Related papers: GFocal: A Global-Focal Neural Operator for Solving…

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…

We introduce methods for obtaining pretrained Geometric Neural Operators (GNPs) that can serve as basal foundation models for use in obtaining geometric features. These can be used within data processing pipelines for machine learning tasks…

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…

Operator learning offers a powerful paradigm for solving parametric partial differential equations (PDEs), but scaling probabilistic neural operators such as the recently proposed Gaussian Processes Operators (GPOs) to high-dimensional,…

Machine-learning-based surrogate models offer significant computational efficiency and faster simulations compared to traditional numerical methods, especially for problems requiring repeated evaluations of partial differential equations.…

Inverse problems governed by partial differential equations (PDEs) are crucial in science and engineering. They are particularly challenging due to ill-posedness, data sparsity, and the added complexity of irregular geometries. Classical…

Geometry problem-solving remains a significant challenge for Large Multimodal Models (LMMs), requiring not only global shape recognition but also attention to intricate local relationships related to geometric theory. To address this, we…

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…

Predicting time-dependent dynamics of complex systems governed by non-linear partial differential equations (PDEs) with varying parameters and domains is a challenging task motivated by applications across various fields. We introduce a…

We propose integrating optimal transport (OT) into operator learning for partial differential equations (PDEs) on complex geometries. Classical geometric learning methods typically represent domains as meshes, graphs, or point clouds. Our…

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…

For partial differential equations on domains of arbitrary shapes, existing works of neural operators attempt to learn a mapping from geometries to solutions. It often requires a large dataset of geometry-solution pairs in order to obtain a…

In this work, we introduce implicit Finite Operator Learning (iFOL) for the continuous and parametric solution of partial differential equations (PDEs) on arbitrary geometries. We propose a physics-informed encoder-decoder network to…

We propose the Factorized Fourier Neural Operator (F-FNO), a learning-based approach for simulating partial differential equations (PDEs). Starting from a recently proposed Fourier representation of flow fields, the F-FNO bridges the…

It is a long-standing problem in robotics to develop agents capable of executing diverse manipulation tasks from visual observations in unstructured real-world environments. To achieve this goal, the robot needs to have a comprehensive…

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…

Transformers have empowered many milestones across various fields and have recently been applied to solve partial differential equations (PDEs). However, since PDEs are typically discretized into large-scale meshes with complex geometries,…

Transformer-based models have emerged as promising tools for time series forecasting. However, these model cannot make accurate prediction for long input time series. On the one hand, they failed to capture global dependencies within time…

Foundation models have transformed natural language processing and computer vision, and their impact is now reshaping remote sensing image analysis. With powerful generalization and transfer learning capabilities, they align naturally with…

Machine learning approaches for solving partial differential equations require learning mappings between function spaces. While convolutional or graph neural networks are constrained to discretized functions, neural operators present a…