Traditional partial differential equation (PDE) solvers can be computationally expensive, which motivates the development of faster methods, such as reduced-order-models (ROMs). We present GPLaSDI, a hybrid deep-learning and Bayesian ROM. GPLaSDI trains an autoencoder on full-order-model (FOM) data and simultaneously learns simpler equations governing the latent space. These equations are interpolated with Gaussian Processes, allowing for uncertainty quantification and active learning, even with limited access to the FOM solver. Our framework is able to achieve up to 100,000 times speed-up and less than 7% relative error on fluid mechanics problems.

翻译：传统偏微分方程求解器计算成本高昂，这促使了更快速方法的发展，例如降阶模型。我们提出GPLaSDI，一种混合深度学习与贝叶斯降阶模型。GPLaSDI在全阶模型数据上训练自编码器，并同时学习控制潜在空间的简化方程。这些方程通过高斯过程进行插值，从而能够实现不确定性量化和主动学习，即使在全阶模型求解器访问受限的情况下也能适用。我们的框架在流体力学问题上可实现高达10万倍的加速，且相对误差低于7%。