We propose a reduced-order deep-learning surrogate model for dynamic systems described by time-dependent partial differential equations. This method employs space–time Karhunen–Loève expansions (KLEs) of the state variables and space-dependent KLEs of space-varying parameters to identify the reduced (latent) dimensions. Subsequently, a deep neural network (DNN) is used to map the parameter latent space to the state variable latent space.

中文翻译：

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偏微分方程描述的动态系统的贝叶斯降阶深度学习代理模型


我们提出了一种由瞬态偏微分方程描述的动态系统的降阶深度学习代理模型。该方法采用状态变量的时空 Karhunen-Loève 展开 (KLE) 和空间变化参数的空间相关 KLE 来识别减小的（潜在）维度。随后，使用深度神经网络（DNN）将参数潜在空间映射到状态变量潜在空间。