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Neural operators have emerged as powerful surrogates for dynamical systems due to their grid-invariant properties and computational efficiency. However, the Fourier-based neural operator framework inherently truncates high-frequency…

Machine Learning · Computer Science 2026-04-09 Tianyue Yang , Xiao Xue

The predictive accuracy of operator learning frameworks depends on the quality and quantity of available training data (input-output function pairs), often requiring substantial amounts of high-fidelity data, which can be challenging to…

Machine Learning · Computer Science 2025-10-29 Sumanta Roy , Bahador Bahmani , Ioannis G. Kevrekidis , Michael D. Shields

Physics-informed neural networks (PINNs) are a class of deep learning models that utilize physics in the form of differential equations to address complex problems, including those with limited data availability. However, solving…

Machine Learning · Computer Science 2026-03-26 Himanshu Pandey , Anshima Singh , Ratikanta Behera

Unsupervised learning with functional data is an emerging paradigm of machine learning research with applications to computer vision, climate modeling and physical systems. A natural way of modeling functional data is by learning operators…

Machine Learning · Computer Science 2023-02-22 Jacob H. Seidman , Georgios Kissas , George J. Pappas , Paris Perdikaris

The purpose of the current work is the development of a so-called physics-encoded Fourier neural operator (PeFNO) for surrogate modeling of the quasi-static equilibrium stress field in solids. Rather than accounting for constraints from…

Computational Engineering, Finance, and Science · Computer Science 2025-02-06 Mohammad S. Khorrami , Pawan Goyal , Jaber R. Mianroodi , Bob Svendsen , Peter Benner , Dierk Raabe

The physics-informed neural operator (PINO) is a machine learning paradigm that has demonstrated promising results for learning solutions to partial differential equations (PDEs). It leverages the Fourier Neural Operator to learn solution…

We introduce MENO (''Matrix Exponential-based Neural Operator''), a hybrid surrogate modeling framework for efficiently solving stiff systems of ordinary differential equations (ODEs) that exhibit a sparse nonlinear structure. In such…

Computational Physics · Physics 2025-07-22 Ivan Zanardi , Simone Venturi , Marco Panesi

Fourier neural operators (FNOs) can learn highly nonlinear mappings between function spaces, and have recently become a popular tool for learning responses of complex physical systems. However, to achieve good accuracy and efficiency, FNOs…

Machine Learning · Computer Science 2023-10-31 Ning Liu , Siavash Jafarzadeh , Yue Yu

We propose a Pretrained Finite Element Method (PFEM),a physics driven framework that bridges the efficiency of neural operator learning with the accuracy and robustness of classical finite element methods (FEM). PFEM consists of a physics…

Neural operators have emerged as powerful tools for learning solution operators of partial differential equations (PDEs). However, standard spectral methods based on Fourier transforms struggle with problems involving discontinuous…

Computational Physics · Physics 2026-05-20 Giorgio M. Cavallazzi , Miguel Pérez Cuadrado , Alfredo Pinelli

Flexible intelligent metasurfaces (FIMs) offer a new solution for wireless communications by introducing morphological degrees of freedom, dynamically morphing their three-dimensional shape to ensure multipath signals interfere…

Information Theory · Computer Science 2026-04-08 Jian Xiao , Ji Wang , Qimei Cui , Yucang Yang , Xingwang Li , Dusit Niyato , Chau Yuen

Graph neural networks (GNNs) naturally align with sparse operators and unstructured discretizations, making them a promising paradigm for physics-informed machine learning in computational mechanics. Motivated by discrete physics losses and…

Machine Learning · Computer Science 2026-02-10 Jianchuan Yang , Xi Chen , Jidong Zhao

We propose derivative-informed neural operators (DINOs), a general family of neural networks to approximate operators as infinite-dimensional mappings from input function spaces to output function spaces or quantities of interest. After…

Numerical Analysis · Mathematics 2023-10-18 Thomas O'Leary-Roseberry , Peng Chen , Umberto Villa , Omar Ghattas

Physics-informed neural networks (PINNs) and neural operators (NOs) for solving the problem of diffraction of Extreme Ultraviolet (EUV) electromagnetic waves from contemporary lithography masks are presented. A novel hybrid Waveguide Neural…

Machine Learning · Computer Science 2026-03-18 Vasiliy A. Es'kin , Egor V. Ivanov

With massive advancements in sensor technologies and Internet-of-things, we now have access to terabytes of historical data; however, there is a lack of clarity in how to best exploit the data to predict future events. One possible…

Computational Physics · Physics 2022-05-05 Tapas Tripura , Souvik Chakraborty

Accurately simulating systems governed by PDEs, such as voltage fields in cardiac electrophysiology (EP) modelling, remains a significant modelling challenge. Traditional numerical solvers are computationally expensive and sensitive to…

Machine Learning · Computer Science 2026-04-22 Hannah Lydon , Milad Kazemi , Martin Bishop , Nicola Paoletti

Numerical simulations are essential tools to evaluate the solution of the wave equation in complex settings, such as three-dimensional (3D) domains with heterogeneous properties. However, their application is limited by high computational…

Machine Learning · Computer Science 2025-04-09 Fanny Lehmann , Filippo Gatti , Didier Clouteau

Accurate characterization of temperature-dependent thermoelectric properties (TEPs), such as thermal conductivity and the Seebeck coefficient, is essential for reliable modeling and efficient design of thermoelectric devices. However, their…

Materials Science · Physics 2025-06-11 Hyeonbin Moon , Songho Lee , Wabi Demeke , Byungki Ryu , Seunghwa Ryu

Solving the wave equation is fundamental for geophysical applications. However, numerical solutions of the Helmholtz equation face significant computational and memory challenges. Therefore, we introduce a physics-informed convolutional…

Geophysics · Physics 2025-07-23 Xiao Ma , Tariq Alkhalifah

Deep operator network (DeepONet) has shown significant promise as surrogate models for systems governed by partial differential equations (PDEs), enabling accurate mappings between infinite-dimensional function spaces. However, when applied…

Machine Learning · Computer Science 2025-10-29 Sharmila Karumuri , Lori Graham-Brady , Somdatta Goswami