In optical communication systems, fibre nonlinearity is the major obstacle in increasing the transmission capacity. Typically, digital signal processing techniques and hardware are used to deal with optical communication signals, but increasing speed and computational complexity create challenges for such approaches. Highly parallel, ultrafast neural networks using photonic devices have the potential to ease the requirements placed on digital signal processing circuits by processing the optical signals in the analogue domain. Here we report a silicon photonic–electronic neural network for solving fibre nonlinearity compensation in submarine optical-fibre transmission systems. Our approach uses a photonic neural network based on wavelength-division multiplexing built on a silicon photonic platform compatible with complementary metal–oxide–semiconductor technology. We show that the platform can be used to compensate for optical fibre nonlinearities and improve the quality factor of the signal in a 10,080 km submarine fibre communication system. The Q-factor improvement is comparable to that of a software-based neural network implemented on a workstation assisted with a 32-bit graphic processing unit.