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We characterize and remedy a failure mode that may arise from multi-scale dynamics with scale imbalances during training of deep neural networks, such as Physics Informed Neural Networks (PINNs). PINNs are popular machine-learning templates…

Machine Learning · Computer Science 2021-07-05 Suryanarayana Maddu , Dominik Sturm , Christian L. Müller , Ivo F. Sbalzarini

Physics-Informed Neural Networks (PINNs) have become a promising research direction in the field of solving Partial Differential Equations (PDEs). Dealing with singular perturbation problems continues to be a difficult challenge in the…

Machine Learning · Computer Science 2024-08-28 Sen Wang , Peizhi Zhao , Qinglong Ma , Tao Song

Solving differential equations efficiently and accurately sits at the heart of progress in many areas of scientific research, from classical dynamical systems to quantum mechanics. There is a surge of interest in using Physics-Informed…

Machine Learning · Computer Science 2022-07-06 Shaan Desai , Marios Mattheakis , Hayden Joy , Pavlos Protopapas , Stephen Roberts

The simulation of power system dynamics poses a computationally expensive task. Considering the growing uncertainty of generation and demand patterns, thousands of scenarios need to be continuously assessed to ensure the safety of power…

Systems and Control · Electrical Eng. & Systems 2023-11-13 Jochen Stiasny , Spyros Chatzivasileiadis

Recently, physics-informed neural networks (PINNs) and their variants have gained significant popularity as a scientific computing method for solving partial differential equations (PDEs), whereas accuracy is still its main shortcoming.…

Computational Physics · Physics 2025-03-11 Feng Chen , Yiran Meng , Kegan Li , Chaoran Yang , Jiong Yang

Physics-Informed Neural Networks (PINNs) have emerged as a powerful tool for integrating physics-based constraints and data to address forward and inverse problems in machine learning. Despite their potential, the implementation of PINNs…

Optimization and Control · Mathematics 2024-12-19 Alan Williams , Christopher Leon , Alexander Scheinker

The solution of partial differential equations (PDES) on irregular domains has long been a subject of significant research interest. In this work, we present an approach utilizing physics-informed neural networks (PINNs) to achieve…

Computational Physics · Physics 2025-06-12 Cuizhi Zhou , Kaien Zhu

Physics informed neural networks (PINNs) are deep learning based techniques for solving partial differential equations (PDEs) encounted in computational science and engineering. Guided by data and physical laws, PINNs find a neural network…

Numerical Analysis · Mathematics 2020-12-30 Yeonjong Shin , Jerome Darbon , George Em Karniadakis

This work compares the advantages and limitations of the Finite Difference Method with Physics-Informed Neural Networks, showing where each can best be applied for different problem scenarios. Analysis on the L2 relative error based on…

General Mathematics · Mathematics 2025-02-06 Batyr Sharimbayev , Shirali Kadyrov , Aleksei Kavokin

Physics Informed Neural Network (PINN) is a scientific computing framework used to solve both forward and inverse problems modeled by Partial Differential Equations (PDEs). This paper introduces IDRLnet, a Python toolbox for modeling and…

Machine Learning · Computer Science 2021-07-12 Wei Peng , Jun Zhang , Weien Zhou , Xiaoyu Zhao , Wen Yao , Xiaoqian Chen

Physics-informed neural networks (PINNs) as a means of discretizing partial differential equations (PDEs) are garnering much attention in the Computational Science and Engineering (CS&E) world. At least two challenges exist for PINNs at…

Computational Physics · Physics 2023-01-23 Michael Penwarden , Shandian Zhe , Akil Narayan , Robert M. Kirby

In this work, we present the physics-informed neural network (PINN) model applied particularly to dynamic problems in solid mechanics. We focus on forward and inverse problems. Particularly, we show how a PINN model can be used efficiently…

Neural and Evolutionary Computing · Computer Science 2025-12-16 Vijay Kag , Venkatesh Gopinath

Physics-informed neural networks (PINNs) are at the forefront of scientific machine learning, making possible the creation of machine intelligence that is cognizant of physical laws and able to accurately simulate them. However, today's…

Neural and Evolutionary Computing · Computer Science 2026-02-23 Jian Cheng Wong , Chin Chun Ooi , Abhishek Gupta , Pao-Hsiung Chiu , Joshua Shao Zheng Low , My Ha Dao , Yew-Soon Ong

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…

Cryptography and Security · Computer Science 2026-04-07 Solon Falas , Charalambos Konstantinou , Maria K. Michael

We consider the approximation of a class of dynamic partial differential equations (PDE) of second order in time by the physics-informed neural network (PINN) approach, and provide an error analysis of PINN for the wave equation, the…

Numerical Analysis · Mathematics 2023-03-23 Yanxia Qian , Yongchao Zhang , Yunqing Huang , Suchuan Dong

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

Physics-informed neural networks (PINNs) have proven to be a promising method for the rapid solving of partial differential equations (PDEs) in both forward and inverse problems. However, due to the smoothness assumption of functions…

Computational Physics · Physics 2026-03-25 Guoqiang Lei , D. Exposito , Xuerui Mao

Deep learning-based numerical schemes such as Physically Informed Neural Networks (PINNs) have recently emerged as an alternative to classical numerical schemes for solving Partial Differential Equations (PDEs). They are very appealing at…

Numerical Analysis · Mathematics 2022-05-11 A. Beguinet , V. Ehrlacher , R. Flenghi , M. Fuente , O. Mula , A. Somacal

Machine learning techniques are employed to perform the full characterization of a quantum system. The particular artificial intelligence technique used to learn the Hamiltonian is called physics informed neural network (PINN). The idea…

The present work investigates the use of physics-informed neural networks (PINNs) for the 3D reconstruction of unsteady gravity currents from limited data. In the PINN context, the flow fields are reconstructed by training a neural network…

Fluid Dynamics · Physics 2023-06-16 Mickaël Delcey , Yoann Cheny , Sébastien Kiesgen de Richter