Browsing by Author "Sharimbayev B."

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    DEVELOPMENT AND OPTIMIZATION OF PHYSICS-INFORMED NEURAL NETWORKS FOR SOLVING PARTIAL DIFFERENTIAL EQUATIONS
    (Vol. 1 No. 1 (2025): Journal of Emerging Technologies and Computing (JETC), 2025) Sharimbayev B.; Kadyrov Sh.; Kavokin A.
    This work compares the advantages and limitations of the Finite Difference Method with Physics-Informed Neural Networks, showing where each can best be applied for different problem scenarios. Analysis on the L2 relative error based on one-dimensional and two-dimensional Poisson equations suggests that FDM gives far more accurate results with a relative error of 7.26 × 10-8 and 2.21 × 10-4 , respectively, in comparison with PINNs, with an error of 5.63 × 10-6 and 6.01 × 10-3 accordingly. Besides forward problems, PINN is realized also for forward-inverse problems which reflect its ability to predict source term after its sufficient training. Visualization of the solution underlines different methodologies adopted by FDM and PINNs, yielding useful insights into their performance and applicability
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    Development and optimization of physics-informed neural networks for solving partial differential equations
    (SDU University, 2025) Sharimbayev B.
    This thesis talks about using physics-informed neural networks (PINNs) to solve Poisson equations in both one-dimensional and two-dimensional areas. These equations are common in many physical problems, like heat transfer and electrostatics. The results from PINNs are compared to the finite difference method (FDM), which is a classical numerical method often used to solve these kinds of equations. The study shows that PINNs can give results that are close to those from FDM, with the added benefit of being more flexible for different types of problems. Another part of this work focuses on using multi-task learning with PINNs. In this part, the neural network does more than one job. It not only finds the solution of the differential equation, but it also learns unknown values or parameters that are part of the equation. For example, in one test problem, the equation had a source term and a coefficient that changes depending on the position. The PINN was able to learn both of them correctly while still solving the equation with a low training error. The results show that PINNs can work well even when the equation is more complex or has unknown parts. The model showed good performance on new or unseen data and was able to find the correct hidden values in the system. Because of this, PINNs may be very useful in future applications for solving advanced problems in science and engineering, especially where traditional methods might be harder to use.