论文标题
PDE逆问题的变异自动编码
Variational Autoencoding of PDE Inverse Problems
论文作者
论文摘要
在缺失物理学并恢复其参数的情况下，指定一个管理物理模型是科学中的两个交织和基本问题。现代的机器学习使人们可以通过模拟器和替代物来规避这些问题，但是这样做会忽略对小型数据制度，可解释性和决策尤其重要的先验知识和物理定律。在这项工作中，我们将机械模型折叠成灵活的数据驱动替代物，以达到物理结构化的解码器网络。这为贝叶斯逆问题提供了加速的推断，并且可以充当编码A-Priori物理信息的液位常规机。我们采用PDE问题的变分形式，并引入随机局部近似值作为基于模型的数据增强形式。我们既展示了现实世界环境和结构化空间过程的框架的准确性和提高的计算效率。
Specifying a governing physical model in the presence of missing physics and recovering its parameters are two intertwined and fundamental problems in science. Modern machine learning allows one to circumvent these, via emulators and surrogates, but in doing so disregards prior knowledge and physical laws that are especially important for small data regimes, interpretability, and decision making. In this work we fold the mechanistic model into a flexible data-driven surrogate to arrive at a physically structured decoder network. This provides accelerated inference for the Bayesian inverse problem, and can act as a drop-in regulariser that encodes a-priori physical information. We employ the variational form of the PDE problem and introduce stochastic local approximations as a form of model based data augmentation. We demonstrate both the accuracy and increased computational efficiency of the framework on real world settings and structured spatial processes.
