high resolution to satisfactorily approximate micro and even macro patterns of an underlying physical model. This issue can be circumvented by appropriate multiscale strategies that are able to…

In recent literature there are plenty of works that combine handcrafted and learnable regularizers to solve inverse imaging problems. While this hybrid approach has demonstrated promising results, the motivation for combining handcrafted…

We prove the well--posedness of a dynamical perfect plasticity model under general assumptions on the stress constraint set and on the reference configuration. The problem is studied by combining both calculus of variations and hyperbolic…

While the acquisition of time series has become more straightforward, developing dynamical models from time series is still a challenging and evolving problem domain. Within the last several years, to address this problem, there has been a…

Graph representation learning in Euclidean space, despite its widespread adoption and proven utility in many domains, often struggles to effectively capture the inherent hierarchical and complex relational structures prevalent in real-world…

Solving partial differential equations (PDEs) with machine learning typically requires training a new neural network for every new equation. This optimization is slow. We introduce MetaColloc. It is an optimization-free and data-free…

We present a divergence-free and $H(div)$-conforming hybridized discontinuous Galerkin (HDG) method and a computationally efficient variant called embedded-HDG (E-HDG) for solving stationary incompressible viso-resistive magnetohydrodynamic…

We present a dimensionally split method for solving hyperbolic conservation laws on Cartesian cut cell meshes. The approach combines local geometric and wave speed information to determine a novel stabilised cut cell flux, and we provide a…

Multi-step reasoning is a fundamental challenge in artificial intelligence, with applications ranging from mathematical problem-solving to decision-making in dynamic environments. Reinforcement Learning (RL) has shown promise in enabling…

Hyperspectral imaging provides precise classification for land use and cover due to its exceptional spectral resolution. However, the challenges of high dimensionality and limited spatial resolution hinder its effectiveness. This study…

Pre-trained deep image representations are useful for post-training tasks such as classification through transfer learning, image retrieval, and object detection. Data augmentations are a crucial aspect of pre-training robust…

Continual learning is the problem of sequentially learning new tasks or knowledge while protecting previously acquired knowledge. However, catastrophic forgetting poses a grand challenge for neural networks performing such learning process.…

In this work a new finite element based Method of Relaxed Streamline Upwinding is proposed to solve hyperbolic conservation laws. Formulation of the proposed scheme is based on relaxation system which replaces hyperbolic conservation laws…

We develop a new spatial semidiscrete multiscale method based upon the edge multiscale methods to solve semilinear parabolic problems with heterogeneous coefficients and smooth initial data. This method allows for a cheap spatial…

We show how to solve hyperbolic equations numerically on unbounded domains by compactification, thereby avoiding the introduction of an artificial outer boundary. The essential ingredient is a suitable transformation of the time coordinate…

Learning based hashing methods have attracted considerable attention due to their ability to greatly increase the scale at which existing algorithms may operate. Most of these methods are designed to generate binary codes that preserve the…

Designing efficient and high-accuracy numerical methods for complex dynamic incompressible magnetohydrodynamics (MHD) equations remains a challenging problem in various analysis and design tasks. This is mainly due to the nonlinear coupling…