English
Related papers

Related papers: Operator Learning for Consolidation: An Architectu…

200 papers

We present a novel training method for deep operator networks (DeepONets), one of the most popular neural network models for operators. DeepONets are constructed by two sub-networks, namely the branch and trunk networks. Typically, the two…

Numerical Analysis · Mathematics 2023-09-06 Sanghyun Lee , Yeonjong Shin

Parametric PDEs power modern simulation, design, and digital-twin systems, yet their many-query workloads still hinge on repeatedly solving large finite-element systems. Existing operator-learning approaches accelerate this process but…

Machine Learning · Computer Science 2025-11-25 Yueqi Wang , Guang Lin

Most neural-operator surrogates for PDEs inherit from DeepONet-style formulations the requirement that the input function be sampled at a fixed, ordered set of sensors. This assumption limits applicability to problems with variable sensor…

Machine Learning · Computer Science 2026-04-02 Stepan Tretiakov , Xingjian Li , Krishna Kumar

The deep operator network (DeepONet) is a popular neural operator architecture that has shown promise in solving partial differential equations (PDEs) by using deep neural networks to map between infinite-dimensional function spaces. In the…

Machine Learning · Computer Science 2025-02-25 Luis Mandl , Somdatta Goswami , Lena Lambers , Tim Ricken

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

FNO and DeepONet are by far the most popular neural operator learning algorithms. FNO seems to enjoy an edge in popularity due to its ease of use, especially with high dimensional data. However, a lesser-acknowledged feature of DeepONet is…

Computational Physics · Physics 2024-01-02 Waleed Diab , Mohammed Al-Kobaisi

Phase-field modeling reformulates fracture problems as energy minimization problems and enables a comprehensive characterization of the fracture process, including crack nucleation, propagation, merging, and branching, without relying on…

Computational Physics · Physics 2025-04-15 Elham Kiyani , Manav Manav , Nikhil Kadivar , Laura De Lorenzis , George Em Karniadakis

The deep operator networks (DeepONet), a class of neural operators that learn mappings between function spaces, have recently been developed as surrogate models for parametric partial differential equations (PDEs). In this work we propose a…

Machine Learning · Computer Science 2024-10-31 Yuan Qiu , Nolan Bridges , Peng Chen

Deep operator networks (DeepONets) have demonstrated their capability of approximating nonlinear operators for initial- and boundary-value problems. One attractive feature of DeepONets is their versatility since they do not rely on prior…

Numerical Analysis · Mathematics 2023-07-27 Ziad Aldirany , Régis Cottereau , Marc Laforest , Serge Prudhomme

Traditional 2D hydraulic models face significant computational challenges that limit their applications that are time-sensitive or require many model evaluations. This study presents a physics-informed Deep Operator Network (DeepONet)…

Fluid Dynamics · Physics 2026-01-14 Xiaofeng Liu , Yong G. Lai

In this work, we introduce a novel neural operator, the Solute Transport Operator Network (STONet), to efficiently model contaminant transport in micro-cracked porous media. STONet's model architecture is specifically designed for this…

Machine Learning · Computer Science 2025-07-02 Ehsan Haghighat , Mohammad Hesan Adeli , S Mohammad Mousavi , Ruben Juanes

This work introduces a neural operator based surrogate modeling framework for neutron transport computation. Two architectures, the Deep Operator Network (DeepONet) and the Fourier Neural Operator (FNO), were trained for fixed source…

Computational Physics · Physics 2026-02-19 Md Hossain Sahadath , Qiyun Cheng , Shaowu Pan , Wei Ji

Standard neural networks can approximate general nonlinear operators, represented either explicitly by a combination of mathematical operators, e.g., in an advection-diffusion-reaction partial differential equation, or simply as a black…

Machine Learning · Computer Science 2022-07-19 Somdatta Goswami , Aniruddha Bora , Yue Yu , George Em Karniadakis

While it is widely known that neural networks are universal approximators of continuous functions, a less known and perhaps more powerful result is that a neural network with a single hidden layer can approximate accurately any nonlinear…

Machine Learning · Computer Science 2021-11-03 Lu Lu , Pengzhan Jin , George Em Karniadakis

We propose a novel fine-tuning method to achieve multi-operator learning through training a distributed neural operator with diverse function data and then zero-shot fine-tuning the neural network using physics-informed losses for…

Machine Learning · Computer Science 2024-11-12 Zecheng Zhang , Christian Moya , Lu Lu , Guang Lin , Hayden Schaeffer

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

Maxwell's equations, a system of linear partial differential equations (PDEs), describe the behavior of electric and magnetic fields in time and space and are essential for many important electromagnetic applications. Although numerical…

Computational Physics · Physics 2026-01-19 Qile Jiang , Marc Salvadori , Dale Ota , Vijaya Shankar , Khemraj Shukla

Deep Operator Networks (DeepOnets) have revolutionized the domain of scientific machine learning for the solution of the inverse problem for dynamical systems. However, their implementation necessitates optimizing a high-dimensional space…

Machine Learning · Computer Science 2024-11-05 Gianluca Fabiani , Ioannis G. Kevrekidis , Constantinos Siettos , Athanasios N. Yannacopoulos

This paper designs an Operator Learning framework to approximate the dynamic response of synchronous generators. One can use such a framework to (i) design a neural-based generator model that can interact with a numerical simulator of the…

Machine Learning · Computer Science 2023-01-31 Christian Moya , Guang Lin , Tianqiao Zhao , Meng Yue

This work demonstrates that neural operator learning provides a powerful and flexible framework for building fast, accurate emulators of moving boundary systems, enabling their integration into digital twin platforms. To this end, a Deep…

Machine Learning · Computer Science 2025-12-24 Marco A. Iglesias , Michael. E. Causon , Mikhail Y. Matveev , Andreas Endruweit , Michael . V. Tretyakov