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Physics-informed neural networks have emerged as a powerful tool in the scientific machine learning community, with applications to both forward and inverse problems. While they have shown considerable empirical success, significant…

Optimization and Control · Mathematics 2025-12-11 Federica Caforio , Martin Holler , Matthias Höfler

Physics-Informed Neural Networks (PINNs) have advanced the data-driven solution of differential equations (DEs) in dynamic physical systems, yet challenges remain in explainability, scalability, and architectural complexity. This paper…

Signal Processing · Electrical Eng. & Systems 2025-12-03 Ibrahim Shahbaz , Mohammad J. Abdel-Rahman , Eman Hammad

The modeling and control of single-phase flow systems governed by Partial Differential Equations (PDEs) present challenges, especially under transient conditions. In this work, we extend the Physics-Informed Neural Nets for Control (PINC)…

Machine Learning · Computer Science 2025-06-09 Luis Kin Miyatake , Eduardo Camponogara , Eric Aislan Antonelo , Alexey Pavlov

Identifying accurate dynamic models is required for the simulation and control of various technical systems. In many important real-world applications, however, the two main modeling approaches often fail to meet requirements: first…

Machine Learning · Computer Science 2021-04-19 Manuel A. Roehrl , Thomas A. Runkler , Veronika Brandtstetter , Michel Tokic , Stefan Obermayer

Accurate models are essential for design, performance prediction, control, and diagnostics in complex engineering systems. Physics-based models excel during the design phase but often become outdated during system deployment due to changing…

Machine Learning · Computer Science 2025-01-22 Zihan Liu , Prashant N. Kambali , C. Nataraj

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…

Recent advances show that neural networks embedded with physics-informed priors significantly outperform vanilla neural networks in learning and predicting the long term dynamics of complex physical systems from noisy data. Despite this…

Machine Learning · Computer Science 2021-10-04 Shaan Desai , Marios Mattheakis , Stephen Roberts

Recently, a class of machine learning methods called physics-informed neural networks (PINNs) has been proposed and gained prevalence in solving various scientific computing problems. This approach enables the solution of partial…

Computational Engineering, Finance, and Science · Computer Science 2023-11-06 Chen Xu , Ba Trung Cao , Yong Yuan , Günther Meschke

Presently, there is a steady state approach in Computational fluid dynamics (CFD) to obtain a steady solution directly from the steady state governing equations. Whereas, for obtaining a time-periodic flow solution, the present unsteady…

Computational Physics · Physics 2026-05-19 Lakshya Chaplot , Harshita Agarwal , Atul Sharma

Physics-informed neural networks (PINNs) integrate fundamental physical principles with advanced data-driven techniques, driving significant advancements in scientific computing. However, PINNs face persistent challenges with stiffness in…

Machine Learning · Computer Science 2024-07-30 Pancheng Niu , Yongming Chen , Jun Guo , Yuqian Zhou , Minfu Feng , Yanchao Shi

Understanding real-world dynamical phenomena remains a challenging task. Across various scientific disciplines, machine learning has advanced as the go-to technology to analyze nonlinear dynamical systems, identify patterns in big data, and…

Machine Learning · Computer Science 2022-12-07 Kevin Linka , Amelie Schafer , Xuhui Meng , Zongren Zou , George Em Karniadakis , Ellen Kuhl

Time-domain simulations are crucial for ensuring power system stability and avoiding critical scenarios that could lead to blackouts. The next-generation power systems require a significant increase in the computational cost and complexity…

Systems and Control · Electrical Eng. & Systems 2025-06-26 Ignasi Ventura Nadal , Jochen Stiasny , Spyros Chatzivasileiadis

The integration of converter-interfaced generation introduces new transient stability challenges to modern power systems. Classical Lyapunov- and scalable passivity-based approaches typically rely on restrictive assumptions, and finding…

Systems and Control · Electrical Eng. & Systems 2026-04-09 Yifei Wang , Han Wang , Kehao Zhuang , Keith Moffat , Florian Dörfler

This paper proposes a novel transient stability assessment tool for networked microgrids based on neural Lyapunov methods. Assessing transient stability is formulated as a problem of estimating the dynamic security region of networked…

Systems and Control · Electrical Eng. & Systems 2020-12-03 Tong Huang , Sicun Gao , Le Xie

The energy transition is causing many stability-related challenges for power systems. Transient stability refers to the ability of a power grid's bus angles to retain synchronism after the occurrence of a major fault. In this paper a…

Optimization and Control · Mathematics 2021-01-12 Tim Aschenbruck , Willem Esterhuizen , Stefan Streif

Accurate and interpretable bearing fault classification is critical for ensuring the reliability of rotating machinery, particularly under variable operating conditions where domain shifts can significantly degrade model performance. This…

Machine Learning · Computer Science 2025-08-12 Tasfiq E. Alam , Md Manjurul Ahsan , Shivakumar Raman

We propose a neural network-based meta-learning method to efficiently solve partial differential equation (PDE) problems. The proposed method is designed to meta-learn how to solve a wide variety of PDE problems, and uses the knowledge for…

Machine Learning · Statistics 2023-10-23 Tomoharu Iwata , Yusuke Tanaka , Naonori Ueda

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

The integration of physics-based knowledge with machine learning models is increasingly shaping the monitoring, diagnostics, and prognostics of electrical transformers. In this two-part series, the first paper introduced the foundations of…

Machine Learning · Computer Science 2025-12-30 Jose I. Aizpurua

Physics-Informed Neural Networks have emerged as a promising methodology for solving PDEs, gaining significant attention in computer science and various physics-related fields. Despite being demonstrated the ability to incorporate the…

Machine Learning · Computer Science 2025-05-01 Yao-Hsuan Tsai , Hsiao-Tung Juan , Pao-Hsiung Chiu , Chao-An Lin