论文标题
物理知识的操作器回归框架，用于提取数据驱动的连续模型
A physics-informed operator regression framework for extracting data-driven continuum models
论文作者
论文摘要
深度学习在发现数据驱动模型的应用需要仔细应用归纳偏差，以获取对物理的描述，该物理既准确又健壮。我们在这里提出了一个从高保真分子模拟数据中发现连续模型的框架。我们的方法应用了模态物理学的神经网络参数化，允许对差异操作员进行表征，同时提供结构，该结构可用于施加与对称性，同型和保护形式相关的偏见。我们证明了框架对各种物理学的有效性，包括局部和非局部扩散过程以及单一和多相流。对于流动物理学，我们证明了这种方法会导致一个学习的操作员，该操作员将概括为未包含在训练集中的系统特征，例如可变粒径，密度和浓度。
The application of deep learning toward discovery of data-driven models requires careful application of inductive biases to obtain a description of physics which is both accurate and robust. We present here a framework for discovering continuum models from high fidelity molecular simulation data. Our approach applies a neural network parameterization of governing physics in modal space, allowing a characterization of differential operators while providing structure which may be used to impose biases related to symmetry, isotropy, and conservation form. We demonstrate the effectiveness of our framework for a variety of physics, including local and nonlocal diffusion processes and single and multiphase flows. For the flow physics we demonstrate this approach leads to a learned operator that generalizes to system characteristics not included in the training sets, such as variable particle sizes, densities, and concentration.
