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.

翻译：随着图神经网络（GNN）的兴起，基于数据的代理建模能力近年来显著增强。GNN可直接处理基于网格表示的数据。本研究旨在提出一种面向GNN的可解释微调策略，并将其应用于非结构化网格流体动力学建模。最终成果是一种经过微调的GNN，通过自适应子图采样策略——该策略能分离出物理空间中与预测任务固有相关的区域——在保留基线预测能力的同时，为预训练基线GNN新增了可解释性。微调后的GNN在前向传播过程中会根据输入自适应生成的显式结构，可成为连接基线模型架构、优化目标与已知问题特定物理机制的可访问桥梁。此外，通过正则化流程，微调后的GNN还能在推理阶段识别出对应绝大多数预期预测误差的图节点，从而为基线模型增添了新颖的可解释误差标记能力。我们采用高雷诺数后向台阶绕流产生的非结构化流场数据进行了方法验证。