Physics-Informed with Power-Enhanced Residual Network: PINN for Solving Inverse Burgers’ Equation by@interpolation
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Physics-Informed with Power-Enhanced Residual Network: PINN for Solving Inverse Burgers’ Equation
by The Interpolation PublicationFebruary 28th, 2024
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Discover the power of Power-Enhancing Residual Networks for superior interpolation in 2D/3D domains with physics-informed solutions, also available on Arxiv.
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The Interpolation Publication
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#1 Publication focused exclusively on Interpolation, ie determining value from the existing values in a given data set.
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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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PINN for Solving Inverse Burgers’ Equation
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:
The PINNs loss function is given by (Fig. 1(II)):
Figure 1: The neural network (interpolation stage) + physics (inverse Burger’s equation). Here, x and t represent two dimensions, each including n examples.
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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