相关论文: Autoregressive Renaissance in Neural PDE Solvers

Developing efficient numerical algorithms for the solution of high dimensional random Partial Differential Equations (PDEs) has been a challenging task due to the well-known curse of dimensionality. We present a new solution framework for…

Partial differential equations (PDEs) are indispensable for modeling many physical phenomena and also commonly used for solving image processing tasks. In the latter area, PDE-based approaches interpret image data as discretizations of…

Autoregressive models are often employed to learn distributions of image data by decomposing the $D$-dimensional density function into a product of one-dimensional conditional distributions. Each conditional depends on preceding variables…

Neural operators have proven to be a promising approach for modeling spatiotemporal systems in the physical sciences. However, training these models for large systems can be quite challenging as they incur significant computational and…

There has been an arising trend of adopting deep learning methods to study partial differential equations (PDEs). In this paper, we introduce a deep recurrent framework for solving time-dependent PDEs without generating large scale data…

Time-independent Partial Differential Equations (PDEs) on large meshes pose significant challenges for data-driven neural PDE solvers. We introduce a novel graph rewiring technique to tackle some of these challenges, such as aggregating…

Neural solvers for partial differential equations (PDEs) have great potential to generate fast and accurate physics solutions, yet their practicality is currently limited by their generalizability. PDEs evolve over broad scales and exhibit…

Communication technologies like voice over IP operate under constrained real-time conditions, with voice packets being subject to delays and losses from the network. In such cases, the packet loss concealment (PLC) algorithm reconstructs…

Backpropagation algorithm is the cornerstone for neural network analysis. Paper extends it for training any derivatives of neural network's output with respect to its input. By the dint of it feedforward networks can be used to solve or…

Neural diffusion on graphs is a novel class of graph neural networks that has attracted increasing attention recently. The capability of graph neural partial differential equations (PDEs) in addressing common hurdles of graph neural…

The numerical solution of partial differential equations (PDEs) is fundamental to scientific and engineering computing. In the presence of strong anisotropy, material heterogeneity, and complex geometries, however, classical iterative…

Modelling the underlying mechanisms of neurodegenerative diseases demands methods that capture heterogeneous and spatially varying dynamics from sparse, high-dimensional neuroimaging data. Integrating partial differential equation (PDE)…

Solving large complex partial differential equations (PDEs), such as those that arise in computational fluid dynamics (CFD), is a computationally expensive process. This has motivated the use of deep learning approaches to approximate the…

Mainstream numerical Partial Differential Equation (PDE) solvers require discretizing the physical domain using a mesh. Mesh movement methods aim to improve the accuracy of the numerical solution by increasing mesh resolution where the…

A growing body of literature has been leveraging techniques of machine learning (ML) to build novel approaches to approximating the solutions to partial differential equations. Noticeably absent from the literature is a systematic…

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…

Non-autoregressive neural machine translation (NAT) generates each target word in parallel and has achieved promising inference acceleration. However, existing NAT models still have a big gap in translation quality compared to…

Solving partial differential equations is difficult. Recently proposed neural resolution-invariant models, despite their effectiveness and efficiency, usually require equispaced spatial points of data. However, sampling in spatial domain is…

The Traveling Salesman Problem (TSP) is a well-known combinatorial optimization problem with broad real-world applications. Recently, neural networks have gained popularity in this research area because as shown in the literature, they…

Message passing neural networks (MPNNs) have emerged as go-to models for learning on graph-structured data in the past decade. Despite their effectiveness, most of such models still incur severe issues such as over-smoothing and…