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A Review of Physics Informed Neural Networks for Multiscale Analysis and Inverse Problems

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Abstract

This paper presents the fundamentals of Physics Informed Neural Networks (PINNs) and reviews literature on the methodology and application of PINNs. PINNs are universal approximators that integrates physical laws that can be described by partial differential equations (PDEs) and given data, in the learning process. The formulations of PINNs are first presented in an example of linear elasticity problem. Then, the characteristics of PINNs are compared with that of conventional numerical analysis approach. A review of the literature on PINNs for solving not only forward, but also inverse problems is discussed. In addition, special attention is given to the employment of PINNs in multiscale analysis.

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Acknowledgements

This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) (NRF-2023R1A2C2003758).

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  1. School of Mechanical Engineering, Gwangju Institute of Science and Technology, 123 Cheomdangwagi-ro, Buk-gu, 61005, Gwangju, South Korea

    Dongjin Kim & Jaewook Lee

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Kim, D., Lee, J. A Review of Physics Informed Neural Networks for Multiscale Analysis and Inverse Problems. Multiscale Sci. Eng. (2024). https://doi.org/10.1007/s42493-024-00106-w

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