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Physics-Informed Neural Networks (PINNs) serve as a flexible alternative for tackling forward and inverse problems in differential equations, displaying impressive advancements in diverse areas of applied mathematics. Despite integrating…

流体动力学 · 物理学 2024-07-12 Shengfeng Xu , Chang Yan , Zhenxu Sun , Renfang Huang , Dilong Guo , Guowei Yang

Physics-Informed Neural Networks (PINN) are neural networks (NNs) that encode model equations, like Partial Differential Equations (PDE), as a component of the neural network itself. PINNs are nowadays used to solve PDEs, fractional…

Physics-informed neural networks (PINNs) are a new tool for solving boundary value problems by defining loss functions of neural networks based on governing equations, boundary conditions, and initial conditions. Recent investigations have…

计算工程、金融与科学 · 计算机科学 2023-11-14 Ali Harandi , Ahmad Moeineddin , Michael Kaliske , Stefanie Reese , Shahed Rezaei

Direct observations of earthquake nucleation and propagation are few and yet the next decade will likely see an unprecedented increase in indirect, surface observations that must be integrated into modeling efforts. Machine learning (ML)…

数学物理 · 物理学 2024-07-25 Cody Rucker , Brittany A. Erickson

Physics-informed neural networks (PINNs) are revolutionizing science and engineering practice by bringing together the power of deep learning to bear on scientific computation. In forward modeling problems, PINNs are meshless partial…

机器学习 · 计算机科学 2023-11-28 Yicheng Wang , Xiaotian Han , Chia-Yuan Chang , Daochen Zha , Ulisses Braga-Neto , Xia Hu

The utilization of Deep Neural Networks (DNNs) in physical science and engineering applications has gained traction due to their capacity to learn intricate functions. While large datasets are crucial for training DNN models in fields like…

机器学习 · 计算机科学 2025-08-05 Vamsi Sai Krishna Malineni , Suresh Rajendran

We apply Physics-Informed Neural Networks (PINNs) for solving identification problems of nonhomogeneous materials. We focus on the problem with a background in elasticity imaging, where one seeks to identify the nonhomogeneous mechanical…

机器学习 · 计算机科学 2020-09-11 Enrui Zhang , Minglang Yin , George Em Karniadakis

Although physics-informed neural networks(PINNs) have progressed a lot in many real applications recently, there remains problems to be further studied, such as achieving more accurate results, taking less training time, and quantifying the…

机器学习 · 计算机科学 2022-12-01 Bin Shan , Ye Li , Shengjun Huang

Surrogate modeling is used to replace computationally expensive simulations. Neural networks have been widely applied as surrogate models that enable efficient evaluations over complex physical systems. Despite this, neural networks are…

机器学习 · 计算机科学 2024-02-13 Hao Chen , Gonzalo E. Constante Flores , Can Li

Physics-Informed Neural Networks have shown unique utility in parameterising the solution of a well-defined partial differential equation using automatic differentiation and residual losses. Though they provide theoretical guarantees of…

机器学习 · 计算机科学 2022-05-17 Vignesh Gopakumar , Stanislas Pamela , Debasmita Samaddar

Physics-informed neural networks (PINNs) is an emerging category of neural networks which can be trained to solve supervised learning tasks while taking into consideration given laws of physics described by general nonlinear partial…

密码学与安全 · 计算机科学 2026-04-07 Solon Falas , Charalambos Konstantinou , Maria K. Michael

Physics-informed neural networks (PINNs) have emerged as a promising numerical method based on deep learning for modeling boundary value problems, showcasing promising results in various fields. In this work, we use PINNs to discretize…

计算物理 · 物理学 2024-06-10 Michel Nohra , Steven Dufour

Physics-informed neural networks (PINNs) are a versatile tool in the burgeoning field of scientific machine learning for solving partial differential equations (PDEs). However, determining suitable training strategies for them is not…

数值分析 · 数学 2026-03-09 Saad Qadeer , Panos Stinis

Scientific machine learning (SciML) represents a significant advancement in integrating machine learning (ML) with scientific methodologies. At the forefront of this development are Physics-Informed Neural Networks (PINNs), which offer a…

机器学习 · 计算机科学 2024-11-19 Reyhaneh Taj

The accurate modelling of structural dynamics is crucial across numerous engineering applications, such as Structural Health Monitoring (SHM), seismic analysis, and vibration control. Often, these models originate from physics-based…

计算物理 · 物理学 2024-10-31 Marcus Haywood-Alexander , Giacomo Arcieri , Antonios Kamariotis , Eleni Chatzi

Physics-informed neural networks (PINNs) have been popularized as a deep learning framework that can seamlessly synthesize observational data and partial differential equation (PDE) constraints. Their practical effectiveness however can be…

机器学习 · 计算机科学 2023-08-17 Sifan Wang , Shyam Sankaran , Hanwen Wang , Paris Perdikaris

Recently developed physics-informed neural network (PINN) has achieved success in many science and engineering disciplines by encoding physics laws into the loss functions of the neural network, such that the network not only conforms to…

数值分析 · 数学 2021-11-17 Weiqi Ji , Weilun Qiu , Zhiyu Shi , Shaowu Pan , Sili Deng

Deep learning has been highly successful in some applications. Nevertheless, its use for solving partial differential equations (PDEs) has only been of recent interest with current state-of-the-art machine learning libraries, e.g.,…

机器学习 · 计算机科学 2024-10-22 Hamid El Bahja , Jan Christian Hauffen , Peter Jung , Bubacarr Bah , Issa Karambal

Physics-Informed Neural Networks (PINNs) have recently been proposed to solve scientific and engineering problems, where physical laws are introduced into neural networks as prior knowledge. With the embedded physical laws, PINNs enable the…

机器学习 · 计算机科学 2022-12-09 Xinle Wu , Dalin Zhang , Miao Zhang , Chenjuan Guo , Shuai Zhao , Yi Zhang , Huai Wang , Bin Yang

Physics-informed neural networks (PINNs) and their variants have been very popular in recent years as algorithms for the numerical simulation of both forward and inverse problems for partial differential equations. This article aims to…

数值分析 · 数学 2024-11-20 Tim De Ryck , Siddhartha Mishra