Related papers: CATO: Charted Attention for Neural PDE Operators

The very challenging task of learning solution operators of PDEs on arbitrary domains accurately and efficiently is of vital importance to engineering and industrial simulations. Despite the existence of many operator learning algorithms to…

Neural operators have emerged as promising frameworks for learning mappings governed by partial differential equations (PDEs), serving as data-driven alternatives to traditional numerical methods. While methods such as the Fourier neural…

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…

Neural operators have achieved promising performance on partial differential equations (PDEs), but most existing models are built on fixed Eulerian coordinates. This mismatch between evolving physical structures and static coordinates…

Neural operators offer a powerful data-driven framework for learning mappings between function spaces, in which the transformer-based neural operator architecture faces a fundamental scalability-accuracy trade-off: softmax attention…

Neural operators effectively solve PDE problems from data without knowing the explicit equations, which learn the map from the input sequences of observed samples to the predicted values. Most existing works build the model in the original…

Attention operators have been widely applied in various fields, including computer vision, natural language processing, and network embedding learning. Attention operators on graph data enables learnable weights when aggregating information…

Despite the recent popularity of attention-based neural architectures in core AI fields like natural language processing (NLP) and computer vision (CV), their potential in modeling complex physical systems remains under-explored. Learning…

We present a novel graph-informed transformer operator (GITO) architecture for learning complex partial differential equation systems defined on irregular geometries and non-uniform meshes. GITO consists of two main modules: a hybrid graph…

Learning partial differential equations' (PDEs) solution operators is an essential problem in machine learning. However, there are several challenges for learning operators in practical applications like the irregular mesh, multiple input…

Scientific machine learning has enabled the extraction of physical insights and data-driven modeling of high-dimensional spatiotemporal data, yet achieving physically interpretable latent representations and computationally efficient…

Sparse-view Computed Tomography (CT) reconstructs images from a limited number of X-ray projections to reduce radiation and scanning time, which makes reconstruction an ill-posed inverse problem. Deep learning methods achieve high-fidelity…

Existing neural operator architectures face challenges when solving multiphysics problems with coupled partial differential equations (PDEs) due to complex geometries, interactions between physical variables, and the limited amounts of…

Operator learning for Partial Differential Equations (PDEs) is rapidly emerging as a promising approach for surrogate modeling of intricate systems. Transformers with the self-attention mechanism$\unicode{x2013}$a powerful tool originally…

Transformers have shown superior performance on various vision tasks. Their large receptive field endows Transformer models with higher representation power than their CNN counterparts. Nevertheless, simply enlarging the receptive field…

While Transformers have demonstrated remarkable potential in modeling Partial Differential Equations (PDEs), modeling large-scale unstructured meshes with complex geometries remains a significant challenge. Existing efficient architectures…

Neural operators have emerged as a powerful data-driven paradigm for solving partial differential equations (PDEs), while their accuracy and scalability are still limited, particularly on irregular domains where fluid flows exhibit rich…

A computed approximation of the solution operator to a system of partial differential equations (PDEs) is needed in various areas of science and engineering. Neural operators have been shown to be quite effective at predicting these…

We propose the geometry-informed neural operator (GINO), a highly efficient approach to learning the solution operator of large-scale partial differential equations with varying geometries. GINO uses a signed distance function and…

The Earth's subsurface is a cornerstone of modern society, providing essential energy resources like hydrocarbons, geothermal, and minerals while serving as the primary reservoir for $CO_2$ sequestration. However, full physics numerical…