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Physics-Informed Neural Networks (PINNs) encounter accuracy limitations when solving the Allen--Cahn (AC) and Cahn--Hilliard (CH) partial differential equations (PDEs). To overcome this, we employ a novel loss function, Residuals-weighted…

Numerical Analysis · Mathematics 2026-02-25 Guangtao Zhang , Jiani Lin , Qijia Zhai , Huiyu Yang , Xujun Chen , Ieng Tak Leong , Fang Zhu

Physics-Informed Neural Networks (PINNs) provide a learning-based framework for solving partial differential equations (PDEs) by embedding governing physical laws into neural network training. In practice, however, their performance is…

Machine Learning · Computer Science 2026-01-21 Pancheng Niu , Jun Guo , Qiaolin He , Yongming Chen , Yanchao Shi

Physics-informed neural networks (PINNs) have garnered significant interest for their potential in solving partial differential equations (PDEs) that govern a wide range of physical phenomena. By incorporating physical laws into the…

Machine Learning · Computer Science 2026-04-24 Jian Cheng Wong , Isaac Yin Chung Lai , Pao-Hsiung Chiu , Chin Chun Ooi , Abhishek Gupta , Yew-Soon Ong

Physics-Informed Neural Networks (PINNs) have revolutionized solving differential equations by integrating physical laws into neural networks training. This paper explores PINNs for open-loop optimal control problems (OCPs) with incomplete…

Optimization and Control · Mathematics 2025-01-27 Alessandro Alla , Giulia Bertaglia , Elisa Calzola

Physics-informed neural networks have gained growing interest. Specifically, they are used to solve partial differential equations governing several physical phenomena. However, physics-informed neural network models suffer from several…

Computational Engineering, Finance, and Science · Computer Science 2022-11-29 Diab W. Abueidda , Seid Koric , Erman Guleryuz , Nahil A. Sobh

Efficient and robust optimization is essential for neural networks, enabling scientific machine learning models to converge rapidly to very high accuracy -- faithfully capturing complex physical behavior governed by differential equations.…

We investigate the inverse problem for Partial Differential Equations (PDEs) in scenarios where the parameters of the given PDE dynamics may exhibit changepoints at random time. We employ Physics-Informed Neural Networks (PINNs) - universal…

Machine Learning · Statistics 2024-04-03 Zhikang Dong , Pawel Polak

In recent years, the researches about solving partial differential equations (PDEs) based on artificial neural network have attracted considerable attention. In these researches, the neural network models are usually designed depend on…

Neural and Evolutionary Computing · Computer Science 2024-05-21 Bo Zhang , Chao Yang

Physics-informed deep learning has emerged as a promising framework for solving partial differential equations (PDEs). Nevertheless, training these models on complex problems remains challenging, often leading to limited accuracy and…

Machine Learning · Statistics 2025-11-13 Wenqian Chen , Amanda Howard , Panos Stinis

Physics informed neural network (PINN) based solution methods for differential equations have recently shown success in a variety of scientific computing applications. Several authors have reported difficulties, however, when using PINNs to…

Numerical Analysis · Mathematics 2023-10-16 Arnav Gangal , Luis Kim , Sean P. Carney

In the recent years, Physics Informed Neural Networks (PINNs) have received strong interest as a method to solve PDE driven systems, in particular for data assimilation purpose. This method is still in its infancy, with many shortcomings…

Machine Learning · Computer Science 2025-03-20 Nilo Schwencke , Cyril Furtlehner

Physics-informed neural networks (PINNs) incorporate physical knowledge from the problem domain as a soft constraint on the loss function, but recent work has shown that this can lead to optimization difficulties. Here, we study the impact…

Machine Learning · Computer Science 2022-07-12 Shashank Subramanian , Robert M. Kirby , Michael W. Mahoney , Amir Gholami

In this paper, we present the adaptive physics-informed neural networks (PINNs) for resolving three dimensional (3D) dynamic thermo-mechanical coupling problems in large-size-ratio functionally graded materials (FGMs). The physical laws…

Computational Engineering, Finance, and Science · Computer Science 2023-06-16 Lin Qiu , Yanjie Wang , Tian He , Yan Gu , Fajie Wang

As a typical application of deep learning, physics-informed neural network (PINN) {has been} successfully used to find numerical solutions of partial differential equations (PDEs), but how to improve the limited accuracy is still a great…

Machine Learning · Computer Science 2022-08-09 Zhi-Yong Zhang , Hui Zhang , Li-Sheng Zhang , Lei-Lei Guo

Although physics-informed neural networks (PINNs) have shown great potential in dealing with nonlinear partial differential equations (PDEs), it is common that PINNs will suffer from the problem of insufficient precision or obtaining…

Machine Learning · Computer Science 2024-10-07 Feilong Jiang , Xiaonan Hou , Min Xia

We consider physics-informed neural networks (PINNs) [Raissi et al., J.~Comput. Phys. 278 (2019) 686-707] for forward physical problems. In order to find optimal PINNs configuration, we introduce a hyper-parameter optimization (HPO)…

Numerical Analysis · Mathematics 2023-02-01 Paul Escapil-Inchauspé , Gonzalo A. Ruz

Physics-Informed Neural Networks (PINNs) have become a popular and powerful framework for solving partial differential equations (PDEs), leveraging neural networks to approximate solutions while embedding PDE constraints, boundary…

Numerical Analysis · Mathematics 2026-02-03 Zijuan Xin , Chenyao Wang , Feng Shi , Yizhong Sun

Physics-informed neural networks (PINNs) are revolutionizing science and engineering practice by bringing together the power of deep learning to bear on scientific computation. In forward modeling problems, PINNs are meshless partial…

Machine Learning · Computer Science 2023-11-28 Yicheng Wang , Xiaotian Han , Chia-Yuan Chang , Daochen Zha , Ulisses Braga-Neto , Xia Hu

Physics-informed Neural Networks (PINNs) have been shown as a promising approach for solving both forward and inverse problems of partial differential equations (PDEs). Meanwhile, the neural operator approach, including methods such as Deep…

Machine Learning · Computer Science 2023-10-31 Bin Lin , Zhiping Mao , Zhicheng Wang , George Em Karniadakis

Physics-Informed Neural Networks (PINNs) have emerged as powerful tools for solving partial differential equations (PDEs). However, training PINNs from scratch is often computationally intensive and time-consuming. To address this problem,…

Numerical Analysis · Mathematics 2024-10-21 Sidi Wu