Stable autoregressive modelling of supercontinuum generation: A 1D-RWKV surrogate model with physical constraints

Abstract

Supercontinuum generation (SCG) plays an important role in various ultrafast optical applications, but modelling this phenomenon using the Generalized Nonlinear Schrödinger Equation (GNLSE) via standard numerical methods is extremely time-consuming and computationally demanding. While traditional deep learning techniques, particularly recurrent neural networks (RNNs) such as LSTMs, have been employed to accelerate this process, they inherently act as low-pass filters that often fail to resolve the high-frequency details of highly complex nonlinear phenomena. In this paper, we propose a 1D-RWKV (Receptance Weighted Key Value) architecture to effectively predict the complex nonlinear dynamics of SCG. Specifically, by integrating physical noise cutoff with an autoregressive rollout mechanism, out-of-distribution shifts caused by numerical noise accumulation are effectively suppressed. By validating across various pulse conditions, the 1D-RWKV model achieved an average NRMSE of 0.048 for 100 unseen test datasets. More importantly, the highly parallelizable linear recurrent formulation of the RWKV architecture enables large-scale batch inference and preserves high-resolution spectral information without down-sampling. This work enables a fast, large-scale parameter sweeping, which will allow the RWKV framework to be established as a robust and scalable surrogate model for extreme nonlinear optical systems.