Том 8

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Browsing Том 8 by Author "Sarana, Maksym"

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    PINN-based machine learning for modeling internal waves insemi-infinite fluids
    (2025) Avramenko, Olha; Kompan, Serhii; Sarana, Maksym
    This study investigates the application of Physics-Informed Neural Networks (PINNs) for modelingwave processes at the interface between two incompressible fluids of differing densities. As a first step,the linear formulation of the problem is considered, which admits an analytical solution based on aspectral method involving Fourier decomposition of the initial perturbation. This solution serves as abenchmark for testing and validating the accuracy of the PINN predictions.The implementation is carried out in Python using specialized libraries such as TensorFlow, NumPy,SciPy, and Matplotlib, which provide both efficient deep learning frameworks and tools for solving mathe-matical physics problems numerically. The approach integrates artificial intelligence with domain-specificknowledge in hydrodynamics, enabling the construction of interpretable and physically consistent mod-els. Particular attention is given to the organization of the computational experiment, automation ofvisualizations, and storage of intermediate results for further analysis. The PINN model includes a lossfunction that encodes the governing equations and boundary conditions, and the training is conductedon randomly sampled points across the spatio-temporal domain. The influence of network architectureand training parameters on solution accuracy is examined. Visualization of loss function evolutionand predicted wave profiles provides insight into convergence behavior and physical plausibility of thesolutions.A comparative analysis between the PINN-based and analytical solutions across different time in-stances is presented, revealing phase shifts and amplitude deviations. The model demonstrates goodagreement at early times and a gradual accumulation of errors as time progresses—an expected featureof this class of methods. The results confirm the feasibility of applying the PINN framework to linearhydrodynamic problems, laying the groundwork for future extensions to weakly and strongly nonlinearregimes, including studies of wave stability and nonlinear wave dynamics.