We introduce the 'Stochastic Latent Transformer', a probabilistic deep learning approach for efficient reduced-order modelling of stochastic partial differential equations (SPDEs). Despite recent advances in deep learning for fluid mechanics, limited research has explored modelling stochastically driven flows - which play a crucial role in understanding a broad spectrum of phenomena, from jets on giant planets to ocean circulation and the variability of midlatitude weather. The model architecture consists of a stochastically-forced transformer, paired with a translation-equivariant autoencoder, that we demonstrate is capable of reproducing system dynamics across various integration periods. We demonstrate its effectiveness applied to a well-researched zonal jet system, with the neural network achieving a five-order-of-magnitude speedup compared to numerical integration. This facilitates the cost-effective generation of large ensembles, enabling the exploration of statistical questions concerning probabilities of spontaneous transition events.

翻译：我们提出“随机潜变量变压器”这一概率深度学习方法，用于随机偏微分方程的高效降阶建模。尽管深度学习在流体力学领域取得了最新进展，但针对随机驱动流动——这类流动在理解从巨行星急流到海洋环流及中纬度天气变化的广泛现象中至关重要——的建模研究仍然有限。该模型架构由一个随机强迫变压器与一个平移等变自编码器组成，我们证明其能够在不同积分周期内重现系统动力学特性。通过将其应用于一个经过充分研究的纬向急流系统，我们验证了该方法的有效性：与数值积分相比，神经网络实现了五个数量级的加速。这有助于以低成本生成大规模集成数据，进而探索关于自发跃迁事件概率的统计问题。