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Deep Operator Network (DeepONet) is a neural network framework for learning nonlinear operators such as those from ordinary differential equations (ODEs) describing complex systems. Multiple-input deep neural operators (MIONet) extended…

Machine Learning · Computer Science 2023-11-30 Zhihao Kong , Amirhossein Mollaali , Christian Moya , Na Lu , Guang Lin

Seismic forward and inverse problems are significant research areas in geophysics. However, the time burden of traditional numerical methods hinders their applications in scenarios that require fast predictions. Machine learning-based…

Geophysics · Physics 2023-06-12 Yifan Mei , Yijie Zhang , Xueyu Zhu , Rongxi Gou

Neural network based data-driven operator learning schemes have shown tremendous potential in computational mechanics. DeepONet is one such neural network architecture which has gained widespread appreciation owing to its excellent…

Machine Learning · Statistics 2022-06-14 Shailesh Garg , Souvik Chakraborty

In this paper, we consider the design of model predictive control (MPC) algorithms based on deep operator neural networks (DeepONets). These neural networks are capable of accurately approximating real and complex valued solutions of…

Optimization and Control · Mathematics 2025-05-26 Thomas Oliver de Jong , Khemraj Shukla , Mircea Lazar

Deep neural networks (DNNs) recently emerged as a promising tool for analyzing and solving complex differential equations arising in science and engineering applications. Alternative to traditional numerical schemes, learning-based solvers…

Numerical Analysis · Mathematics 2023-08-09 Yuan Lan , Zhen Li , Jie Sun , Yang Xiang

Multi-task learning (MTL) is an inductive transfer mechanism designed to leverage useful information from multiple tasks to improve generalization performance compared to single-task learning. It has been extensively explored in traditional…

Machine Learning · Computer Science 2025-01-13 Varun Kumar , Somdatta Goswami , Katiana Kontolati , Michael D. Shields , George Em Karniadakis

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

In this paper, we present an initial attempt to learn evolution PDEs from data. Inspired by the latest development of neural network designs in deep learning, we propose a new feed-forward deep network, called PDE-Net, to fulfill two…

Numerical Analysis · Mathematics 2018-01-03 Zichao Long , Yiping Lu , Xianzhong Ma , Bin Dong

Physics-informed deep operator networks (DeepONets) have emerged as a promising approach toward numerically approximating the solution of partial differential equations (PDEs). In this work, we aim to develop further understanding of what…

Machine Learning · Computer Science 2024-11-28 Emily Williams , Amanda Howard , Brek Meuris , Panos Stinis

Focused ultrasound (FUS) therapy is a promising tool for optimally targeted treatment of spinal cord injuries (SCI), offering submillimeter precision to enhance blood flow at injury sites while minimizing impact on surrounding tissues.…

Medical Physics · Physics 2024-12-23 Avisha Kumar , Xuzhe Zhi , Zan Ahmad , Minglang Yin , Amir Manbachi

Operator learning provides methods to approximate mappings between infinite-dimensional function spaces. Deep operator networks (DeepONets) are a notable architecture in this field. Recently, an extension of DeepONet based on model…

Machine Learning · Computer Science 2024-03-28 Hamidreza Eivazi , Stefan Wittek , Andreas Rausch

Deep Operator Networks (DeepONets) are among the most prominent frameworks for operator learning, grounded in the universal approximation theorem for operators. However, training DeepONets typically requires significant computational…

Machine Learning · Computer Science 2025-01-17 Hwijae Son

Deep Operator Networks (DeepONets) have emerged as a powerful surrogate modeling framework for learning solution operators in PDE-governed systems. While their use is expanding across engineering disciplines, applications in geotechnical…

Machine Learning · Computer Science 2026-03-11 Yongjin Choi , Chenying Liu , Jorge Macedo

Neural networks have been applied to control problems, typically by combining data, differential equation residuals, and objective costs in the training loss or by incorporating auxiliary architectural components. Instead, we propose a…

Optimization and Control · Mathematics 2026-04-10 Oliver G. S. Lundqvist , Fabricio Oliveira

This paper proposes a new data-driven method for the reliable prediction of power system post-fault trajectories. The proposed method is based on the fundamentally new concept of Deep Operator Networks (DeepONets). Compared to traditional…

Numerical Analysis · Mathematics 2022-02-16 Christian Moya , Shiqi Zhang , Meng Yue , Guang Lin

Operator regression provides a powerful means of constructing discretization-invariant emulators for partial-differential equations (PDEs) describing physical systems. Neural operators specifically employ deep neural networks to approximate…

Machine Learning · Computer Science 2023-04-18 Katiana Kontolati , Somdatta Goswami , George Em Karniadakis , Michael D. Shields

Spectral methods are an important part of scientific computing's arsenal for solving partial differential equations (PDEs). However, their applicability and effectiveness depend crucially on the choice of basis functions used to expand the…

Numerical Analysis · Mathematics 2021-11-10 Brek Meuris , Saad Qadeer , Panos Stinis

Operator learning has the potential to strongly impact scientific computing by learning solution operators for differential equations, potentially accelerating multi-query tasks such as design optimization and uncertainty quantification by…

Machine Learning · Computer Science 2026-02-26 Alexander Heinlein , Johannes Taraz

Operator learning techniques have recently emerged as a powerful tool for learning maps between infinite-dimensional Banach spaces. Trained under appropriate constraints, they can also be effective in learning the solution operator of…

Machine Learning · Computer Science 2021-10-13 Sifan Wang , Hanwen Wang , Paris Perdikaris

Deep neural operators can learn nonlinear mappings between infinite-dimensional function spaces via deep neural networks. As promising surrogate solvers of partial differential equations (PDEs) for real-time prediction, deep neural…

Machine Learning · Computer Science 2023-05-17 Min Zhu , Handi Zhang , Anran Jiao , George Em Karniadakis , Lu Lu