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Physics-informed neural networks (PINNs) are one popular approach to incorporate a priori knowledge about physical systems into the learning framework. PINNs are known to be robust for smaller training sets, derive better generalization…

Machine Learning · Computer Science 2024-06-19 Birgit Hillebrecht , Benjamin Unger

We show that the physics-informed neural networks (PINNs), in combination with some recently developed discontinuity capturing neural networks, can be applied to solve optimal control problems subject to partial differential equations…

Optimization and Control · Mathematics 2026-02-16 Ming-Chih Lai , Yongcun Song , Xiaoming Yuan , Hangrui Yue , Tianyou Zeng

Physics-informed neural networks (PINNs) show great advantages in solving partial differential equations. In this paper, we for the first time propose to study conformable time fractional diffusion equations by using PINNs. By solving the…

Numerical Analysis · Mathematics 2021-08-18 Yinlin Ye , Yajing Li , Hongtao Fan , Xinyi Liu , Hongbing Zhang

Despite the great promise of the physics-informed neural networks (PINNs) in solving forward and inverse problems, several technical challenges are present as roadblocks for more complex and realistic applications. First, most existing…

Computational Engineering, Finance, and Science · Computer Science 2022-01-26 Han Gao , Matthew J. Zahr , Jian-Xun Wang

Neural networks have recently gained attention in solving inverse problems. One prominent methodology are Physics-Informed Neural Networks (PINNs) which can solve both forward and inverse problems. In the paper at hand, full waveform…

Numerical Analysis · Mathematics 2023-12-05 Leon Herrmann , Tim Bürchner , Felix Dietrich , Stefan Kollmannsberger

Learning the solution of partial differential equations (PDEs) with a neural network is an attractive alternative to traditional solvers due to its elegance, greater flexibility and the ease of incorporating observed data. However, training…

Machine Learning · Computer Science 2024-07-18 Katsiaryna Haitsiukevich , Alexander Ilin

Inverse problems in partial differential equations (PDEs) involve estimating the physical parameters of a system from observed spatiotemporal solution fields. Neural networks are well-suited for PDE parameter estimation due to their…

Machine Learning · Computer Science 2026-05-27 Divyam Goel , Nithin Chalapathi , Sanjeev Raja , Aditi S. Krishnapriyan

Physics-Informed Neural Networks (PINNs) have emerged as powerful tools for solving partial differential equations (PDEs). However, training PINNs from scratch is often computationally intensive and time-consuming. To address this problem,…

Numerical Analysis · Mathematics 2024-10-21 Sidi Wu

Physics-Informed Neural Networks (PINNs) integrate machine learning with differential equations to solve forward and inverse problems while ensuring that predictions adhere to physical laws. Physiologically based pharmacokinetic (PBPK)…

Physics-informed Neural Networks (PINNs) have been shown to be effective in solving partial differential equations by capturing the physics induced constraints as a part of the training loss function. This paper shows that a PINN can be…

Machine Learning · Computer Science 2023-05-08 Chandrajit Bajaj , Luke McLennan , Timothy Andeen , Avik Roy

Inverse problems involving differential equations often require identifying unknown parameters or functions from data. Existing approaches, such as Physics-Informed Neural Networks (PINNs), Universal Differential Equations (UDEs) and…

Machine Learning · Computer Science 2025-05-23 Shalev Manor , Mohammad Kohandel

This paper investigates the application of Physics-Informed Neural Networks (PINNs) for solving the inverse advection-diffusion problem to localize pollution sources. The study focuses on optimizing neural network architectures to…

Neural and Evolutionary Computing · Computer Science 2025-03-25 Ivan Chuprov , Denis Derkach , Dmitry Efremenko , Aleksei Kychkin

Solving time-dependent Partial Differential Equations (PDEs) is one of the most critical problems in computational science. While Physics-Informed Neural Networks (PINNs) offer a promising framework for approximating PDE solutions, their…

Physics-informed neural networks (PINN) is a machine learning (ML)-based method to solve partial differential equations that has gained great popularity due to the fast development of ML libraries in the last few years. The…

Chemical Physics · Physics 2024-12-31 Martin A. Achondo , Jehanzeb H. Chaudhry , Christopher D. Cooper

Physics-informed neural networks (PINNs) commonly address ill-posed inverse problems by uncovering unknown physics. This study presents a novel unsupervised learning framework that identifies spatial subdomains with specific governing…

Machine Learning · Computer Science 2024-12-11 Arturo Rodriguez , Ashesh Chattopadhyay , Piyush Kumar , Luis F. Rodriguez , Vinod Kumar

This study focuses on the solution of partial differential equations (PDEs) by using physics-informed neural networks (PINNs). The Newell-Whitehead-Segel (NWS) equation and the Allen-Cahn equation belong to fundamental PDEs used mostly in…

Analysis of PDEs · Mathematics 2025-11-20 Ali Haider Shah , Naveed R. Butt , Asif Ahmad , Muhammad Omer Bin Saeed

Flexoelectricity, the coupling between strain gradients and electric polarization, poses significant computational challenges due to its governing fourth-order partial differential equations that require C1-continuous solutions. To address…

Computational Physics · Physics 2025-06-30 Hyeonbin Moon , Donggeun Park , Jinwook Yeo , Seunghwa Ryu

Eigenvalue problems have a distinctive forward-inverse structure and are fundamental to characterizing a system's thermal response, stability, and natural modes. Physics-Informed Neural Networks (PINNs) offer a mesh-free alternative for…

Machine Learning · Computer Science 2025-11-04 Akshay Sai Banderwaar , Abhishek Gupta

Physics-informed neural networks (PINNs) impose known physical laws into the learning of deep neural networks, making sure they respect the physics of the process while decreasing the demand of labeled data. For systems represented by…

"AI for Science" aims to solve fundamental scientific problems using AI techniques. As most physical phenomena can be described as Partial Differential Equations (PDEs) , approximating their solutions using neural networks has evolved as a…

Machine Learning · Computer Science 2024-07-31 Mohan Ren , Zhihao Fang , Keren Li , Anirbit Mukherjee