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Multi-parallelized PINNs for the inverse problem study of NLS typed equations in optical fiber communications: Discovery on diverse high-order terms and variable coefficients

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  • Yin, Yu-Hang
  • Lü, Xing

Abstract

In this paper, we focus on the inverse problem study of nonlinear Schrödinger (NLS) typed equations in optical fiber communicaitons. As an extension of the physics-informed neural network (PINN), multi-parallelized PINNs are constructed and trained for the discovery of diverse high-order terms and variable coefficients. We firstly study various constant-coefficient combinations of a generalized high-order NLS typed equation, where the Chen-Lee-Liu equation, the Gerdjikov-Ivanov equation and the Kundu-Eckhaus equation are included. With small amount of exact solutions available to us, we predict the value of multiple coefficients under different cases to deduce the undetermined terms of the generalized equation based on the multi-parallelized PINN. Different categories of NLS typed equations are then inferred. In the meantime, high accuracy numerical solutions on localized regions can be accordingly obtained.

Suggested Citation

  • Yin, Yu-Hang & Lü, Xing, 2024. "Multi-parallelized PINNs for the inverse problem study of NLS typed equations in optical fiber communications: Discovery on diverse high-order terms and variable coefficients," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    • Handle: RePEc:eee:chsofr:v:181:y:2024:i:c:s0960077924001462
    DOI: 10.1016/j.chaos.2024.114595
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