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This paper is available on arxiv under CC 4.0 license.

Authors:

(1) Amir Noorizadegan, Department of Civil Engineering, National Taiwan University;

(2) D.L. Young, Core Tech System Co. Ltd, Moldex3D, Department of Civil Engineering, National Taiwan University & dlyoung@ntu.edu.tw;

(3) Y.C. Hon, Department of Mathematics, City University of Hong Kong;

(4) C.S. Chen, Department of Civil Engineering, National Taiwan University & dchen@ntu.edu.tw.

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Abstract & Introduction

Neural Networks

PINN for Solving Inverse Burgers’ Equation

Residual Network

Numerical Results

Results, Acknowledgments & References

3 PINN for Solving Inverse Burgers’ Equation

In this section, we explore the application of Physics-Informed Neural Networks (PINN) [1] to solve the inverse Burgers’ equation in one dimension. The 1D Burgers’ equation is given by:

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The PINNs loss function is given by (Fig. 1(II)):

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Figure 1: The neural network (interpolation stage) + physics (inverse Burger’s equation). Here, x and t represent two dimensions, each including n examples.

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We aim to minimize MSE to obtain the neural network parameters (w, bi) and the Burgers’ equation parameters λ1 and λ2.

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