Related papers: PGOT: A Physics-Geometry Operator Transformer for …

Contemporary graph learning algorithms are not well-defined for large molecules since they do not consider the hierarchical interactions among the atoms, which are essential to determine the molecular properties of macromolecules. In this…

In this paper, a Feature-preserving Particle Generation (FPPG) method for arbitrary complex geometry is proposed. Instead of basing on implicit geometries, such as level-set, FPPG employs an explicit geometric representation for the…

In this paper, we evaluate the effectiveness of deep operator networks (DeepONets) in solving both forward and inverse problems of partial differential equations (PDEs) on unknown manifolds. By unknown manifolds, we identify the manifold by…

Complex-valued Transformers have largely inherited softmax attention from real-valued architectures. However, row-normalised token competition is not necessarily aligned with phase-preserving computation. In this paper, we introduce the…

Learning solution operators of partial differential equations (PDEs) from data has emerged as a promising route to fast surrogate models in multi-query scientific workflows. However, for geometric PDEs whose inputs and outputs transform…

Detecting transmission towers from synthetic aperture radar (SAR) images remains a challenging task due to the comparatively small size and side-looking geometry, with background clutter interference frequently hindering tower…

We introduce Perturbative Gradient Training (PGT), a novel training paradigm that overcomes a critical limitation of physical reservoir computing: the inability to perform backpropagation due to the black-box nature of physical reservoirs.…

Recently, leveraging pre-training techniques to enhance point cloud models has become a prominent research topic. However, existing approaches typically require full fine-tuning of pre-trained models to achieve satisfactory performance on…

Accurate and physically consistent modeling of Earth system dynamics requires machine-learning architectures that operate directly on continuous geophysical fields and preserve their underlying geometric structure. Here we introduce…

We introduce ECHO, a transformer-operator framework for generating million-point PDE trajectories. While existing neural operators (NOs) have shown promise for solving partial differential equations, they remain limited in practice due to…

Although deep models have been widely explored in solving partial differential equations (PDEs), previous works are primarily limited to data only with up to tens of thousands of mesh points, far from the million-point scale required by…

Modern digital engineering design process commonly involves expensive repeated simulations on varying three-dimensional (3D) geometries. The efficient prediction capability of neural networks (NNs) makes them a suitable surrogate to provide…

Preserving geometric structure is important in learning. We propose a unified class of geometry-aware architectures that interleave geometric updates between layers, where both projection layers and intrinsic exponential map updates arise…

Problems involving geometric data arise in physics, chemistry, robotics, computer vision, and many other fields. Such data can take numerous forms, for instance points, direction vectors, translations, or rotations, but to date there is no…

LiDAR-based 3D single object tracking is a challenging issue in robotics and autonomous driving. Currently, existing approaches usually suffer from the problem that objects at long distance often have very sparse or partially-occluded point…

Point scene understanding is a challenging task to process real-world scene point cloud, which aims at segmenting each object, estimating its pose, and reconstructing its mesh simultaneously. Recent state-of-the-art method first segments…

Jet tagging is an essential categorization problem in high energy physics. In recent times, Deep Learning has not only risen to the challenge of jet tagging but also significantly improved its performance. In this article, we proposed an…

Accurate segmentation of aortic vascular structures is critical for diagnosing and treating cardiovascular diseases.Traditional Transformer-based models have shown promise in this domain by capturing long-range dependencies between vascular…

Gradient-based meta-learning methods have primarily been applied to classical machine learning tasks such as image classification. Recently, PDE-solving deep learning methods, such as neural operators, are starting to make an important…

Motivation: Despite its great success in various physical modeling, differential geometry (DG) has rarely been devised as a versatile tool for analyzing large, diverse and complex molecular and biomolecular datasets due to the limited…