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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

Quantum state tomography (QST) faces exponential measurement requirements and noise sensitivity in multi-qubit systems, bottlenecking practical quantum technologies. We present a physics-informed neural network (PINN) framework integrating…

Quantum Physics · Physics 2025-12-17 Changchun Feng , Laifa Tao , Lin Chen

Physics-Informed Neural Network (PINN) is a novel multi-task learning framework useful for solving physical problems modeled using differential equations (DEs) by integrating the knowledge of physics and known constraints into the…

Machine Learning · Computer Science 2024-09-18 Shivprasad Kathane , Shyamprasad Karagadde

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

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

Physics-Informed Neural Networks (PINNs) are machine learning tools that approximate the solution of general partial differential equations (PDEs) by adding them in some form as terms of the loss/cost function of a Neural Network. Most…

Numerical Analysis · Mathematics 2022-08-29 Antonio Tadeu Azevedo Gomes , Larissa Miguez da Silva , Frederic Valentin

This dissertation investigates physics-informed neural networks (PINNs) as candidate models for encoding governing equations, and assesses their performance on experimental data from two different systems. The first system is a simple…

Machine Learning · Computer Science 2024-01-09 Hamza Alsharif

Physics-informed neural networks (PINNs) are numerical solvers that embed all the physical information of a system into the loss function of a neural network. In this way the learned solution accounts for data (if available), the governing…

Computational Physics · Physics 2025-07-30 Andrés Martínez-Esteban , Pablo Calvo-Barlés , Luis Martín-Moreno , Sergio G Rodrigo

Physics-informed neural networks (PINNs) provide a powerful framework for learning governing equations of dynamical systems from data. Biologically-informed neural networks (BINNs) are a variant of PINNs that preserve the known differential…

Machine Learning · Computer Science 2026-04-21 William Lavery , Jodie A. Cochrane , Christian Olesen , Dagim S. Tadele , John T. Nardini , Sara Hamis

In this paper, we review the new method Physics-Informed Neural Networks (PINNs) that has become the main pillar in scientific machine learning, we present recent practical extensions, and provide a specific example in data-driven discovery…

Machine Learning · Computer Science 2024-09-02 Maziar Raissi , Paris Perdikaris , Nazanin Ahmadi , George Em Karniadakis

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…

Deep learning models trained on finite data lack a complete understanding of the physical world. On the other hand, physics-informed neural networks (PINNs) are infused with such knowledge through the incorporation of mathematically…

Neural and Evolutionary Computing · Computer Science 2026-02-23 Jian Cheng Wong , Abhishek Gupta , Chin Chun Ooi , Pao-Hsiung Chiu , Jiao Liu , Yew-Soon Ong

Machine learning techniques have proven to be effective in addressing the structure of atomic nuclei. Physics$-$Informed Neural Networks (PINNs) are a promising machine learning technique suitable for solving integro-differential problems…

Computational Physics · Physics 2026-02-13 Lorenzo Brevi , Antonio Mandarino , Carlo Barbieri , Enrico Prati

Optimal and safety-critical control are fundamental problems for stochastic systems, and are widely considered in real-world scenarios such as robotic manipulation and autonomous driving. In this paper, we consider the problem of…

Systems and Control · Electrical Eng. & Systems 2024-05-10 Zhuoyuan Wang , Reece Keller , Xiyu Deng , Kenta Hoshino , Takashi Tanaka , Yorie Nakahira

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

Quantum Physics-Informed Neural Networks (QPINNs) integrate quantum computing and machine learning to impose physical biases on the output of a quantum neural network, aiming to either solve or discover differential equations. The approach…

Quantum Physics · Physics 2025-11-13 Giorgio Panichi , Sebastiano Corli , Enrico Prati

We propose a self-supervised physics-informed neural network (PINN) framework that adaptively balances physics-based and data-driven supervision for scientific machine learning under data scarcity. Unlike prior PINNs that rely on fixed or…

Machine Learning · Computer Science 2026-05-08 Reza Pirayeshshirazinezhad

In order to drastically reduce the heavy computational burden associated with time-domain simulations, this paper introduces a Physics-Informed Neural Network (PINN) to directly learn the solutions of power system dynamics. In contrast to…

Systems and Control · Electrical Eng. & Systems 2021-07-01 Jochen Stiasny , Samuel Chevalier , Spyros Chatzivasileiadis

In this paper we employ the emerging paradigm of physics-informed neural networks (PINNs) for the solution of representative inverse scattering problems in photonic metamaterials and nano-optics technologies. In particular, we successfully…

Computational Physics · Physics 2020-04-22 Yuyao Chen , Lu Lu , George Em Karniadakis , Luca Dal Negro

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