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Partial differential equations (PDEs) play a crucial role in studying a vast number of problems in science and engineering. Numerically solving nonlinear and/or high-dimensional PDEs is often a challenging task. Inspired by the traditional…

Numerical Analysis · Mathematics 2022-01-11 Yihao Hu , Tong Zhao , Shixin Xu , Zhiliang Xu , Lizhen Lin

Operator learning has emerged as a promising paradigm for developing efficient surrogate models to solve partial differential equations (PDEs). However, existing approaches often overlook the domain knowledge inherent in the underlying PDEs…

Machine Learning · Computer Science 2025-10-20 Ziqian Li , Kang Liu , Yongcun Song , Hangrui Yue , Enrique Zuazua

In computational physics, a longstanding challenge lies in finding numerical solutions to partial differential equations (PDEs). Recently, research attention has increasingly focused on Neural Operator methods, which are notable for their…

Machine Learning · Computer Science 2025-09-26 Yichen Song , Yalun Wu , Yunbo Wang , Xiaokang Yang

Reliable robotic grasping in unstructured environments is a crucial but challenging task. The main problem is to generate the optimal grasp of novel objects from partial noisy observations. This paper presents an end-to-end grasp detection…

Robotics · Computer Science 2021-03-26 Binglei Zhao , Hanbo Zhang , Xuguang Lan , Haoyu Wang , Zhiqiang Tian , Nanning Zheng

Developing accurate, data-efficient surrogate models is central to advancing AI for Science. Neural operators (NOs), which approximate mappings between infinite-dimensional function spaces using conventional neural architectures, have…

Machine Learning · Computer Science 2025-09-26 Dibyajyoti Nayak , Somdatta Goswami

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…

Machine Learning · Computer Science 2024-12-02 Zan Ahmad , Shiyi Chen , Minglang Yin , Avisha Kumar , Nicolas Charon , Natalia Trayanova , Mauro Maggioni

Graph neural networks (GNNs) are widely used for modelling graph-structured data in numerous applications. However, with their inherently finite aggregation layers, existing GNN models may not be able to effectively capture long-range…

Machine Learning · Computer Science 2022-02-23 Juncheng Liu , Kenji Kawaguchi , Bryan Hooi , Yiwei Wang , Xiaokui Xiao

We explore the use of graph neural networks (GNNs) to model spatial processes in which there is no a priori graphical structure. Similar to finite element analysis, we assign nodes of a GNN to spatial locations and use a computational…

Machine Learning · Computer Science 2019-11-19 Ferran Alet , Adarsh K. Jeewajee , Maria Bauza , Alberto Rodriguez , Tomas Lozano-Perez , Leslie Pack Kaelbling

Learning the mapping between two function spaces has garnered considerable research attention. However, learning the solution operator of partial differential equations (PDEs) remains a challenge in scientific computing. Fourier neural…

Machine Learning · Computer Science 2024-03-05 Jin Young Shin , Jae Yong Lee , Hyung Ju Hwang

Predicting the microstructural and morphological evolution of materials through phase-field modelling is computationally intensive, particularly for high-throughput parametric studies. While neural operators such as the Fourier neural…

Machine Learning · Computer Science 2026-03-11 Nanxi Chen , Airong Chen , Rujin Ma

Graph Neural Networks (GNNs) have become a central tool for learning on graph-structured data, yet their applicability to real-world systems remains limited by key challenges such as scalability, temporality, directionality, data…

Machine Learning · Computer Science 2025-10-28 Emanuele Rossi

Accurately simulating physics is crucial across scientific domains, with applications spanning from robotics to materials science. While traditional mesh-based simulations are precise, they are often computationally expensive and require…

Machine Learning · Computer Science 2025-10-23 Philipp Dahlinger , Tai Hoang , Denis Blessing , Niklas Freymuth , Gerhard Neumann

Accurate sensing of spatially distributed physical fields typically requires dense instrumentation, which is often infeasible in real-world systems due to cost, accessibility, and environmental constraints. Physics-based solvers address…

Machine Learning · Computer Science 2026-04-03 William Howes , Jason Yoo , Kazuma Kobayashi , Subhankar Sarkar , Farid Ahmed , Souvik Chakraborty , Syed Bahauddin Alam

Wave propagation problems are typically formulated as partial differential equations (PDEs) on unbounded domains to be solved. The classical approach to solving such problems involves truncating them to problems on bounded domains by…

Numerical Analysis · Mathematics 2024-04-11 Jihong Wang , Xin Wang , Jing Li , Bin Liu

The simulation of complex physical systems using a discretized mesh is a cornerstone of applied mechanics, but traditional numerical solvers are often computationally prohibitive for many-query tasks. While Graph Neural Networks (GNNs) have…

Machine Learning · Computer Science 2025-09-24 Kangzheng Liu , Leixin Ma

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

Physics-informed neural networks (PINNs) have been widely applied to solve partial differential equations (PDEs) by enforcing outputs and gradients of deep models to satisfy target equations. Due to the limitation of numerical computation,…

Machine Learning · Computer Science 2024-10-24 Haixu Wu , Huakun Luo , Yuezhou Ma , Jianmin Wang , Mingsheng Long

Neural operators learn mappings from function-dependent inputs to solutions, providing an effective framework for solving partial differential equations (PDEs). For time-dependent PDEs, existing methods typically perform long-horizon…

Machine Learning · Computer Science 2026-05-29 Jiaquan Zhang , Caiyan Qin , Haoyu Bian , Libin Cai , Yi Lu , Chaoning Zhang , Wei Dong , Yuanfang Guo , Yang Yang , Hen Tao Shen

Interfacial dynamics underlie a wide range of phenomena, including phase transitions, microstructure coarsening, pattern formation, and thin-film growth, and are typically described by stiff, time-dependent nonlinear partial differential…

Utilizing machine learning to address partial differential equations (PDEs) presents significant challenges due to the diversity of spatial domains and their corresponding state configurations, which complicates the task of encompassing all…

Machine Learning · Computer Science 2024-05-28 Masanobu Horie , Naoto Mitsume