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The equilibrium reconstruction of plasma is a core step in real-time diagnostic tasks in fusion research. This paper explores a multi-stage Physics-Informed Neural Networks(PINNs) approach to solve the Grad-Shafranov equation, achieving…

Plasma Physics · Physics 2025-07-23 Cuizhi Zhou , Kaien Zhu

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

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) are effective in solving integer-order partial differential equations (PDEs) based on scattered and noisy data. PINNs employ standard feedforward neural networks (NNs) with the PDEs explicitly…

Computational Physics · Physics 2021-11-03 Guofei Pang , Lu Lu , George Em Karniadakis

Physics-informed neural networks (PINNs) offer a powerful framework for seismic wavefield modeling, yet they typically require time-consuming retraining when applied to different velocity models. Moreover, their training can suffer from…

Geophysics · Physics 2025-06-03 Shijun Cheng , Tariq Alkhalifah

Inverse problems arise across scientific and engineering domains, where the goal is to infer hidden parameters or physical fields from indirect and noisy observations. Classical approaches, such as variational regularization and Bayesian…

Machine Learning · Statistics 2025-12-03 Ali Mohammad-Djafari , Ning Chu , Li Wang

Frequency-domain wavefield solutions corresponding to the anisotropic acoustic wave equations can be used to describe the anisotropic nature of the earth. To solve a frequency-domain wave equation, we often need to invert the impedance…

Computational Physics · Physics 2021-02-03 Chao Song , Tariq Alkhalifah , Umair bin Waheed

Physics-informed neural networks (PINNs), rooted in deep learning, have emerged as a promising approach for solving partial differential equations (PDEs). By embedding the physical information described by PDEs into feedforward neural…

Machine Learning · Computer Science 2024-01-26 Yanzhi Liu , Ruifan Wu , Ying Jiang

We develop a physics-informed neural network (PINN) to significantly augment state-of-the-art experimental data and apply it to stratified flows. The PINN is a fully-connected deep neural network fed with time-resolved, three-component…

Fluid Dynamics · Physics 2023-09-27 Lu Zhu , Xianyang Jiang , Adrien Lefauve , Rich R. Kerswell , P. F. Linden

Many types of physics-informed neural network models have been proposed in recent years as approaches for learning solutions to differential equations. When a particular task requires solving a differential equation at multiple…

Machine Learning · Computer Science 2021-11-02 Filipe de Avila Belbute-Peres , Yi-fan Chen , Fei Sha

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

This study takes advantage of recent advances in machine learning to establish a physics-based data analytic platform for distributed reconstruction of mechanical properties in layered components from full waveform data. In this vein, two…

Numerical Analysis · Mathematics 2023-10-20 Yang Xu , Fatemeh Pourahmadian , Jian Song , Conglin Wang

We propose a two-scale neural network method for solving partial differential equations (PDEs) with small parameters using physics-informed neural networks (PINNs). We directly incorporate the small parameters into the architecture of…

Numerical Analysis · Mathematics 2024-10-15 Qiao Zhuang , Chris Ziyi Yao , Zhongqiang Zhang , George Em Karniadakis

Physics-informed neural networks (PINNs) are neural networks (NNs) that directly encode model equations, like Partial Differential Equations (PDEs), in the network itself. While most of the PINN algorithms in the literature minimize the…

Computational Engineering, Finance, and Science · Computer Science 2024-06-05 Marco Baldan , Paolo Di Barba

Physics-informed neural networks (PINNs) are an increasingly powerful way to solve partial differential equations, generate digital twins, and create neural surrogates of physical models. In this manuscript we detail the inner workings of…

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

Physics-Informed Neural Networks (PINNs) are a class of deep learning neural networks that learn the response of a physical system without any simulation data, and only by incorporating the governing partial differential equations (PDEs) in…

Machine Learning · Computer Science 2023-12-19 Rini J. Gladstone , Mohammad A. Nabian , N. Sukumar , Ankit Srivastava , Hadi Meidani

A new iterative technique is presented for solving of initial value problem for certain classes of multidimensional linear and nonlinear partial differential equations. Proposed iterative scheme does not require any discretization,…

Numerical Analysis · Mathematics 2016-02-23 Josef Rebenda , Zdeněk Šmarda

Physics-Informed Neural Networks (PINNs) are a class of deep learning models aiming to approximate solutions of PDEs by training neural networks to minimize the residual of the equation. Focusing on non-equilibrium fluctuating systems, we…

Machine Learning · Computer Science 2025-09-25 Javier Castro , Benjamin Gess

This work presents a two-stage adaptive framework for progressively developing deep neural network (DNN) architectures that generalize well for a given training data set. In the first stage, a layerwise training approach is adopted where a…

Machine Learning · Computer Science 2024-09-24 C G Krishnanunni , Tan Bui-Thanh