Data-Driven Solutions and Discoveries in Mechanics Using Physics Informed Neural Network

Qi Zhang; Yilin Chen; Ziyi Yang

doi:10.20944/preprints202006.0258.v2

Preprint Article Version 2 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 18 June 2020 / Approved: 21 June 2020 / Online: 21 June 2020 (10:56:06 CEST)
Version 2 : Received: 30 September 2020 / Approved: 30 September 2020 / Online: 30 September 2020 (03:51:25 CEST)

Deep learning has achieved remarkable success in diverse computer science applications, however, its use in other traditional engineering fields has emerged only recently. In this project, we solved several mechanics problems governed by differential equations, using physics informed neural networks (PINN). The PINN embeds the differential equations into the loss of the neural network using automatic differentiation. We present our developments in the context of solving two main classes of problems: data-driven solutions and data-driven discoveries, and we compare the results with either analytical solutions or numerical solutions using the finite element method. The remarkable achievements of the PINN model shown in this report suggest the bright prospect of the physics-informed surrogate models that are fully differentiable with respect to all input coordinates and free parameters. More broadly, this study shows that PINN provides an attractive alternative to solve traditional engineering problems.

Conservation laws; Data inference; Data discovery; Dimensionless form; PINN

Comment 1

Received: 30 September 2020
Commenter: Qi Zhang
Commenter's Conflict of Interests: Author

Comment: Change the LaTeX template, suppress the hyperlink, add more details to figure captions, correct some grammar issues

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Data-Driven Solutions and Discoveries in Mechanics Using Physics Informed Neural Network

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