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Physics-Informed Neural Networks (PINNs) have recently emerged as a novel approach to simulate complex physical systems on the basis of both data observations and physical models. In this work, we investigate the use of PINNs for various…

Analysis of PDEs · Mathematics 2024-03-27 Guillaume Coulaud , Maxime Le , Régis Duvigneau

In recent years, scientific machine learning, particularly physic-informed neural networks (PINNs), has introduced new innovative methods to understanding the differential equations that describe power system dynamics, providing a more…

Systems and Control · Electrical Eng. & Systems 2024-03-12 Huynh T. T. Tran , Hieu T. Nguyen

Physically informed neural networks (PINNs) are a promising emerging method for solving differential equations. As in many other deep learning approaches, the choice of PINN design and training protocol requires careful craftsmanship. Here,…

Machine Learning · Statistics 2023-10-09 Inbar Seroussi , Asaf Miron , Zohar Ringel

Physics-Informed Neural Networks (PINN) are neural networks encoding the problem governing equations, such as Partial Differential Equations (PDE), as a part of the neural network. PINNs have emerged as a new essential tool to solve various…

Numerical Analysis · Mathematics 2021-07-07 Stefano Markidis

There has been a growing interest in the use of Deep Neural Networks (DNNs) to solve Partial Differential Equations (PDEs). Despite the promise that such approaches hold, there are various aspects where they could be improved. Two such…

Machine Learning · Computer Science 2022-12-26 Amuthan A. Ramabathiran , Prabhu Ramachandran

Physics-informed neural networks (PINNs) have recently emerged as an alternative way of solving partial differential equations (PDEs) without the need of building elaborate grids, instead, using a straightforward implementation. In…

Analysis of PDEs · Mathematics 2019-09-04 Dongkun Zhang , Lu Lu , Ling Guo , George Em Karniadakis

In this study, we propose a new numerical scheme for physics-informed neural networks (PINNs) that enables precise and inexpensive solution for partial differential equations (PDEs) in case of arbitrary geometries while strictly enforcing…

Numerical Analysis · Mathematics 2024-07-30 Hamed Saidaoui , Luis Espath , Rául Tempone

This study presents a discrete physics-informed neural network (dPINN) framework, enhanced with enforced interface constraints (EIC), for modeling physical systems using the domain decomposition method (DDM). Built upon finite element-style…

Computational Engineering, Finance, and Science · Computer Science 2025-05-19 Jichao Yin , Mingxuan Li , Jianguang Fang , Hu Wang

Successfully training Physics Informed Neural Networks (PINNs) for highly nonlinear PDEs on complex 3D domains remains a challenging task. In this paper, PINNs are employed to solve the 3D incompressible Navier-Stokes (NS) equations at…

Computational Engineering, Finance, and Science · Computer Science 2024-08-23 Saakaar Bhatnagar , Andrew Comerford , Araz Banaeizadeh

Physics-Informed Neural Networks (PINNs) have emerged as a powerful class of mesh-free numerical methods for solving partial differential equations (PDEs), particularly those involving complex geometries. In this work, we present an…

Numerical Analysis · Mathematics 2025-08-05 Ran Bi , Weibing Deng , Yameng Zhu

Solving inverse problems in dynamical systems governed by high-dimensional coupled ordinary differential equations (ODEs) is a ubiquitous challenge in scientific machine learning. In many real-world applications, researchers seek to uncover…

Machine Learning · Computer Science 2026-05-06 Zhao Wei , Kenneth Hor Cheng Koh , Sheng Yuan Chin , James Chun Yip Chan , Chin Chun Ooi , Yew-Soon Ong

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 Neural Networks (PINNs) incorporate physics into neural networks by embedding partial differential equations (PDEs) into their loss function. Despite their success in learning the underlying physics, PINN models remain…

Machine Learning · Computer Science 2026-03-04 Alberto Miño Calero , Luis Salamanca , Konstantinos E. Tatsis

Physics-Informed Neural Networks (PINNs) have emerged as a promising paradigm for solving partial differential equations (PDEs) by embedding physical laws into neural network training objectives. However, their deployment on…

Machine Learning · Computer Science 2025-12-11 Jinming Lu , Jiayi Tian , Yequan Zhao , Hai Li , Zheng Zhang

A significant advancement in Neural Network (NN) research is the integration of domain-specific knowledge through custom loss functions. This approach addresses a crucial challenge: how can models utilize physics or mathematical principles…

Machine Learning · Computer Science 2025-03-27 Seyedeh Azadeh Fallah Mortezanejad , Ruochen Wang , Ali Mohammad-Djafari

We introduce NewPINNs, a physics-informing learning framework that couples neural networks with conventional numerical solvers for solving differential equations. Rather than enforcing governing equations and boundary conditions through…

Machine Learning · Computer Science 2026-01-27 Maedeh Makki , Satish Chandran , Maziar Raissi , Adrien Grenier , Behzad Mohebbi

Physics-informed neural networks (PINNs) [4, 10] are an approach for solving boundary value problems based on differential equations (PDEs). The key idea of PINNs is to use a neural network to approximate the solution to the PDE and to…

Numerical Analysis · Mathematics 2023-05-23 Victorita Dolean , Alexander Heinlein , Siddhartha Mishra , Ben Moseley

Physics-informed Neural Networks (PINNs) have been shown as a promising approach for solving both forward and inverse problems of partial differential equations (PDEs). Meanwhile, the neural operator approach, including methods such as Deep…

Machine Learning · Computer Science 2023-10-31 Bin Lin , Zhiping Mao , Zhicheng Wang , George Em Karniadakis

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…

Physics-Informed Neural Networks (PINNs) represent a significant advancement in Scientific Machine Learning (SciML), which integrate physical domain knowledge into an empirical loss function as soft constraints and apply existing machine…

Machine Learning · Computer Science 2024-09-18 Xiaoran Cheng , Sen Na