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The eikonal equation is utilized across a wide spectrum of science and engineering disciplines. In seismology, it regulates seismic wave traveltimes needed for applications like source localization, imaging, and inversion. Several numerical…

Computational Physics · Physics 2021-07-07 Umair bin Waheed , Ehsan Haghighat , Tariq Alkhalifah , Chao Song , Qi Hao

The high cost of acquiring a sufficient amount of seismic data for training has limited the use of machine learning in seismic tomography. In addition, the inversion uncertainty due to the noisy data and data scarcity is less discussed in…

Geophysics · Physics 2023-08-09 Rongxi Gou , Yijie Zhang , Xueyu Zhu , Jinghuai Gao

Seismic traveltime is critical information conveyed by seismic waves, widely utilized in various geophysical applications. Conventionally, the simulation of seismic traveltime involves solving the eikonal equation. However, the efficiency…

Geophysics · Physics 2024-04-09 Chao Song , Tianshuo Zhao , Umair bin Waheed , Cai Liu , Tian You

Seismic tomography has long been an effective tool for constructing reliable subsurface structures. However, simultaneous inversion of P- and S-wave velocities presents a significant challenge for conventional seismic tomography methods,…

Geophysics · Physics 2024-07-24 Chao Song , Hang Geng , Umair bin Waheed , Cai Liu

In this study, we propose a Bayesian seismic tomography inference method using physics-informed neural networks (PINN). PINN represents a recent advance in deep learning, offering the possibility to enhance physics-based simulations and…

Geophysics · Physics 2023-07-19 Ryoichiro Agata , Kazuya Shiraishi , Gou Fujie

Physics-Informed Neural Networks (PINN) are a machine learning tool that can be used to solve direct and inverse problems related to models described by Partial Differential Equations. This paper proposes an adaptive inverse PINN applied to…

Numerical Analysis · Mathematics 2024-11-28 Marco Berardi , Fabio Difonzo , Matteo Icardi

Accurate vessel trajectory prediction is crucial for navigational safety, route optimization, traffic management, search and rescue operations, and autonomous navigation. Traditional data-driven models lack real-world physical constraints,…

Machine Learning · Computer Science 2025-06-17 Md Mahbub Alam , Amilcar Soares , José F. Rodrigues-Jr , Gabriel Spadon

Physics-Informed Neural Networks (PINNs) have become a kind of attractive machine learning method for obtaining solutions of partial differential equations (PDEs). Training PINNs can be seen as a semi-supervised learning task, in which only…

Machine Learning · Computer Science 2022-10-25 Jia Guo , Haifeng Wang , Chenping Hou

We harness the physics-informed neural network (PINN) approach to extend the utility of phenomenological models for particle migration in shear flow. Specifically, we propose to constrain the neural network training via a model for the…

Fluid Dynamics · Physics 2023-04-28 Daihui Lu , Ivan C. Christov

Seismic wave forward and inverse modeling are fundamental tools for subsurface imaging and geological hazard assessment. Conventional grid-based numerical methods, such as finite-difference and finite-element approaches, often require dense…

Geophysics · Physics 2026-01-23 Chaohua Liang , Xingliang Peng , Jun Matsushima

The measurement of black hole spin is considered one of the key problems in relativistic astrophysics. Existing methods, such as continuum fitting, X-ray reflection spectroscopy and quasi-periodic oscillation analysis, have systematic…

High Energy Astrophysical Phenomena · Physics 2025-08-13 Stella Menziltsidou

Physics-informed neural networks (PINNs) have emerged as a promising mesh-free paradigm for solving partial differential equations, yet adoption in science and engineering is limited by slow training and modest accuracy relative to modern…

Computational Engineering, Finance, and Science · Computer Science 2026-02-24 Pao-Hsiung Chiu , Jian Cheng Wong , Chin Chun Ooi , Chang Wei , Yuchen Fan , Yew-Soon Ong

Physics-Informed Neural Networks (PINNs) have emerged as an influential technology, merging the swift and automated capabilities of machine learning with the precision and dependability of simulations grounded in theoretical physics. PINNs…

Physics-informed neural networks (PINNs) offer a powerful framework for seismic wavefield modeling, yet they typically require time-consuming retraining when applied to different velocity models. Moreover, their training can suffer from…

Geophysics · Physics 2025-06-03 Shijun Cheng , Tariq Alkhalifah

While the popularity of physics-informed neural networks (PINNs) is steadily rising, to this date PINNs have not been successful in simulating dynamical systems whose solution exhibits multi-scale, chaotic or turbulent behavior. In this…

Machine Learning · Computer Science 2022-03-16 Sifan Wang , Shyam Sankaran , Paris Perdikaris

Physics-informed neural networks (PINNs) have recently emerged as a promising alternative for extracting unknown quantities from experimental data. Despite this potential, much of the recent literature has relied on sparse, high-fidelity…

Fluid Dynamics · Physics 2026-01-09 Christian Toma , Bharathram Ganapathisubramani , Sean Symon

A physics-informed neural network (PINN) uses physics-augmented loss functions, e.g., incorporating the residual term from governing partial differential equations (PDEs), to ensure its output is consistent with fundamental physics laws.…

Machine Learning · Computer Science 2022-12-16 Jian Cheng Wong , Chinchun Ooi , Abhishek Gupta , Yew-Soon Ong

In this research, the application of the Physics-Informed Neural Network (PINN) model is explored to solve transport equation-based Partial Differential Equations (PDEs). The primary objective is to analyze the impact of different…

Machine Learning · Computer Science 2023-12-04 Akshansh Mishra

Physics-informed neural networks (PINNs) solve time-dependent partial differential equations (PDEs) by learning a mesh-free, differentiable solution that can be evaluated anywhere in space and time. However, standard space--time PINNs take…

Machine Learning · Computer Science 2026-01-29 Chen-Yang Dai , Che-Chia Chang , Te-Sheng Lin , Ming-Chih Lai , Chieh-Hsin Lai

Steady-state electrothermal systems involve strongly coupled heat transfer, fluid flow, and electric-potential transport, creating severe numerical challenges for standard physics-informed neural networks (PINNs) due to stark disparities in…

Computational Physics · Physics 2026-04-17 Yuqing Zhou , Ze Tao , Hanxuan Wang , Fujun Liu
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