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Related papers: Physics-Informed Extreme Learning Machine (PIELM):…

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This paper explores the difficulties in solving partial differential equations (PDEs) using physics-informed neural networks (PINNs). PINNs use physics as a regularization term in the objective function. However, a drawback of this approach…

Machine Learning · Computer Science 2023-06-21 Shamsulhaq Basir

Motivated by recent research on Physics-Informed Neural Networks (PINNs), we make the first attempt to introduce the PINNs for numerical simulation of the elliptic Partial Differential Equations (PDEs) on 3D manifolds. PINNs are one of the…

Numerical Analysis · Mathematics 2021-03-05 Zhuochao Tang , Zhuojia Fu

Physics-informed machine learning (PIML) as a means of solving partial differential equations (PDE) has garnered much attention in the Computational Science and Engineering (CS&E) world. This topic encompasses a broad array of methods and…

Machine Learning · Computer Science 2024-09-05 Michael Penwarden , Houman Owhadi , Robert M. Kirby

We consider the use of extreme learning machines (ELM) for computational partial differential equations (PDE). In ELM the hidden-layer coefficients in the neural network are assigned to random values generated on $[-R_m,R_m]$ and fixed,…

Computational Physics · Physics 2022-06-01 Suchuan Dong , Jielin Yang

As the key component that facilitates long-haul transmission in optical fiber communications by increasing capacity and reducing costs, accurate characterization and gain settings of erbium-doped fiber amplifiers (EDFAs) are essential for…

Optics · Physics 2025-02-24 Xiaotian Jiang , Jiawei Dong , Yuchen Song , Jin Li , Min Zhang , Danshi Wang

In recent engineering applications using deep learning, physics-informed neural network (PINN) is a new development as it can exploit the underlying physics of engineering systems. The novelty of PINN lies in the use of partial differential…

Computational Engineering, Finance, and Science · Computer Science 2026-02-26 Kart Leong Lim , Rahul Dutta , Mihai Rotaru

We develop improved physics-informed neural networks (PINNs) for high-order and high-dimensional power system models described by nonlinear ordinary differential equations. We propose some novel enhancements to improve PINN training and…

Machine Learning · Computer Science 2024-10-11 Vineet Jagadeesan Nair

Physics-informed machine learning (PIML) is crucial in modern traffic flow modeling because it combines the benefits of both physics-based and data-driven approaches. In conventional PIML, physical information is typically incorporated by…

Machine Learning · Computer Science 2025-09-23 Yuan-Zheng Lei , Yaobang Gong , Dianwei Chen , Yao Cheng , Xianfeng Terry Yang

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…

Machine Learning · Computer Science 2023-08-17 Sifan Wang , Shyam Sankaran , Hanwen Wang , Paris Perdikaris

Physics-informed deep operator networks (DeepONets) have emerged as a promising approach toward numerically approximating the solution of partial differential equations (PDEs). In this work, we aim to develop further understanding of what…

Machine Learning · Computer Science 2024-11-28 Emily Williams , Amanda Howard , Brek Meuris , Panos Stinis

Large language models (LLMs) have rapidly advanced and are increasingly capable of tackling complex scientific problems, including those in physics. Despite this progress, current LLMs often fail to emulate the concise, principle-based…

Machine Learning · Computer Science 2025-06-02 Yinggan Xu , Yue Liu , Zhiqiang Gao , Changnan Peng , Di Luo

In the context of proxy modeling for process systems, traditional data-driven deep learning approaches frequently encounter significant challenges, such as substantial training costs induced by large amounts of data, and limited…

Machine Learning · Computer Science 2024-07-09 Pengwei Liu , Zhongkai Hao , Xingyu Ren , Hangjie Yuan , Jiayang Ren , Dong Ni

Physics-informed machine learning combines the expressiveness of data-based approaches with the interpretability of physical models. In this context, we consider a general regression problem where the empirical risk is regularized by a…

Artificial Intelligence · Computer Science 2025-07-15 Nathan Doumèche , Francis Bach , Gérard Biau , Claire Boyer

In this study, physics-informed supervised residual learning (PhiSRL) is proposed to enable an effective, robust, and general deep learning framework for 2D electromagnetic (EM) modeling. Based on the mathematical connection between the…

Computational Physics · Physics 2023-09-29 Tao Shan , Jinhong Zeng , Xiaoqian Song , Rui Guo , Maokun Li , Fan Yang , Shenheng Xu

Deep learning has been shown to be an effective tool in solving partial differential equations (PDEs) through physics-informed neural networks (PINNs). PINNs embed the PDE residual into the loss function of the neural network, and have been…

Machine Learning · Computer Science 2022-04-06 Jeremy Yu , Lu Lu , Xuhui Meng , George Em Karniadakis

While significant progress has been made on Physics-Informed Neural Networks (PINNs), a comprehensive comparison of these methods across a wide range of Partial Differential Equations (PDEs) is still lacking. This study introduces PINNacle,…

Machine Learning · Computer Science 2023-10-06 Zhongkai Hao , Jiachen Yao , Chang Su , Hang Su , Ziao Wang , Fanzhi Lu , Zeyu Xia , Yichi Zhang , Songming Liu , Lu Lu , Jun Zhu

Physics-informed neural networks (PINNs) have emerged as a powerful paradigm for solving partial differential equations (PDEs) by embedding physical laws directly into neural network training. However, solving high-fidelity PDEs remains…

Machine Learning · Computer Science 2026-02-03 Olaf Yunus Laitinen Imanov

We present a fast and accurate analytical method for fluorescence lifetime imaging microscopy (FLIM) using the extreme learning machine (ELM). We used extensive metrics to evaluate ELM and existing algorithms. First, we compared these…

Biological Physics · Physics 2022-03-28 Zhenya Zang , Dong Xiao , Quan Wang , Zinuo Li , Wujun Xie , Yu Chen , David Day Uei Li

In this paper, we investigate the use of single hidden-layer neural networks as a family of ansatz functions for the resolution of partial differential equations (PDEs). In particular, we train the network via Extreme Learning Machines…

Numerical Analysis · Mathematics 2025-06-30 Davide Elia De Falco , Enrico Schiassi , Francesco Calabrò

Real-world optimization problems are often constrained by complex physical laws that limit computational scalability. These constraints are inherently tied to complex regions, and thus learning models that incorporate physical and geometric…

Machine Learning · Computer Science 2026-03-10 Yilin Wen , Yi Guo , Bo Zhao , Wei Qi , Zechun Hu , Colin Jones , Jian Sun