Perturbation Theory with Accelerated Convergence for Fibre-Optic Nonlinearity Compensation

Communications in Nonlinear Science and Numerical Simulation. 2026. Vol. 153. Article 109492.

Delitsyn A., Konyaev D., Vasiliy Kakurin, Gromov V.

This paper presents an enhanced perturbation theory-based approach for compensating nonlinear distortion in long-haul fibre-optic communication systems. The proposed method combines perturbation-based compensator for fibre nonlinearity with machine learning, achieving high compensation accuracy with reduced computational complexity. We derive the theoretical framework for a modified perturbation method that leverages an effective lossless fibre model, uses a data-driven optimisation of the first-order perturbation term, and is naturally parallelisable. Numerical simulations for a dual-polarisation 16-QAM transmission link demonstrate that the learned first-order perturbation compensator can achieve performance comparable to SSFM, while maintaining lower complexity. We compare the proposed method with standard SSFM, both in the full link model and in an effective lossless model, as well as with conventional perturbation-based and purely linear compensation techniques. The results show that the machine learning-augmented perturbation approach provides superior accuracy over standard perturbation methods, often matching the benchmark SSFM on an effective model. The study also reveals that higher-order perturbation terms beyond the first order yield diminishing returns and can even degrade performance if not properly handled.

Keywords: машинное обучение, perturbation theory, теория возмущений, нелинейное уравнение Шрёдингера, NLSE approximation, machine learning, SSFM

Publication based on the results of: Complex language and semantic models in artificial intelligence (2025)