相关论文: PGOT: A Physics-Geometry Operator Transformer for …

We present a novel architecture for learning geometry-aware preconditioners for linear partial differential equations (PDEs). We show that a deep operator network (Deeponet) can be trained on a simple geometry and remain a robust…

Physics-Informed Neural Operators provide efficient, high-fidelity simulations for systems governed by partial differential equations (PDEs). However, most existing studies focus only on multi-scale, multi-physics systems within a single…

The convergence behavior of classical iterative solvers for parametric partial differential equations (PDEs) is often highly sensitive to the domain and specific discretization of PDEs. Previously, we introduced hybrid solvers by combining…

Solving parametric Partial Differential Equations (PDEs) for a broad range of parameters is a critical challenge in scientific computing. To this end, neural operators, which \textcolor{black}{predicts the PDE solution with variable PDE…

Neural operators have achieved strong performance in learning solution operators of partial differential equations (PDEs), but their inherently continuous representations struggle to capture discontinuities and sharp transitions. Existing…

Transformers achieve strong performance across diverse domains but implicitly assume Euclidean geometry in their attention mechanisms, limiting their effectiveness on data with non-Euclidean structure. While recent extensions to hyperbolic…

Transparent object perception remains a major challenge in computer vision research, as transparency confounds both depth estimation and semantic segmentation. Recent work has explored multi-task learning frameworks to improve robustness,…

Point clouds are versatile representations of 3D objects and have found widespread application in science and engineering. Many successful deep-learning models have been proposed that use them as input. The domain of chemical and materials…

As transformers are equivariant to the permutation of input tokens, encoding the positional information of tokens is necessary for many tasks. However, since existing positional encoding schemes have been initially designed for NLP tasks,…

Utilizing patch-based transformers for unstructured geometric data such as polygon meshes presents significant challenges, primarily due to the absence of a canonical ordering and variations in input sizes. Prior approaches to handling 3D…

Segmenting multiple objects (e.g., organs) in medical images often requires an understanding of their topology, which simultaneously quantifies the shape of the objects and their positions relative to each other. This understanding is…

3D geometric shape completion hinges on representation learning and a deep understanding of geometric data. Without profound insights into the three-dimensional nature of the data, this task remains unattainable. Our work addresses this…

Recent advances in diffusion models have significantly improved image editing. However, challenges persist in handling geometric transformations, such as translation, rotation, and scaling, particularly in complex scenes. Existing…

Deep operator network (DeepONet) has shown significant promise as surrogate models for systems governed by partial differential equations (PDEs), enabling accurate mappings between infinite-dimensional function spaces. However, when applied…

The challenge of applying learned knowledge from one domain to solve problems in another related but distinct domain, known as transfer learning, is fundamental in operator learning models that solve Partial Differential Equations (PDEs).…

Surrogate models are critical for accelerating computationally expensive simulations in science and engineering, particularly for solving parametric partial differential equations (PDEs). Developing practical surrogate models poses…

As an important and challenging problem in computer vision, PAnoramic Semantic Segmentation (PASS) gives complete scene perception based on an ultra-wide angle of view. Usually, prevalent PASS methods with 2D panoramic image input focus on…

Neural operator learning accelerates PDE solution by approximating operators as mappings between continuous function spaces. Yet in many engineering settings, varying geometry induces discrete structural changes, including topological…

Point-based representations have consistently played a vital role in geometric data structures. Most point cloud learning and processing methods typically leverage the unordered and unconstrained nature to represent the underlying geometry…

Accurate and efficient simulations of physical phenomena governed by partial differential equations (PDEs) are important for scientific and engineering progress. While traditional numerical solvers are powerful, they are often…