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Studying physics-informed neural networks (PINNs) for modeling partial differential equations to solve the acoustic wave field has produced promising results for simple geometries in two-dimensional domains. One option is to compute the…

Computational Engineering, Finance, and Science · Computer Science 2025-06-16 Stefan Schoder , Aneta Furmanová , Viktor Hruška

In the study of subsurface seismic imaging, solving the acoustic wave equation is a pivotal component in existing models. The advancement of deep learning enables solving partial differential equations, including wave equations, by applying…

Machine Learning · Computer Science 2023-03-10 Bian Li , Hanchen Wang , Shihang Feng , Xiu Yang , Youzuo Lin

Accurate long-term forecasting of spatiotemporal dynamics remains a fundamental challenge across scientific and engineering domains. Existing machine learning methods often neglect governing physical laws and fail to quantify inherent…

Machine Learning · Computer Science 2025-10-27 Qingsong Xu , Jonathan L Bamber , Nils Thuerey , Niklas Boers , Paul Bates , Gustau Camps-Valls , Yilei Shi , Xiao Xiang Zhu

Solving partial differential equations (PDEs) is a required step in the simulation of natural and engineering systems. The associated computational costs significantly increase when exploring various scenarios, such as changes in initial or…

Big-data-based artificial intelligence (AI) supports profound evolution in almost all of science and technology. However, modeling and forecasting multi-physical systems remain a challenge due to unavoidable data scarcity and noise.…

Machine Learning · Computer Science 2022-02-08 Pengpeng Shi , Zhi Zeng , Tianshou Liang

A sound field estimation method based on a physics-informed convolutional neural network (PICNN) using spline interpolation is proposed. Most of the sound field estimation methods are based on wavefunction expansion, making the estimated…

Sound · Computer Science 2022-07-25 Kazuhide Shigemi , Shoichi Koyama , Tomohiko Nakamura , Hiroshi Saruwatari

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

Neural operators have been explored as surrogate models for simulating physical systems to overcome the limitations of traditional partial differential equation (PDE) solvers. However, most existing operator learning methods assume that the…

Machine Learning · Computer Science 2024-02-13 Rui Zhang , Qi Meng , Zhi-Ming Ma

Numerical simulations of seismic wave propagation in heterogeneous 3D media are central to investigating subsurface structures and understanding earthquake processes, yet are computationally expensive for large problems. This is…

Geophysics · Physics 2025-03-27 Caifeng Zou , Kamyar Azizzadenesheli , Zachary E. Ross , Robert W. Clayton

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

Solving Singularly Perturbed Differential Equations (SPDEs) poses computational challenges arising from the rapid transitions in their solutions within thin regions. The effectiveness of deep learning in addressing differential equations…

Machine Learning · Computer Science 2024-09-10 Ye Li , Ting Du , Yiwen Pang , Zhongyi Huang

Wavefield reconstruction inversion (WRI) formulates a PDE-constrained optimization problem to reduce cycle skipping in full-waveform inversion (FWI). WRI often requires expensive matrix inversions to reconstruct frequency-domain wavefields.…

Geophysics · Physics 2022-05-04 Chao Song , Tariq Alkhalifah

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

We investigate the use of Physics-Informed Neural Networks (PINNs) for solving the wave equation. Whilst PINNs have been successfully applied across many physical systems, the wave equation presents unique challenges due to the multi-scale,…

Computational Physics · Physics 2020-06-23 Ben Moseley , Andrew Markham , Tarje Nissen-Meyer

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

We propose a physics-informed neural network as the forward model for tomographic reconstructions of biological samples. We demonstrate that by training this network with the Helmholtz equation as a physical loss, we can predict the…

Optics · Physics 2022-07-29 Amirhossein Saba , Carlo Gigli , Ahmed B. Ayoub , Demetri Psaltis

Engineering design problems often involve solving parametric Partial Differential Equations (PDEs) under variable PDE parameters and domain geometry. Recently, neural operators have shown promise in learning PDE operators and quickly…

Machine Learning · Computer Science 2024-11-14 Weiheng Zhong , Hadi Meidani

As artificial intelligence emerges as a transformative enabler for fusion energy commercialization, fast and accurate solvers become increasingly critical. In magnetic confinement nuclear fusion, rapid and accurate solution of the…

Solving for the frequency-domain scattered wavefield via physics-informed neural network (PINN) has great potential in seismic modeling and inversion. However, when dealing with high-frequency wavefields, its accuracy and training cost…

Machine Learning · Computer Science 2022-06-22 Xinquan Huang , Tariq Alkhalifah

This paper proposes a plane wave activation based neural network (PWNN) for solving Helmholtz equation, the basic partial differential equation to represent wave propagation, e.g. acoustic wave, electromagnetic wave, and seismic wave.…

Numerical Analysis · Mathematics 2020-12-29 Ziming Wang , Tao Cui , Xueshuang Xiang