Datadriven forwardinverse problems for YajimaOikawa system using deep learning with parameter regularization
Abstract
We investigate datadriven forwardinverse problems for YajimaOikawa (YO) system by employing two technologies which improve the performance of neural network in deep physicsinformed neural network (PINN), namely neuronwise locally adaptive activation functions and $L^2$ norm parameter regularization. Indeed, we not only recover three different forms of vector rogue waves (RWs) by means of three distinct initialboundary value conditions in the forward problem of YO system, including brightbright RWs, intermediatebright RWs and darkbright RWs, but also study the inverse problem of YO system by using training data with different noise intensity. In order to deal with the problem that the capacity of learning unknown parameters is not ideal when the PINN with only locally adaptive activation functions utilizes training data with noise interference in the inverse problem of YO system, thus we introduce $L^2$ norm regularization, which can drive the weights closer to origin, into PINN with locally adaptive activation functions, then find that the PINN model with two strategies shows amazing training effect by using training data with noise interference to investigate the inverse problem of YO system.
 Publication:

arXiv eprints
 Pub Date:
 December 2021
 arXiv:
 arXiv:2112.04062
 Bibcode:
 2021arXiv211204062P
 Keywords:

 Mathematics  Numerical Analysis;
 Nonlinear Sciences  Exactly Solvable and Integrable Systems;
 Physics  Computational Physics
 EPrint:
 arXiv admin note: text overlap with arXiv:2109.09266