The numerical simulations of physical systems are heavily dependent on mesh-based models. While neural networks have been extensively explored to assist such tasks, they often ignore the interactions or hierarchical relations between input features, and process them as concatenated mixtures. In this work, we generalize the idea of conditional parametrization -- using trainable functions of input parameters to generate the weights of a neural network, and extend them in a flexible way to encode information critical to the numerical simulations. Inspired by discretized numerical methods, choices of the parameters include physical quantities and mesh topology features. The functional relation between the modeled features and the parameters are built into the network architecture. The method is implemented on different networks, which are applied to several frontier scientific machine learning tasks, including the discovery of unmodeled physics, super-resolution of coarse fields, and the simulation of unsteady flows with chemical reactions. The results show that the conditionally parameterized networks provide superior performance compared to their traditional counterparts. A network architecture named CP-GNet is also proposed as the first deep learning model capable of standalone prediction of reacting flows on irregular meshes.
翻译:物理系统的数字模拟严重依赖基于网状的模型。 虽然对神经网络进行了广泛的探索以协助完成这些任务,但它们往往忽视输入特征之间的相互作用或等级关系,并将它们作为混合混合物处理。在这项工作中,我们推广有条件的准光化概念 -- -- 使用输入参数的训练功能来生成神经网络的重量,并以灵活的方式扩展它们,以编码对数字模拟至关重要的信息。在离散数字方法的启发下,参数的选择包括物理数量和网状地形特征。模型特征和参数之间的功能关系被建在网络结构中。该方法被应用于不同的网络,用于若干前沿科学机器学习任务,包括发现非模型物理学,粗糙场的超分辨率,以及模拟不稳定的流动与化学反应。结果显示,条件参数化网络比传统对应者提供优异的性能。还提议将称为CP-GNet的网络结构作为第一个深度学习模型,能够独立地预测非正常的Mashes的流动。