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Predicting the microstructural and morphological evolution of materials through phase-field modelling is computationally intensive, particularly for high-throughput parametric studies. While neural operators such as the Fourier neural…

Machine Learning · Computer Science 2026-03-11 Nanxi Chen , Airong Chen , Rujin Ma

In the present work, a machine learning based constitutive model for electro-mechanically coupled material behavior at finite deformations is proposed. Using different sets of invariants as inputs, an internal energy density is formulated…

Computational Engineering, Finance, and Science · Computer Science 2022-08-30 Dominik K. Klein , Rogelio Ortigosa , Jesús Martínez-Frutos , Oliver Weeger

Engineering problems frequently require solution of governing equations with spatially-varying discontinuous coefficients. Even for linear elliptic problems, mapping large ensembles of coefficient fields to solutions can become a major…

Machine Learning · Computer Science 2024-11-12 Conlain Kelly , Surya R. Kalidindi

An innovative physics-guided learning algorithm for predicting the mechanical response of materials and structures is proposed in this paper. The key concept of the proposed study is based on the fact that physics models are governed by…

Computational Engineering, Finance, and Science · Computer Science 2020-04-22 Houpu Yao , Yi Gao , Yongming Liu

Neural operators extend data-driven models to map between infinite-dimensional functional spaces. These models have successfully solved continuous dynamical systems represented by differential equations, viz weather forecasting, fluid flow,…

Machine Learning · Computer Science 2023-10-13 Karn Tiwari , N M Anoop Krishnan , Prathosh A P

Modelling complex multiphysics systems governed by nonlinear and strongly coupled partial differential equations (PDEs) is a cornerstone in computational science and engineering. However, it remains a formidable challenge for traditional…

Machine Learning · Computer Science 2025-02-28 Biao Yuan , He Wang , Yanjie Song , Ana Heitor , Xiaohui Chen

Neural Operators (NOs) are a leading method for surrogate modeling of partial differential equations. Unlike traditional neural networks, which approximate individual functions, NOs learn the mappings between function spaces. While NOs have…

Astrophysics of Galaxies · Physics 2025-08-01 Keith Poletti , Stella S. R. Offner , Rachel A. Ward

This work presents a finite element-guided physics-informed operator learning framework for multiphysics problems with coupled partial differential equations (PDEs) on arbitrary domains. The proposed framework learns an operator from the…

Machine Learning · Computer Science 2026-04-22 Yusuke Yamazaki , Reza Najian Asl , Markus Apel , Mayu Muramatsu , Shahed Rezaei

Vision transformers have delivered tremendous success in representation learning. This is primarily due to effective token mixing through self attention. However, this scales quadratically with the number of pixels, which becomes infeasible…

Computer Vision and Pattern Recognition · Computer Science 2022-03-29 John Guibas , Morteza Mardani , Zongyi Li , Andrew Tao , Anima Anandkumar , Bryan Catanzaro

Neural operators extend data-driven models to map between infinite-dimensional functional spaces. While these operators perform effectively in either the time or frequency domain, their performance may be limited when applied to…

Machine Learning · Computer Science 2024-06-06 Karn Tiwari , N M Anoop Krishnan , A P Prathosh

We applied physics-informed neural networks to solve the constitutive relations for nonlinear, path-dependent material behavior. As a result, the trained network not only satisfies all thermodynamic constraints but also instantly provides…

Computational Engineering, Finance, and Science · Computer Science 2023-09-07 Shahed Rezaei , Ahmad Moeineddin , Ali Harandi

Constitutive modelling is crucial for engineering design and simulations to accurately describe material behavior. However, traditional phenomenological models often struggle to capture the complexities of real materials under varying…

Computational Engineering, Finance, and Science · Computer Science 2024-12-13 Tushar , Sawan Kumar , Souvik Chakraborty

Fourier neural operators (FNOs) are a recently introduced neural network architecture for learning solution operators of partial differential equations (PDEs), which have been shown to perform significantly better than comparable deep…

Inverse microstructure design plays a central role in materials discovery, yet remains challenging due to the complexity of structure-property linkages and the scarcity of labeled training data. We propose Design-GenNO, a physics-informed…

Mathematical Physics · Physics 2025-09-11 Yaohua Zang , Phaedon-Stelios Koutsourelakis

Neural operators, which aim to approximate mappings between infinite-dimensional function spaces, have been widely applied in the simulation and prediction of physical systems. However, the limited representational capacity of network…

Machine Learning · Computer Science 2025-06-03 Jin Song , Kenji Kawaguchi , Zhenya Yan

This short note proposes a model-driven conditional Fourier neural operator (MD-CFNO) for synthetic turbulence generation. Spectrum-consistent synthetic turbulence is essential for inflow boundary construction in computational fluid…

Fluid Dynamics · Physics 2026-01-22 Hongyuan Lin , Shizhao Wang

In this work we present a hybrid physics-based and data-driven learning approach to construct surrogate models for concurrent multiscale simulations of complex material behavior. We start from robust but inflexible physics-based…

Numerical Analysis · Mathematics 2023-02-01 I. B. C. M. Rocha , P. Kerfriden , F. P. van der Meer

Long-term predictions of nonlinear dynamics of three-dimensional (3D) turbulence are very challenging for machine learning approaches. In this paper, we propose an implicit U-Net enhanced Fourier neural operator (IU-FNO) for stable and…

Fluid Dynamics · Physics 2023-08-02 Zhijie Li , Wenhui Peng , Zelong Yuan , Jianchun Wang

To obtain fast solutions for governing physical equations in solid mechanics, we introduce a method that integrates the core ideas of the finite element method with physics-informed neural networks and concept of neural operators. This…

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