We present a data-driven, space-time continuous framework to learn surrogatemodels for complex physical systems described by advection-dominated partialdifferential equations. Those systems have slow-decaying Kolmogorovn-widththat hinders standard methods, including reduced order modeling, from producinghigh-fidelity simulations at low cost. In this work, we construct hypernetwork-based latent dynamical models directly on the parameter space of a compactrepresentation network. We leverage the expressive power of the network and aspecially designed consistency-inducing regularization to obtain latent trajectoriesthat are both low-dimensional and smooth. These properties render our surrogatemodels highly efficient at inference time. We show the efficacy of our frameworkby learning models that generate accurate multi-step rollout predictions at muchfaster inference speed compared to competitors, for several challenging examples.

翻译：我们提出了一种数据驱动的时空连续框架，用于学习由平流主导偏微分方程描述的复杂物理系统的代理模型。这类系统具有缓慢衰减的科尔莫戈罗夫n宽度，阻碍了包括降阶建模在内的标准方法以低成本生成高保真模拟。在本工作中，我们直接在紧凑表示网络的参数空间上构建基于超网络的潜在动态模型。利用网络的表达能力以及专门设计的一致性诱导正则化，我们获得了既低维又平滑的潜在轨迹。这些特性使得我们的代理模型在推理时高效。通过几个具有挑战性的例子，我们展示了该框架的有效性：所学习的模型能够生成准确的多步滚动预测，且推理速度远快于竞争对手。