This work presents a novel resolution-invariant model order reduction strategy for multifidelity applications. We base our architecture on a novel neural network layer developed in this work, the graph feedforward network, which extends the concept of feedforward networks to graph-structured data by creating a direct link between the weights of a neural network and the nodes of a mesh, enhancing the interpretability of the network. We exploit the method's capability of training and testing on different mesh sizes in an autoencoder-based reduction strategy for parametrised partial differential equations. We show that this extension comes with provable guarantees on the performance via error bounds. The capabilities of the proposed methodology are tested on three challenging benchmarks, including advection-dominated phenomena and problems with a high-dimensional parameter space. The method results in a more lightweight and highly flexible strategy when compared to state-of-the-art models, while showing excellent generalisation performance in both single fidelity and multifidelity scenarios.

这项工作提出了一种新的解析度无关的模型降阶策略，适用于多保真度应用。我们基于一种新型的神经网络层，即图向前传播网络，构建了我们的架构，将前馈网络的概念扩展到图结构化数据上，通过在神经网络的权重和网格的节点之间创建直接链接，提高了网络的可解释性。我们利用该方法在自参数化偏微分方程的自动编码器降维策略中训练和测试不同网格尺寸。通过误差边界，我们证明了该扩展在性能方面具有可证明的保证。该方法在三个具有挑战性的基准测试中展示了其能力，包括以平流为主的现象和高维参数空间的问题。与最先进的模型相比，该方法的结果更加轻量且高度灵活，在单一保真度和多保真度情境下展现出了卓越的泛化性能。

GFN: 用于多保真应用中无分辨率限制的精简算子学习的图传递网络