Browsing by Author "Aleksei Kavokin"

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    Development and optimization ofphysics-informed neural networks for solving partial differential equations
    (SDU University, 2025) Batyr Sharimbayev; Shirali Kadyrov; Aleksei Kavokin
    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.