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This paper introduces a data-driven operator learning method for multiscale partial differential equations, with a particular emphasis on preserving high-frequency information. Drawing inspiration from the representation of multiscale…

Machine Learning · Computer Science 2024-08-05 Bo Xu , Xinliang Liu , Lei Zhang

Solving partial differential equations (PDEs) efficiently and accurately remains a cornerstone challenge in science and engineering, especially for problems involving complex geometries and limited labeled data. We introduce a Physics- and…

Machine Learning · Computer Science 2025-08-14 Subhankar Sarkar , Souvik Chakraborty

Attention operators have been applied on both 1-D data like texts and higher-order data such as images and videos. Use of attention operators on high-order data requires flattening of the spatial or spatial-temporal dimensions into a…

Computer Vision and Pattern Recognition · Computer Science 2020-07-17 Hongyang Gao , Zhengyang Wang , Shuiwang Ji

Learning dynamics governed by differential equations is crucial for predicting and controlling the systems in science and engineering. Neural Ordinary Differential Equation (NODE), a deep learning model integrated with differential…

Machine Learning · Computer Science 2021-11-09 Shiqi Gong , Qi Meng , Yue Wang , Lijun Wu , Wei Chen , Zhi-Ming Ma , Tie-Yan Liu

Neural ordinary differential equations (NODEs) presented a new paradigm to construct (continuous-time) neural networks. While showing several good characteristics in terms of the number of parameters and the flexibility in constructing…

Machine Learning · Computer Science 2021-06-01 Sheo Yon Jhin , Minju Jo , Taeyong Kong , Jinsung Jeon , Noseong Park

Neural operators (NO) are discretization invariant deep learning methods with functional output and can approximate any continuous operator. NO have demonstrated the superiority of solving partial differential equations (PDEs) over other…

Numerical Analysis · Mathematics 2024-02-02 Jianguo Huang , Yue Qiu

Vision transformers have delivered tremendous success in representation learning. This is primarily due to effective token mixing through self attention. However, this scales quadratically with the number of pixels, which becomes infeasible…

Computer Vision and Pattern Recognition · Computer Science 2022-03-29 John Guibas , Morteza Mardani , Zongyi Li , Andrew Tao , Anima Anandkumar , Bryan Catanzaro

Neural Operators (NOs) are machine learning models designed to solve partial differential equations (PDEs) by learning to map between function spaces. Neural Operators such as the Deep Operator Network (DeepONet) and the Fourier Neural…

Machine Learning · Computer Science 2025-04-30 W. Diab , M. Al-Kobaisi

Accurately simulating systems governed by PDEs, such as voltage fields in cardiac electrophysiology (EP) modelling, remains a significant modelling challenge. Traditional numerical solvers are computationally expensive and sensitive to…

Machine Learning · Computer Science 2026-04-22 Hannah Lydon , Milad Kazemi , Martin Bishop , Nicola Paoletti

Deformable Attention Transformers (DAT) have shown remarkable performance in computer vision tasks by adaptively focusing on informative image regions. However, their data-dependent sampling mechanism introduces irregular memory access…

Computer Vision and Pattern Recognition · Computer Science 2025-07-29 Wendong Mao , Mingfan Zhao , Jianfeng Guan , Qiwei Dong , Zhongfeng Wang

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…

We present CARTO, a novel approach for reconstructing multiple articulated objects from a single stereo RGB observation. We use implicit object-centric representations and learn a single geometry and articulation decoder for multiple object…

Computer Vision and Pattern Recognition · Computer Science 2025-03-10 Nick Heppert , Muhammad Zubair Irshad , Sergey Zakharov , Katherine Liu , Rares Andrei Ambrus , Jeannette Bohg , Abhinav Valada , Thomas Kollar

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…

Machine Learning · Computer Science 2024-05-03 Zongyi Li , Daniel Zhengyu Huang , Burigede Liu , Anima Anandkumar

Fast and accurate surrogates for physics-driven partial differential equations (PDEs) are essential in fields such as aerodynamics, porous media design, and flow control. However, many transformer-based models and existing neural operators…

Machine Learning · Computer Science 2026-01-27 Prajwal Chauhan , Salah Eddine Choutri , Saif Eddin Jabari

Detection Transformers represent end-to-end object detection approaches based on a Transformer encoder-decoder architecture, exploiting the attention mechanism for global relation modeling. Although Detection Transformers deliver results on…

Computer Vision and Pattern Recognition · Computer Science 2023-06-30 Bastian Wittmann , Fernando Navarro , Suprosanna Shit , Bjoern Menze

Neural operators have emerged as powerful data-driven surrogates for learning solution operators of parametric partial differential equations (PDEs). However, widely used Fourier Neural Operators (FNOs) rely on global Fourier…

We propose derivative-informed neural operators (DINOs), a general family of neural networks to approximate operators as infinite-dimensional mappings from input function spaces to output function spaces or quantities of interest. After…

Numerical Analysis · Mathematics 2023-10-18 Thomas O'Leary-Roseberry , Peng Chen , Umberto Villa , Omar Ghattas

Dexterous manipulation requires precise geometric reasoning, yet existing visuo-tactile learning methods struggle with sub-millimeter precision tasks that are routine for traditional model-based approaches. We identify a key limitation:…

Robotics · Computer Science 2026-02-27 Jialei Huang , Yang Ye , Yuanqing Gong , Xuezhou Zhu , Yang Gao , Kaifeng Zhang

Deep learning offers a promising avenue for automating many recognition tasks in fields such as medicine and forensics. However, the black-box nature of these models hinders their adoption in high-stakes applications where trust and…

Computer Vision and Pattern Recognition · Computer Science 2025-09-10 Barkin Buyukcakir , Rocharles Cavalcante Fontenele , Reinhilde Jacobs , Jannick De Tobel , Patrick Thevissen , Dirk Vandermeulen , Peter Claes

Neural operators have shown great potential in solving a family of Partial Differential Equations (PDEs) by modeling the mappings between input and output functions. Fourier Neural Operator (FNO) implements global convolutions via…

Machine Learning · Computer Science 2025-11-25 Chenhong Zhou , Jie Chen , Zaifeng Yang