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The Physics-Informed Neural Network (PINN) framework introduced recently incorporates physics into deep learning, and offers a promising avenue for the solution of partial differential equations (PDEs) as well as identification of the…

Machine Learning · Computer Science 2021-08-04 Ehsan Haghighat , Ali Can Bekar , Erdogan Madenci , Ruben Juanes

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…

Many types of physics-informed neural network models have been proposed in recent years as approaches for learning solutions to differential equations. When a particular task requires solving a differential equation at multiple…

Machine Learning · Computer Science 2021-11-02 Filipe de Avila Belbute-Peres , Yi-fan Chen , Fei Sha

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

The operator learning has received significant attention in recent years, with the aim of learning a mapping between function spaces. Prior works have proposed deep neural networks (DNNs) for learning such a mapping, enabling the learning…

Machine Learning · Statistics 2024-02-15 Yusuke Tanaka , Takaharu Yaguchi , Tomoharu Iwata , Naonori Ueda

Modeling complex spatiotemporal dynamical systems, such as the reaction-diffusion processes, have largely relied on partial differential equations (PDEs). However, due to insufficient prior knowledge on some under-explored dynamical…

Machine Learning · Computer Science 2023-05-23 Chengping Rao , Pu Ren , Qi Wang , Oral Buyukozturk , Hao Sun , Yang Liu

There have been growing interests in leveraging experimental measurements to discover the underlying partial differential equations (PDEs) that govern complex physical phenomena. Although past research attempts have achieved great success…

Machine Learning · Computer Science 2023-05-23 Chengping Rao , Pu Ren , Yang Liu , Hao Sun

Deep Operator Networks (DeepONets) have recently emerged as powerful data-driven frameworks for learning nonlinear operators, particularly suited for approximating solutions to partial differential equations. Despite their promising…

Machine Learning · Computer Science 2026-04-21 Arth Sojitra , Mrigank Dhingra , Omer San

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

In this work, we explore the integration of Sequence Encoding for Online Parameter Identification with Physics-Informed Neural Networks to create a model that, once trained, can be utilized for real time applications with variable…

Machine Learning · Computer Science 2025-08-25 Mouad Elaarabi , Domenico Borzacchiello , Philippe Le Bot , Nathan Lauzeral , Sebastien Comas-Cardona

Parameter estimation remains a challenging task across many areas of engineering. Because data acquisition can often be costly, limited, or prone to inaccuracies (noise, uncertainty) it is crucial to identify sensor configurations that…

Machine Learning · Statistics 2025-11-20 Georgios Venianakis , Constantinos Theodoropoulos , Michail Kavousanakis

Deriving governing equations in Electromagnetic (EM) environment based on first principles can be quite tough when there are some unknown sources of noise and other uncertainties in the system. For nonlinear multiple-physics electromagnetic…

Computational Physics · Physics 2019-10-31 Bing Xiong , Haiyang Fu , Feng Xu , Yaqiu Jin

In recent years, data-driven methods have been developed to learn dynamical systems and partial differential equations (PDE). The goal of such work is discovering unknown physics and the corresponding equations. However, prior to achieving…

Machine Learning · Statistics 2021-02-17 Hao Xu , Haibin Chang , Dongxiao Zhang

Solving inverse problems governed by partial differential equations (PDEs) is central to science and engineering, yet remains challenging when measurements are sparse, noisy, or when the underlying coefficients are high-dimensional or…

Machine Learning · Computer Science 2025-11-06 Gang Bao , Yaohua Zang

We introduce \emph{Dynamical Physics-Modeled Neural Networks} (DynPMNNs), a continuous-time deep learning architecture in which each hidden layer is defined as the solution of an ordinary differential equation. Unlike classical feed-forward…

Machine Learning · Computer Science 2026-05-12 Raul Felipe-Sosa , Angel Martin del Rey , Maria Flores Ceballos

Current physics-informed (standard or deep operator) neural networks still rely on accurately learning the initial and/or boundary conditions of the system of differential equations they are solving. In contrast, standard numerical methods…

Machine Learning · Computer Science 2024-06-25 Rüdiger Brecht , Dmytro R. Popovych , Alex Bihlo , Roman O. Popovych

Neural operators have emerged as promising surrogate models for solving partial differential equations (PDEs), but struggle to generalise beyond training distributions and are often constrained to a fixed temporal discretisation. This work…

In scientific and engineering applications, solving partial differential equations (PDEs) across various parameters and domains normally relies on resource-intensive numerical methods. Neural operators based on deep learning offered a…

Numerical Analysis · Mathematics 2024-06-21 Zhiwei Zhao , Changqing Liu , Yingguang Li , Zhibin Chen , Xu Liu

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

Physics-informed neural networks (PINNs) have emerged as a promising deep learning method, capable of solving forward and inverse problems governed by differential equations. Despite their recent advance, it is widely acknowledged that…

Machine Learning · Computer Science 2024-06-11 Franz M. Rohrhofer , Stefan Posch , Clemens Gößnitzer , Bernhard C. Geiger