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.

提出一种名为 AdaLED 的新型系统框架，以自动编码器为主要工具，利用概率递归神经网络进行时间步进，通过在线训练不断改进，建立预测模型从而实现大规模模拟的高速运行和在线适应性学习，应用在 Van der Pol 振荡器，2D 反应扩散方程和 2D Navier-Stokes 圆柱流中，具有较高的准确性和鲁棒性。

自适应学习有效动态：适应复杂系统的实时在线建模

Adaptive learning of effective dynamics: Adaptive real-time, online  modeling for complex systems

Predictive simulations of complex systems are essential for applications
ranging from weather forecasting to drug design. The veracity of these
predictions hinges on their capacity to capture the effective system dynamics.
Massively parallel simulations predict the system dynamics by resolving all
spatiotemporal scales, often at a cost that prevents experimentation while
their findings may not allow for generalisation. On the other hand reduced
order models are fast but limited by the frequently adopted linearization of
the system dynamics and/or the utilization of heuristic closures. Here we
present a novel systematic framework that bridges large scale simulations and
reduced order models to Learn the Effective Dynamics (LED) of diverse complex
systems. The framework forms algorithmic alloys between non-linear machine
learning algorithms and the Equation-Free approach for modeling complex
systems. LED deploys autoencoders to formulate a mapping between fine and
coarse-grained representations and evolves the latent space dynamics using
recurrent neural networks. The algorithm is validated on benchmark problems and
we find that it outperforms state of the art reduced order models in terms of
predictability and large scale simulations in terms of cost. LED is applicable
to systems ranging from chemistry to fluid mechanics and reduces the
computational effort by up to two orders of magnitude while maintaining the
prediction accuracy of the full system dynamics. We argue that LED provides a
novel potent modality for the accurate prediction of complex systems.

我们提出了一种通过使用深度学习自编码器模型，将大规模模拟和降阶模型结合起来，以有效地预测各种复杂系统的动态特性的算法，该算法在验证中显示出可行性，并可降低两个数量级的计算成本。