Related papers: GITO: Graph-Informed Transformer Operator for Lear…

Scientific machine learning has seen significant progress with the emergence of operator learning. However, existing methods encounter difficulties when applied to problems on unstructured grids and irregular domains. Spatial graph neural…

Neural operators have emerged as powerful data-driven solvers for PDEs, offering substantial acceleration over classical numerical methods. However, existing transformer-based operators still face critical challenges when modeling PDEs on…

We combine vision transformers with operator learning to solve diverse inverse problems described by partial differential equations (PDEs). Our approach, named ViTO, combines a U-Net based architecture with a vision transformer. We apply…

Network topology optimization (NTO) via busbar splitting can mitigate transmission grid congestion and reduce redispatch costs. However, solving this mixed-integer nonlinear problem for large-scale systems in near-real-time is currently…

While Transformers have revolutionized machine learning on various data, existing Transformers for temporal graphs face limitations in (1) restricted receptive fields, (2) overhead of subgraph extraction, and (3) suboptimal generalization…

Recently the Transformer structure has shown good performances in graph learning tasks. However, these Transformer models directly work on graph nodes and may have difficulties learning high-level information. Inspired by the vision…

Topology optimization is a critical task in engineering design, where the goal is to optimally distribute material in a given space for maximum performance. We introduce Neural Implicit Topology Optimization (NITO), a novel approach to…

Transformers have recently emerged as powerful neural networks for graph learning, showcasing state-of-the-art performance on several graph property prediction tasks. However, these results have been limited to small-scale graphs, where the…

Deep learning surrogate models have shown promise in solving partial differential equations (PDEs). Among them, the Fourier neural operator (FNO) achieves good accuracy, and is significantly faster compared to numerical solvers, on a…

There is a recent surge in the development of spatio-temporal forecasting models in the transportation domain. Long-range traffic forecasting, however, remains a challenging task due to the intricate and extensive spatio-temporal…

Transformers serve as the backbone architectures of Foundational Models, where domain-specific tokenizers allow them to adapt to various domains. Graph Transformers (GTs) have recently emerged as leading models in geometric deep learning,…

Graph classification is an important learning task for graph-structured data. Graph neural networks (GNNs) have recently gained growing attention in graph learning and have shown significant improvements in many important graph problems.…

Graph Neural Networks (GNNs) have been successfully used in many problems involving graph-structured data, achieving state-of-the-art performance. GNNs typically employ a message-passing scheme, in which every node aggregates information…

The Transformer architecture has gained growing attention in graph representation learning recently, as it naturally overcomes several limitations of graph neural networks (GNNs) by avoiding their strict structural inductive biases and…

Operator learning seeks to approximate mappings from input functions to output solutions, particularly in the context of partial differential equations (PDEs). While recent advances such as DeepONet and Fourier Neural Operator (FNO) have…

Neural operators on irregular meshes face a fundamental tension. Spectral positional encodings, the natural choice for capturing geometry, require cubic-complexity eigendecomposition and inadvertently break gauge invariance through…

Neural operators have emerged as powerful tools for learning mappings between function spaces, enabling efficient solutions to partial differential equations across varying inputs and domains. Despite the success, existing methods often…

Graph Neural Networks (GNNs) have been widely applied to various fields due to their powerful representations of graph-structured data. Despite the success of GNNs, most existing GNNs are designed to learn node representations on the fixed…

Accurate long-term traffic forecasting remains a critical challenge in intelligent transportation systems, particularly when predicting high-frequency traffic phenomena such as shock waves and congestion boundaries over extended rollout…

In this paper, we propose physics-informed neural operators (PINO) that combine training data and physics constraints to learn the solution operator of a given family of parametric Partial Differential Equations (PDE). PINO is the first…