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Physics-informed neural networks (PINNs) have shown remarkable prospects in solving forward and inverse problems involving partial differential equations (PDEs). However, PINNs still face the challenge of high computational cost in solving…

Fluid Dynamics · Physics 2025-01-22 Jiahao Song , Wenbo Cao , Weiwei Zhang

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

Physics-informed neural networks (PINNs) have gained prominence in recent years and are now effectively used in a number of applications. However, their performance remains unstable due to the complex landscape of the loss function. To…

Machine Learning · Computer Science 2025-09-30 Dmitry Bylinkin , Mikhail Aleksandrov , Savelii Chezhegov , Aleksandr Beznosikov

Physics-informed neural networks (PINNs) have shown promising potential for solving partial differential equations (PDEs) using deep learning. However, PINNs face training difficulties for evolutionary PDEs, particularly for dynamical…

Neural and Evolutionary Computing · Computer Science 2023-12-25 Siqi Chen , Bin Shan , Ye Li

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…

Partial differential equation (PDE) solvers are fundamental to engineering simulation. Classical mesh-based approaches (finite difference/volume/element) are fast and accurate on high-quality meshes but struggle with higher-order operators…

Computational Engineering, Finance, and Science · Computer Science 2025-10-07 Akshay Govind Srinivasan , Vikas Dwivedi , Balaji Srinivasan

In this work, a novel Eig-PIELM framework is proposed that extends physics-informed extreme learning machine for an efficient and accurate solution of linear eigenvalue problems. The method reformulates the governing differential equations…

Numerical Analysis · Mathematics 2026-02-25 Rishi Mishra , Smriti , Ganapathy Krishnamurthi , Balaji Srinivasan , Sundararajan Natarajan

Direct observations of earthquake nucleation and propagation are few and yet the next decade will likely see an unprecedented increase in indirect, surface observations that must be integrated into modeling efforts. Machine learning (ML)…

Mathematical Physics · Physics 2024-07-25 Cody Rucker , Brittany A. Erickson

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

Physics-informed neural networks (PINNs) have emerged as a promising approach to solving partial differential equations (PDEs) using neural networks, particularly in data-scarce scenarios, due to their unsupervised training capability.…

Machine Learning · Computer Science 2025-03-25 Edgar Torres , Jonathan Schiefer , Mathias Niepert

Physics-informed machine learning (PIML) is an emerging framework that integrates physical knowledge into machine learning models. This physical prior often takes the form of a partial differential equation (PDE) system that the regression…

Machine Learning · Statistics 2025-07-15 Nathan Doumèche

With the increases in computational power and advances in machine learning, data-driven learning-based methods have gained significant attention in solving PDEs. Physics-informed neural networks (PINNs) have recently emerged and succeeded…

Machine Learning · Computer Science 2023-02-07 Namgyu Kang , Byeonghyeon Lee , Youngjoon Hong , Seok-Bae Yun , Eunbyung Park

The utilization of Deep Neural Networks (DNNs) in physical science and engineering applications has gained traction due to their capacity to learn intricate functions. While large datasets are crucial for training DNN models in fields like…

Machine Learning · Computer Science 2025-08-05 Vamsi Sai Krishna Malineni , Suresh Rajendran

We present a physics-informed machine-learning (PIML) approach for the approximation of slow invariant manifolds (SIMs) of singularly perturbed systems, providing functionals in an explicit form that facilitate the construction and…

Dynamical Systems · Mathematics 2024-11-05 Dimitrios G. Patsatzis , Gianluca Fabiani , Lucia Russo , Constantinos Siettos

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

In this paper, a physics-informed multiresolution wavelet neural network (PIMWNN) method is proposed for solving partial differential equations (PDEs). This method uses the multiresolution wavelet neural network (MWNN) to approximate…

Numerical Analysis · Mathematics 2025-08-12 Feng Han , Jianguo Wang , Guoliang Peng , Xueting Shi

Solving Stefan problems via neural networks is inherently challenged by the nonlinear coupling between the solutions and the free boundary, which results in a non-convex optimization problem. To address this, this work proposes an Operator…

Numerical Analysis · Mathematics 2026-01-26 Siyuan Lang , Zhiyue Zhang

Physics-informed machine learning (PIML) integrates partial differential equations (PDEs) into machine learning models to solve inverse problems, such as estimating coefficient functions (e.g., the Hamiltonian function) that characterize…

Computational Physics · Physics 2025-11-07 Yoh-ichi Mototake , Makoto Sasaki

Parameter estimation for differential equations from measured data is an inverse problem prevalent across quantitative sciences. Physics-Informed Neural Networks (PINNs) have emerged as effective tools for solving such problems, especially…

Machine Learning · Computer Science 2025-04-08 Marius Almanstötter , Roman Vetter , Dagmar Iber

Deep learning has been shown to be an effective tool in solving partial differential equations (PDEs) through physics-informed neural networks (PINNs). PINNs embed the PDE residual into the loss function of the neural network, and have been…

Machine Learning · Computer Science 2022-04-06 Jeremy Yu , Lu Lu , Xuhui Meng , George Em Karniadakis