Physics-informed neural Volterra compensation enabling over 2600× efficiency improvement in 12,057-km ultra-long-haul...

Fiber nonlinearity limits reach and capacity in long-haul coherent systems. Here we present a single-step, physics-informed neural approach to nonlinear compensation that preserves the parallel structure of the Volterra-series transfer function while learning data-driven corrections, unlike widely used digital back-propagation, which reconstructs propagation with numerous cascaded steps and therefore incurs high computational complexity and latency at comparable performance. The method integrates a trainable linear kernel with a compact nonlinear mapping and provides a hardware-suitable architecture. In a 1125-km WDM link, NN-VS matches the maximum performance achieved by leading digital back-propagation variants at 19% computational complexity and 1/25 latency; in a 12,057-km WDM system, the reductions increase to ~6.6% and ~1/176, yielding an efficiency improvement exceeding 2,600×. These results demonstrate that single-step, parallel compensation-augmented by learned corrections-helps mitigate performance-complexity-latency trade-offs, suggesting a pathway for the efficient deployment of nonlinear compensation in next-generation coherent optical networks.