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Physics informed neural networks (PINNs) have drawn attention in recent years in engineering problems due to their effectiveness and ability to tackle the problems without generating complex meshes. PINNs use automatic differentiation to…

Fluid Dynamics · Physics 2022-06-20 Atakan Aygun , Ali Karakus

Approximating solutions to partial differential equations (PDEs) is fundamental for the modeling of dynamical systems in science and engineering. Physics-informed neural networks (PINNs) are a recent machine learning-based approach, for…

The physics informed neural network (PINN) is evolving as a viable method to solve partial differential equations. In the recent past PINNs have been successfully tested and validated to find solutions to both linear and non-linear partial…

Machine Learning · Computer Science 2024-03-28 Vikas Dwivedi , Nishant Parashar , Balaji Srinivasan

Differential equations are indispensable to engineering and hence to innovation. In recent years, physics-informed neural networks (PINN) have emerged as a novel method for solving differential equations. PINN method has the advantage of…

Computational Engineering, Finance, and Science · Computer Science 2022-01-07 Mayank Raj , Pramod Kumbhar , Ratna Kumar Annabattula

Given the facts of the extensiveness of multi-material diffusion problems and the inability of the standard PINN(Physics-Informed Neural Networks) method for such problems, in this paper we present a novel PINN method that can accurately…

Numerical Analysis · Mathematics 2023-09-28 Yanzhong Yao , Jiawei Guo , Tongxiang Gu

In this work, we propose the Residual-Weighted Physics-Informed Neural Network (RW-PINN), a new method designed to enhance the accuracy of Physics-Informed Neural Network (PINN) based algorithms. We construct a deep learning framework with…

Numerical Analysis · Mathematics 2025-09-03 K. Murari , P. Roul , S. Sundar

Physics-Informed Neural Networks (PINNs) solve partial differential equations using deep learning. However, conventional PINNs perform pointwise predictions that neglect dependencies within a domain, which may result in suboptimal…

Machine Learning · Computer Science 2025-05-26 Mayank Nagda , Phil Ostheimer , Thomas Specht , Frank Rhein , Fabian Jirasek , Stephan Mandt , Marius Kloft , Sophie Fellenz

In recent years, Physics-Informed Neural Networks (PINNs) have become a representative method for solving partial differential equations (PDEs) with neural networks. PINNs provide a novel approach to solving PDEs through optimization…

Computational Physics · Physics 2024-11-28 Weiwei Zhang , Wei Suo , Jiahao Song , Wenbo Cao

Physics-informed neural networks (PINNs) have been proposed to learn the solution of partial differential equations (PDE). In PINNs, the residual form of the PDE of interest and its boundary conditions are lumped into a composite objective…

Computational Physics · Physics 2022-05-24 Shamsulhaq Basir , Inanc Senocak

Physics-informed neural networks (PINNs) are effective in solving inverse problems based on differential and integral equations with sparse, noisy, unstructured, and multi-fidelity data. PINNs incorporate all available information into a…

Analysis of PDEs · Mathematics 2020-04-10 Guofei Pang , Marta D'Elia , Michael Parks , George E. Karniadakis

Physics-informed neural networks (PINNs) are a powerful approach for solving problems involving differential equations, yet they often struggle to solve problems with high frequency and/or multi-scale solutions. Finite basis…

Numerical Analysis · Mathematics 2024-06-21 Victorita Dolean , Alexander Heinlein , Siddhartha Mishra , Ben Moseley

Physics-informed neural networks (PINNs) have demonstrated promise in solving forward and inverse problems involving partial differential equations. Despite recent progress on expanding the class of problems that can be tackled by PINNs,…

Machine Learning · Computer Science 2025-02-18 Francisco Sahli Costabal , Simone Pezzuto , Paris Perdikaris

Physics-informed neural networks (PINNs) have recently become a powerful tool for solving partial differential equations (PDEs). However, finding a set of neural network parameters that lead to fulfilling a PDE can be challenging and…

Machine Learning · Computer Science 2023-04-12 Aleksandr Dekhovich , Marcel H. F. Sluiter , David M. J. Tax , Miguel A. Bessa

A physics informed neural network (PINN) incorporates the physics of a system by satisfying its boundary value problem through a neural network's loss function. The PINN approach has shown great success in approximating the map between the…

Numerical Analysis · Mathematics 2022-03-17 Revanth Mattey , Susanta Ghosh

Resolving the diffusion coefficient is a key element in many biological and engineering systems, including pharmacological drug transport and fluid mechanics analyses. Additionally, these systems often have spatial variation in the…

Quantitative Methods · Quantitative Biology 2024-03-08 Sukirt Thakur , Ehsan Esmaili , Sarah Libring , Luis Solorio , Arezoo M. Ardekani

Physics-Informed Neural Networks (PINNs) have emerged as a promising framework for solving forward and inverse problems governed by differential equations. However, their reliability when used in ill-posed inverse problems remains poorly…

Systems and Control · Electrical Eng. & Systems 2025-11-12 J. Penuela , H. Ouerdane

Physics-Informed Neural Networks (PINNs) represent a groundbreaking paradigm in scientific computing, seamlessly integrating the robust framework of deep learning with fundamental physical laws. This paper meticulously applies the standard…

Numerical Analysis · Mathematics 2026-01-19 Ahmed Aberqi , Ahmed Miloudi

Physics-informed deep learning has drawn tremendous interest in recent years to solve computational physics problems, whose basic concept is to embed physical laws to constrain/inform neural networks, with the need of less data for training…

Fluid Dynamics · Physics 2020-11-24 Chengping Rao , Hao Sun , Yang Liu

Physics-informed neural networks (PINNs) are successful machine-learning methods for the solution and identification of partial differential equations (PDEs). We employ PINNs for solving the Reynolds-averaged Navier$\unicode{x2013}$Stokes…

Fluid Dynamics · Physics 2022-07-20 Hamidreza Eivazi , Mojtaba Tahani , Philipp Schlatter , Ricardo Vinuesa

Inverse problems are extensively studied in applied mathematics, with applications ranging from acoustic tomography for medical diagnosis to geophysical exploration. Physics informed neural networks (PINNs) have emerged as a powerful tool…