Deep neural networks are an attractive alternative for simulating complex dynamical systems, as in comparison to traditional scientific computing methods, they offer reduced computational costs during inference and can be trained directly from observational data. Existing methods, however, cannot extrapolate accurately and are prone to error accumulation in long-time integration. Herein, we address this issue by combining neural operators with recurrent neural networks, learning the operator mapping, while offering a recurrent structure to capture temporal dependencies. The integrated framework is shown to stabilize the solution and reduce error accumulation for both interpolation and extrapolation of the Korteweg-de Vries equation.

翻译：深度神经网络是模拟复杂动力系统的有吸引力的替代方案，与传统科学计算方法相比，它们在推理过程中降低了计算成本，并可直接从观测数据中训练。然而，现有方法无法精确外推，且在长时间积分中容易产生误差累积。本文通过将神经算子与递归神经网络相结合来解决这一问题，学习算子映射，同时提供递归结构以捕捉时间依赖性。该集成框架被证明能够稳定解，并减少Korteweg-de Vries方程在插值和外推中的误差累积。