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Physics-informed Neural Networks (PINNs) have been shown as a promising approach for solving both forward and inverse problems of partial differential equations (PDEs). Meanwhile, the neural operator approach, including methods such as Deep…

Machine Learning · Computer Science 2023-10-31 Bin Lin , Zhiping Mao , Zhicheng Wang , George Em Karniadakis

Shape optimization is essential in aerospace vehicle design, including reentry systems, and propulsion system components, as it directly influences aerodynamic efficiency, structural integrity, and overall mission success. Rapid and…

Machine Learning · Computer Science 2025-05-27 Ahmad Peyvan , Varun Kumar , George Em Karniadakis

Coupled multiphysics simulations for high-dimensional, large-scale problems can be prohibitively expensive due to their computational demands. This article presents a novel framework integrating a deep operator network (DeepONet) with the…

Computational Engineering, Finance, and Science · Computer Science 2025-09-03 Fouad M. Amin , Diab W. Abueidda , Panos Pantidis , Mostafa E. Mobasher

Burn injuries present a significant global health challenge. Among the most severe long-term consequences are contractures, which can lead to functional impairments and disfigurement. Understanding and predicting the evolution of post-burn…

Numerical Analysis · Mathematics 2024-11-25 Selma Husanovic , Ginger Egberts , Alexander Heinlein , Fred Vermolen

This focused review explores a range of neural operator architectures for approximating solutions to parametric partial differential equations (PDEs), emphasizing high-level concepts and practical implementation strategies. The study covers…

Computational Engineering, Finance, and Science · Computer Science 2025-03-10 Prashant K. Jha

Compressive sensing (CS) has been widely applied in signal and image processing fields. Traditional CS reconstruction algorithms have a complete theoretical foundation but suffer from the high computational complexity, while fashionable…

Signal Processing · Electrical Eng. & Systems 2025-05-06 Xiumei Li , Zhijie Zhang , Huang Bai , Ljubiša Stanković , Junpeng Hao , Junmei Sun

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…

Neural operators have shown great potential in surrogate modeling. However, training a well-performing neural operator typically requires a substantial amount of data, which can pose a major challenge in complex applications. In such…

Machine Learning · Computer Science 2026-02-05 Keyan Chen , Yile Li , Da Long , Zhitong Xu , Wei Xing , Jacob Hochhalter , Shandian Zhe

With the development of digital twins and smart manufacturing systems, there is an urgent need for real-time distortion field prediction to control defects in metal Additive Manufacturing (AM). However, numerical simulation methods suffer…

Machine Learning · Computer Science 2025-11-18 Mingxuan Tian , Haochen Mu , Donghong Ding , Mengjiao Li , Yuhan Ding , Jianping Zhao

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…

The Deep Operator Networks~(DeepONet) is a fundamentally different class of neural networks that we train to approximate nonlinear operators, including the solution operator of parametric partial differential equations (PDE). DeepONets have…

Numerical Analysis · Mathematics 2021-11-05 Guang Lin , Christian Moya , Zecheng Zhang

Many real-life applications involve controlling high-dimensional multi-agent systems in real-time. Existing optimal control solvers often suffer from the curse-of-dimensionality and require complete rerunning for each new problem setting.…

Optimization and Control · Mathematics 2026-05-15 Alan John Varghese , Shanqing Liu , Paula Chen , Yaochen Zhu , Jérôme Darbon , George Em Karniadakis

Simulating fluid flows in different virtual scenarios is of key importance in engineering applications. However, high-fidelity, full-order models relying, e.g., on the finite element method, are unaffordable whenever fluid flows must be…

Fluid Dynamics · Physics 2021-11-24 Stefania Fresca , Andrea Manzoni

Physics-informed neural operators have emerged as a powerful paradigm for solving parametric partial differential equations (PDEs), particularly in the aerospace field, enabling the learning of solution operators that generalize across…

Machine Learning · Computer Science 2025-06-24 Jing Wang , Biao Chen , Hairun Xie , Rui Wang , Yifan Xia , Jifa Zhang , Hui Xu

We propose PO-CKAN, a physics-informed deep operator framework based on Chunkwise Rational Kolmogorov--Arnold Networks (KANs), for approximating the solution operators of partial differential equations. This framework leverages a Deep…

Machine Learning · Computer Science 2025-11-04 Junyi Wu , Guang Lin

In recent years, large-scale numerical simulations played an essential role in estimating the effects of explosion events in urban environments, for the purpose of ensuring the security and safety of cities. Such simulations are…

Deep Operator Networks are emerging as fundamental tools among various neural network types to learn mappings between function spaces, and have recently gained attention due to their ability to approximate nonlinear operators. In…

Machine Learning · Computer Science 2026-01-15 Beatrice Ceccanti , Mattia Galanti , Ivo Roghair , Martin van Sint Annaland

AI for science (AI4Science) models often suffer from discretization: learned representations remain tied to the training grid, limiting transfer across resolutions, solvers and applications. We introduce Neural Proper Orthogonal…

Computational Physics · Physics 2026-03-03 Changhong Mou , Binghang Lu , Guang Lin

The solution of partial differential equations (PDEs) plays a central role in numerous applications in science and engineering, particularly those involving multiphase flow in porous media. Complex, nonlinear systems govern these problems…

Modeling plays a critical role in additive manufacturing (AM), enabling a deeper understanding of underlying processes. Parametric solutions for such models are of great importance, enabling the optimization of production processes and…

Computational Engineering, Finance, and Science · Computer Science 2025-02-05 Hesameddin Safari , Henning Wessels