Data-based surrogate modeling has surged in capability in recent years with
the emergence of graph neural networks (GNNs), which can operate directly on
mesh-based representations of data. The goal of this work is to introduce an
interpretable fine-tuning strategy for GNNs, with application to unstructured
mesh-based fluid dynamics modeling. The end result is a fine-tuned GNN that
adds interpretability to a pre-trained baseline GNN through an adaptive
sub-graph sampling strategy that isolates regions in physical space
intrinsically linked to the forecasting task, while retaining the predictive
capability of the baseline. The structures identified by the fine-tuned GNNs,
which are adaptively produced in the forward pass as explicit functions of the
input, serve as an accessible link between the baseline model architecture, the
optimization goal, and known problem-specific physics. Additionally, through a
regularization procedure, the fine-tuned GNNs can also be used to identify,
during inference, graph nodes that correspond to a majority of the anticipated
forecasting error, adding a novel interpretable error-tagging capability to
baseline models. Demonstrations are performed using unstructured flow data
sourced from flow over a backward-facing step at high Reynolds numbers.

使用图神经网络的可解释微调策略对基于网格的流体动力学建模进行研究，以提高其可预测性和解释性，并通过正则化过程识别与预测错误相关的图节点。