相关论文: Transolver: A Fast Transformer Solver for PDEs on …

Machine learning methods have been successful in many areas, like image classification and natural language processing. However, it still needs to be determined how to apply ML to areas with mathematical constraints, like solving PDEs.…

Transformers have proven superior performance for a wide variety of tasks since they were introduced. In recent years, they have drawn attention from the vision community in tasks such as image classification and object detection. Despite…

Variational Autoencoders and their many variants have displayed impressive ability to perform dimensionality reduction, often achieving state-of-the-art performance. Many current methods however, struggle to learn good representations in…

Partial differential equations (PDEs) are often computationally challenging to solve, and in many settings many related PDEs must be be solved either at every timestep or for a variety of candidate boundary conditions, parameters, or…

We present a convolutional framework which significantly reduces the complexity and thus, the computational effort for distributed reinforcement learning control of dynamical systems governed by partial differential equations (PDEs).…

Developing fast surrogates for Partial Differential Equations (PDEs) will accelerate design and optimization in almost all scientific and engineering applications. Neural networks have been receiving ever-increasing attention and…

In this work, we aim to improve the 3D reasoning ability of Transformers in multi-view 3D human pose estimation. Recent works have focused on end-to-end learning-based transformer designs, which struggle to resolve geometric information…

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…

Solving partial differential equations (PDEs) with machine learning has recently attracted great attention, as PDEs are fundamental tools for modeling real-world systems that range from fundamental physical science to advanced engineering…

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…

Advances in differentiable numerical integrators have enabled the use of gradient descent techniques to learn ordinary differential equations (ODEs). In the context of machine learning, differentiable solvers are central for Neural ODEs…

Partial Differential Equations (PDEs) have long been recognized as powerful tools for image processing and analysis, providing a framework to model and exploit structural and geometric properties inherent in visual data. Over the years,…

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…

Solving large-scale Partial Differential Equations (PDEs) on complex three-dimensional geometries represents a central challenge in scientific and engineering computing, often impeded by expensive pre-processing stages and substantial…

Mixed-dimensional partial differential equations arise in several physical applications, wherein parts of the domain have extreme aspect ratios. In this case, it is often appealing to model these features as lower-dimensional manifolds…

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…

Recent years have witnessed a growth in mathematics for deep learning--which seeks a deeper understanding of the concepts of deep learning with mathematics and explores how to make it more robust--and deep learning for mathematics, where…

Real-world optimization problems are often constrained by complex physical laws that limit computational scalability. These constraints are inherently tied to complex regions, and thus learning models that incorporate physical and geometric…

The convergence of Krylov-based linear iterative solvers applied to parametric partial differential equations (PDEs) is often highly sensitive to the domain, its discretization, the location/values of the applied Dirichlet/Neumann boundary…

Recently, neural networks have been extensively employed to solve partial differential equations (PDEs) in physical system modeling. While major studies focus on learning system evolution on predefined static mesh discretizations, some…