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The precise simulation of turbulent flows is of immense importance in a variety of scientific and engineering fields, including climate science, freshwater science, and the development of energy-efficient manufacturing processes. Within the…

Fluid Dynamics · Physics 2024-06-10 Shengyu Chen , Peyman Givi , Can Zheng , Xiaowei Jia

Designing universal artificial intelligence (AI) solver for partial differential equations (PDEs) is an open-ended problem and a significant challenge in science and engineering. Currently, data-driven solvers have achieved great success,…

Machine Learning · Computer Science 2025-02-24 Qinglong Ma , Peizhi Zhao , Sen Wang , Tao Song

As a fundamental mathmatical tool in many engineering disciplines, coupled differential equation groups are being widely used to model complex structures containing multiple physical quantities. Engineers constantly adjust structural…

Machine Learning · Computer Science 2023-06-26 Wenhao Ding , Qing He , Hanghang Tong , Qingjing Wang , Ping Wang

As artificial intelligence emerges as a transformative enabler for fusion energy commercialization, fast and accurate solvers become increasingly critical. In magnetic confinement nuclear fusion, rapid and accurate solution of the…

The physics-informed neural operator (PINO) is a machine learning paradigm that has demonstrated promising results for learning solutions to partial differential equations (PDEs). It leverages the Fourier Neural Operator to learn solution…

This work proposes an autoencoder neural network as a non-linear generalization of projection-based methods for solving Partial Differential Equations (PDEs). The proposed deep learning architecture presented is capable of generating the…

Computational Physics · Physics 2020-06-25 Jaime Lopez Garcia , Angel Rivero Jimenez

Neural operators have emerged as a powerful tool for learning the mapping between infinite-dimensional parameter and solution spaces of partial differential equations (PDEs). In this work, we focus on multiscale PDEs that have important…

Machine Learning · Computer Science 2024-06-11 Xinliang Liu , Bo Xu , Shuhao Cao , Lei Zhang

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

We present a numerical framework for deep neural network (DNN) modeling of unknown time-dependent partial differential equations (PDE) using their trajectory data. Unlike the recent work of [Wu and Xiu, J. Comput. Phys. 2020], where the…

Machine Learning · Computer Science 2021-11-24 Zhen Chen , Victor Churchill , Kailiang Wu , Dongbin Xiu

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

Artificial intelligence (AI) shows great potential to reduce the huge cost of solving partial differential equations (PDEs). However, it is not fully realized in practice as neural networks are defined and trained on fixed domains and…

Machine Learning · Computer Science 2025-04-16 Hongyu Li , Ximeng Ye , Peng Jiang , Guoliang Qin , Tiejun Wang

Partial differential equations (PDEs) govern a wide variety of dynamical processes in science and engineering, yet obtaining their numerical solutions often requires high-resolution discretizations and repeated evaluations of complex…

Machine Learning · Computer Science 2026-01-26 Valentin Duruisseaux , Jean Kossaifi , Anima Anandkumar

Accurate prediction of machining deformation in structural components is essential for ensuring dimensional precision and reliability. Such deformation often originates from residual stress fields, whose distribution and influence vary…

Machine Learning · Computer Science 2025-09-17 Changqing Liu , Kaining Dai , Zhiwei Zhao , Tianyi Wu , Yingguang Li

We present approximation theories and efficient training methods for derivative-informed Fourier neural operators (DIFNOs) with applications to PDE-constrained optimization. A DIFNO is an FNO trained by minimizing its prediction error…

Machine Learning · Computer Science 2026-03-17 Boyuan Yao , Dingcheng Luo , Lianghao Cao , Nikola Kovachki , Thomas O'Leary-Roseberry , Omar Ghattas

Purpose: Depth estimation in robotic surgery is vital in 3D reconstruction, surgical navigation and augmented reality visualization. Although the foundation model exhibits outstanding performance in many vision tasks, including depth…

Computer Vision and Pattern Recognition · Computer Science 2024-01-15 Beilei Cui , Mobarakol Islam , Long Bai , Hongliang Ren

Neural operator learning directly constructs the mapping relationship from the equation parameter space to the solution space, enabling efficient direct inference in practical applications without the need for repeated solution of partial…

Machine Learning · Computer Science 2026-04-28 Heng Wu , Junjie Wang , Benzhuo Lu

Artificial neural network (ANN) is a versatile tool to study the neural representation in the ventral visual stream, and the knowledge in neuroscience in return inspires ANN models to improve performance in the task. However, it is still…

Machine Learning · Computer Science 2022-06-13 Xuming Ran , Jie Zhang , Ziyuan Ye , Haiyan Wu , Qi Xu , Huihui Zhou , Quanying Liu

Object-centric understanding is fundamental to human vision and required for complex reasoning. Traditional methods define slot-based bottlenecks to learn object properties explicitly, while recent self-supervised vision models like DINO…

Computer Vision and Pattern Recognition · Computer Science 2025-10-03 Stefan Sylvius Wagner , Stefan Harmeling

The order/dimension of models derived on the basis of data is commonly restricted by the number of observations, or in the context of monitored systems, sensing nodes. This is particularly true for structural systems (e.g., civil or…

Machine Learning · Computer Science 2022-12-01 Zhilu Lai , Wei Liu , Xudong Jian , Kiran Bacsa , Limin Sun , Eleni Chatzi

Simulation and optimization are crucial for advancing the engineering design of complex systems and processes. Traditional optimization methods require substantial computational time and effort due to their reliance on resource-intensive…

Machine Learning · Computer Science 2025-08-28 Janak M. Patel , Milad Ramezankhani , Anirudh Deodhar , Dagnachew Birru