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The measurement of deep water gravity wave elevations using in-situ devices, such as wave gauges, typically yields spatially sparse data. This sparsity arises from the deployment of a limited number of gauges due to their installation…

As an emerging technology in deep learning, physics-informed neural networks (PINNs) have been widely used to solve various partial differential equations (PDEs) in engineering. However, PDEs based on practical considerations contain…

Machine Learning · Computer Science 2021-11-11 Yuhao Huang

This paper proposes a new framework using physics-informed neural networks (PINNs) to simulate complex structural systems that consist of single and double beams based on Euler-Bernoulli and Timoshenko theory, where the double beams are…

Machine Learning · Computer Science 2023-09-26 Taniya Kapoor , Hongrui Wang , Alfredo Nunez , Rolf Dollevoet

Recent work in scientific machine learning has developed so-called physics-informed neural network (PINN) models. The typical approach is to incorporate physical domain knowledge as soft constraints on an empirical loss function and use…

Machine Learning · Computer Science 2021-11-12 Aditi S. Krishnapriyan , Amir Gholami , Shandian Zhe , Robert M. Kirby , Michael W. Mahoney

Physics-Informed Neural Networks (PINNs) are a new family of numerical methods, based on deep learning, for modeling boundary value problems. They offer an advantage over traditional numerical methods for high-dimensional, parametric, and…

Computational Physics · Physics 2024-07-31 Michel Nohra , Steven Dufour

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

Inverse problems arise almost everywhere in science and engineering where we need to infer on a quantity from indirect observation. The cases of medical, biomedical, and industrial imaging systems are the typical examples. A very high…

Machine Learning · Computer Science 2025-02-20 Ali Mohammad-Djafari

Recent studies have demonstrated the success of deep learning in solving forward and inverse problems in engineering and scientific computing domains, such as physics-informed neural networks (PINNs). Source inversion problems under sparse…

Machine Learning · Statistics 2026-04-10 Brenda Anague , Bamdad Hosseini , Issa Karambal , Jean Medard Ngnotchouye

Physics-informed neural networks (PINNs) are extensively employed to solve partial differential equations (PDEs) by ensuring that the outputs and gradients of deep learning models adhere to the governing equations. However, constrained by…

Machine Learning · Computer Science 2025-07-21 Chenhao Si , Ming Yan

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

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

We propose a Hybrid Quantum-Classical Physics-Informed Neural Network (HQC-PINN) that integrates parameterized variational quantum circuits into the PINN framework for hydrological PDE-constrained learning. Our architecture encodes…

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

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

Accurately and stably solving the incompressible Navier--Stokes equations with physics-informed neural networks (PINNs) remains challenging, particularly for sparse or noisy observations and for flow regimes in which the local balance among…

Fluid Dynamics · Physics 2026-03-31 Ke Xu , Ze Tao , Fujun Liu

Physics-Informed Neural Networks (PINNs) offer a powerful paradigm for flow reconstruction, seamlessly integrating sparse velocity measurements with the governing Navier-Stokes equations to recover complete velocity and latent pressure…

Machine Learning · Computer Science 2026-02-19 Yixiao Qian , Jiaxu Liu , Zewei Xia , Song Chen , Chao Xu , Shengze Cai

We present our progress on the application of physics informed deep learning to reservoir simulation problems. The model is a neural network that is jointly trained to respect governing physical laws and match boundary conditions. The…

Fluid Dynamics · Physics 2021-04-26 Cedric Fraces Gasmi , Hamdi Tchelepi

In this study, we present and validate the predictive capability of the Physics-Informed Neural Networks (PINNs) methodology for solving a variety of engineering and biological dynamical systems governed by ordinary differential equations…

Machine Learning · Computer Science 2025-11-19 Tyrus Whitman , Andrew Particka , Christopher Diers , Ian Griffin , Charuka Wickramasinghe , Pradeep Ranaweera

Real-time, physically-consistent predictions on low-power edge devices is critical for the next generation embodied AI systems, yet it remains a major challenge. Physics-Informed Neural Networks (PINNs) combine data-driven learning with…

Machine Learning · Computer Science 2025-12-01 Chi Zhang , Lin Wang

This paper uses Physics-Informed Neural Network (PINN) to design Frequency Selective Surface (FSS). PINN integrates physical information into the loss function, so training PINN does not require a dataset, which will be faster than…

Applied Physics · Physics 2024-01-09 Yu-Hang Liu , Bing-Zhong Wang , Ren Wang