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.

中文翻译：

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用于提取数据驱动的连续模型的物理信息算子回归框架

将深度学习应用于数据驱动模型的发现需要仔细应用归纳偏差以获得准确而稳健的物理描述。我们在这里提出了一个框架，用于从高保真分子模拟数据中发现连续模型。我们的方法应用了模态空间中控制物理的神经网络参数化，允许对微分算子进行表征，同时提供可用于施加与对称性、各向同性和守恒形式相关的偏差的结构。我们展示了我们的框架对各种物理的有效性，包括局部和非局部扩散过程以及单相和多相流。