Predictive simulations are essential for applications ranging from weather forecasting to material design. The veracity of these simulations hinges on their capacity to capture the effective system dynamics. Massively parallel simulations predict the systems dynamics by resolving all spatiotemporal scales, often at a cost that prevents experimentation. On the other hand, reduced order models are fast but often limited by the linearization of the system dynamics and the adopted heuristic closures. We propose a novel systematic framework that bridges large scale simulations and reduced order models to extract and forecast adaptively the effective dynamics (AdaLED) of multiscale systems. AdaLED employs an autoencoder to identify reduced-order representations of the system dynamics and an ensemble of probabilistic recurrent neural networks (RNNs) as the latent time-stepper. The framework alternates between the computational solver and the surrogate, accelerating learned dynamics while leaving yet-to-be-learned dynamics regimes to the original solver. AdaLED continuously adapts the surrogate to the new dynamics through online training. The transitions between the surrogate and the computational solver are determined by monitoring the prediction accuracy and uncertainty of the surrogate. The effectiveness of AdaLED is demonstrated on three different systems - a Van der Pol oscillator, a 2D reaction-diffusion equation, and a 2D Navier-Stokes flow past a cylinder for varying Reynolds numbers (400 up to 1200), showcasing its ability to learn effective dynamics online, detect unseen dynamics regimes, and provide net speed-ups. To the best of our knowledge, AdaLED is the first framework that couples a surrogate model with a computational solver to achieve online adaptive learning of effective dynamics. It constitutes a potent tool for applications requiring many expensive simulations.

翻译：预测性模拟对于从天气预报到材料设计等应用至关重要。这些模拟的准确性取决于其捕捉系统有效动力学的能力。大规模并行模拟通过解析所有时空尺度来预测系统动力学，但其高昂成本往往阻碍了实验探索。另一方面，降阶模型虽速度快，但常受限于系统动力学的线性化以及采用的启发式闭合方法。我们提出一种新颖的系统性框架，该框架桥接大规模模拟与降阶模型，能够自适应提取并预测多尺度系统的有效动力学（AdaLED）。AdaLED采用自编码器识别系统动力学的降阶表征，并利用概率循环神经网络（RNN）集成模型作为潜在时间步进器。该框架在计算求解器与替代模型之间交替切换，加速已学习的动力学过程，同时将尚未学习的动力学区域交由原始求解器处理。通过在线训练，AdaLED持续使替代模型适应新出现的动力学行为。替代模型与计算求解器之间的转换通过监测替代模型的预测精度和不确定性来确定。在三个不同系统（凡德波尔振荡器、二维反应扩散方程、以及雷诺数从400至1200变化的二维圆柱绕流纳维-斯托克斯流动）上的实验结果验证了AdaLED的有效性，展现了其在线学习有效动力学、检测未见动力学区域以及实现净加速的能力。据我们所知，AdaLED是首个将替代模型与计算求解器相结合以实现有效动力学在线自适应学习的框架。对于需要大量昂贵模拟的应用场景，该框架构成了一个强大的工具。