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Neural operators have emerged as promising surrogate models for solving partial differential equations (PDEs), but struggle to generalise beyond training distributions and are often constrained to a fixed temporal discretisation. This work…

Deep learning is increasingly becoming a promising pathway to improving the accuracy of sub-grid scale (SGS) turbulence closure models for large eddy simulations (LES). We leverage the concept of differentiable turbulence, whereby an…

Harnessing modern parallel computing resources to achieve complex multi-physics simulations is a daunting task. The Multiphysics Object Oriented Simulation Environment (MOOSE) aims to enable such development by providing simplified…

Differentiable rendering is a technique to connect 3D scenes with corresponding 2D images. Since it is differentiable, processes during image formation can be learned. Previous approaches to differentiable rendering focus on mesh-based…

Computer Vision and Pattern Recognition · Computer Science 2020-03-25 Cong Gao , Xingtong Liu , Wenhao Gu , Benjamin Killeen , Mehran Armand , Russell Taylor , Mathias Unberath

Medical image segmentation - the prerequisite of numerous clinical needs - has been significantly prospered by recent advances in convolutional neural networks (CNNs). However, it exhibits general limitations on modeling explicit long-range…

Computer Vision and Pattern Recognition · Computer Science 2021-07-13 Yundong Zhang , Huiye Liu , Qiang Hu

Decomposition of shapes into (approximate) convex parts is essential for applications such as part-based shape representation, shape matching, and collision detection. In this paper, we propose a novel convex decomposition using a…

Computer Vision and Pattern Recognition · Computer Science 2016-06-27 Fitsum Mesadi , Tolga Tasdizen

Recently, self-supervised pre-training has advanced Vision Transformers on various tasks w.r.t. different data modalities, e.g., image and 3D point cloud data. In this paper, we explore this learning paradigm for 3D mesh data analysis based…

Computer Vision and Pattern Recognition · Computer Science 2022-07-22 Yaqian Liang , Shanshan Zhao , Baosheng Yu , Jing Zhang , Fazhi He

Neural operator learning models have emerged as very effective surrogates in data-driven methods for partial differential equations (PDEs) across different applications from computational science and engineering. Such operator learning…

Machine Learning · Computer Science 2024-05-30 Benjamin Shih , Ahmad Peyvan , Zhongqiang Zhang , George Em Karniadakis

Across numerous applications, forecasting relies on numerical solvers for partial differential equations (PDEs). Although the use of deep-learning techniques has been proposed, actual applications have been restricted by the fact the…

Machine Learning · Computer Science 2020-01-28 Philipp Haehnel , Jakub Marecek , Julien Monteil , Fearghal O'Donncha

Neural networks have shown promising potential in accelerating the numerical simulation of systems governed by partial differential equations (PDEs). Different from many existing neural network surrogates operating on high-dimensional…

Machine Learning · Computer Science 2025-01-09 Zijie Li , Saurabh Patil , Francis Ogoke , Dule Shu , Wilson Zhen , Michael Schneier , John R. Buchanan, , Amir Barati Farimani

In this paper, inspired by the multigrid method, we propose a multi-level deep framework for deep solvers. Overall, it divides the entire training process into different levels of training. At each level of training, an adaptive sampling…

Numerical Analysis · Mathematics 2026-02-23 Yu Yang , Qiaolin He

Several different approaches are proposed for solving fully implicit discretizations of a simplified Boltzmann-Poisson system with a linear relaxation-type collision kernel. This system models the evolution of free electrons in…

Computational Physics · Physics 2020-07-15 M. Paul Laiu , Zheng Chen , Cory D. Hauck

The key idea of current deep learning methods for dense prediction is to apply a model on a regular patch centered on each pixel to make pixel-wise predictions. These methods are limited in the sense that the patches are determined by…

Computer Vision and Pattern Recognition · Computer Science 2017-06-09 Jun Li , Yongjun Chen , Lei Cai , Ian Davidson , Shuiwang Ji

Mechanistic knowledge about the physical world is virtually always expressed via partial differential equations (PDEs). Recently, there has been a surge of interest in probabilistic PDE solvers -- Bayesian statistical models mostly based on…

Machine Learning · Computer Science 2025-03-12 Tim Weiland , Marvin Pförtner , Philipp Hennig

We propose SymPlex, a reinforcement learning framework for discovering analytical symbolic solutions to partial differential equations (PDEs) without access to ground-truth expressions. SymPlex formulates symbolic PDE solving as…

Machine Learning · Computer Science 2026-02-04 Yesom Park , Annie C. Lu , Shao-Ching Huang , Qiyang Hu , Y. Sungtaek Ju , Stanley Osher

Constructing fast numerical solvers for partial differential equations (PDEs) is crucial for many scientific disciplines. A leading technique for solving large-scale PDEs is using multigrid methods. At the core of a multigrid solver is the…

Numerical Analysis · Mathematics 2019-08-07 Daniel Greenfeld , Meirav Galun , Ron Kimmel , Irad Yavneh , Ronen Basri

We introduce variational spectral learning (VSL), a machine learning framework for solving partial differential equations (PDEs) that operates directly in the coefficient space of spectral expansions. VSL offers a principled bridge between…

Numerical Analysis · Mathematics 2026-01-07 M. M. Hammad

Visual place recognition (VPR) aims to determine the general geographical location of a query image by retrieving visually similar images from a large geo-tagged database. To obtain a global representation for each place image, most…

Computer Vision and Pattern Recognition · Computer Science 2025-05-27 Tong Jin , Feng Lu , Shuyu Hu , Chun Yuan , Yunpeng Liu

Operator learning has emerged as a promising tool for accelerating the solution of partial differential equations (PDEs). The Deep Operator Networks (DeepONets) represent a pioneering framework in this area: the "vanilla" DeepONet is valued…

Machine Learning · Computer Science 2025-09-03 Zhi-Feng Wei , Wenqian Chen , Panos Stinis

Transformers have achieved great success across a wide range of applications, yet the theoretical foundations underlying their success remain largely unexplored. To demystify the strong capacities of transformers applied to versatile…

Machine Learning · Computer Science 2026-03-25 Chenyang Zhang , Qingyue Zhao , Quanquan Gu , Yuan Cao