Conditionally Parameterized, Discretization-Aware Neural Networks for Mesh-Based Modeling of Physical Systems

Abstract

The numerical simulations of physical systems are heavily dependent on meshbased 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, superresolution 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.Preprint. Under review.

Predicting Physics in Mesh-reduced Space with Temporal Attention

“…In particular, methods based on Graph Neural Networks (GNN) have shown to be powerful and flexible. These methods can directly work with unstructured simulation meshes, simulate systems with complex domain boundaries, and adaptively allocate computation to the spatial regions where it is needed [7,38,34,51].…”