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In this work, we study physics-informed neural networks (PINNs) constrained by partial differential equations (PDEs) and their application in approximating PDEs with two characteristic scales. From a continuous perspective, our formulation…

Optimization and Control · Mathematics 2024-09-06 Michael Hintermüller , Denis Korolev

Physics-informed neural networks (PINNs) have emerged as a promising mesh-free paradigm for solving partial differential equations, yet adoption in science and engineering is limited by slow training and modest accuracy relative to modern…

Computational Engineering, Finance, and Science · Computer Science 2026-02-24 Pao-Hsiung Chiu , Jian Cheng Wong , Chin Chun Ooi , Chang Wei , Yuchen Fan , Yew-Soon Ong

Physics-Informed Neural Networks (PINNs) have shown promise in solving partial differential equations (PDEs), including the frequency-domain Helmholtz equation. However, standard training of PINNs using gradient descent (GD) suffers from…

Machine Learning · Computer Science 2025-04-24 Mohammad Mahdi Abedi , David Pardo , Tariq Alkhalifah

In recent engineering applications using deep learning, physics-informed neural network (PINN) is a new development as it can exploit the underlying physics of engineering systems. The novelty of PINN lies in the use of partial differential…

Computational Engineering, Finance, and Science · Computer Science 2026-02-26 Kart Leong Lim , Rahul Dutta , Mihai Rotaru

We revisit the original approach of using deep learning and neural networks to solve differential equations by incorporating the knowledge of the equation. This is done by adding a dedicated term to the loss function during the optimization…

Machine Learning · Computer Science 2023-04-05 Hubert Baty , Leo Baty

Recently, physics informed neural networks (PINNs) have been explored extensively for solving various forward and inverse problems and facilitating querying applications in fluid mechanics applications. However, work on PINNs for unsteady…

Fluid Dynamics · Physics 2024-02-28 Rahul Sundar , Dipanjan Majumdar , Didier Lucor , Sunetra Sarkar

Physics-informed neural networks (PINNs) have great potential for flexibility and effectiveness in forward modeling and inversion of seismic waves. However, coordinate-based neural networks (NNs) commonly suffer from the "spectral bias"…

Geophysics · Physics 2025-06-19 Yi Ding , Su Chen , Hiroe Miyake , Xiaojun Li

Accurate computational modeling of damage and fracture remains a central challenge in solid mechanics. The finite element method (FEM) is widely used for numerical modeling of fracture problems; however, classical damage models without…

Soft Condensed Matter · Physics 2025-11-07 Aditya Konale , Vikas Srivastava

The accurate determination of electron properties is fundamental to low-temperature plasma simulations, necessitating precise solutions to the spatially inhomogeneous electron Boltzmann equation (EBE). This work explores the use of…

Plasma Physics · Physics 2026-05-07 Ihda Chaerony Siffa , Detlef Loffhagen , Markus M. Becker , Jan Trieschmann

Flexural wave scattering plays a crucial role in optimizing and designing structures for various engineering applications. Mathematically, the flexural wave scattering problem on an infinite thin plate is described by a fourth-order…

Numerical Analysis · Mathematics 2023-07-27 Junhong Yue , Peijun Li

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

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

This research introduces an innovative application of physics-informed neural networks (PINNs) to tackle the intricate challenges of radiative transfer (RT) modeling in exoplanetary atmospheres, with a special focus on efficiently handling…

Earth and Planetary Astrophysics · Physics 2024-08-02 David Dahlbüdding , Karan Molaverdikhani , Barbara Ercolano , Tommaso Grassi

In solving partial differential equations (PDEs), machine learning utilizing physical laws has received considerable attention owing to advantages such as mesh-free solutions, unsupervised learning, and feasibility for solving…

Machine Learning · Computer Science 2026-03-25 Tetsuro Tsuchino , Motoki Shiga

Mathematical models in neural networks are powerful tools for solving complex differential equations and optimizing their parameters; that is, solving the forward and inverse problems, respectively. A forward problem predicts the output of…

Machine Learning · Computer Science 2025-07-29 Aarush Gupta , Kendric Hsu , Syna Mathod

Parameter estimation remains a challenging task across many areas of engineering. Because data acquisition can often be costly, limited, or prone to inaccuracies (noise, uncertainty) it is crucial to identify sensor configurations that…

Machine Learning · Statistics 2025-11-20 Georgios Venianakis , Constantinos Theodoropoulos , Michail Kavousanakis

The research in Artificial Intelligence methods with potential applications in science has become an essential task in the scientific community last years. Physics Informed Neural Networks (PINNs) is one of this methods and represent a…

Computational Physics · Physics 2023-07-24 Luis Medrano Navarro , Luis Martín Moreno , Sergio G Rodrigo

Physics-Informed Neural Networks (PINNs) provide a framework for integrating physical laws with data. However, their application to Prognostics and Health Management (PHM) remains constrained by the limited uncertainty quantification (UQ)…

Machine Learning · Computer Science 2026-01-08 Ibai Ramirez , Jokin Alcibar , Joel Pino , Mikel Sanz , Jose I. Aizpurua

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

Domain-decomposed variants of physics-informed neural networks (PINNs) such as finite basis PINNs (FBPINNs) mitigate some of PINNs' issues like slow convergence and spectral bias through localisation, but still rely on iterative nonlinear…

Numerical Analysis · Mathematics 2026-05-20 Samuel Anderson , Victorita Dolean , Ben Moseley , Jennifer Pestana