Development and optimization ofphysics-informed neural networks for solving partial differential equations
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Date
2025
Journal Title
Journal ISSN
Volume Title
Publisher
SDU University
Abstract
This study investigates the application of physics-informed neural networks (PINNs) for solving Poissonequations in both 1D and 2D domains and compares them with finite difference method. Additionally, thestudy explores the capability of multi-task learning with PINNs, where the network not only predicts thesolution but also estimates unknown parameters. In the case of a second-order differential equation witha varying coefficient, PINNs successfully approximated both the source term and the varying coefficientwhile achieving low training loss. The model demonstrated excellent generalization capabilities and accuratereconstruction of the underlying system parameters, showing the potential of PINNs in complex physicalsimulations.
Description
Keywords
numerical analysis, multi-task learning, deep learning, PINNs, FDM
Citation
Batyr Sharimbayev, Shirali Kadyrov, Aleksei Kavokin / Development and optimization ofphysics-informed neural networks forsolving partial differential equations / Journal of Emerging Technologies and Computing (JETC), Vol. 1 No. 1 / SDU University / 2025