Semi-Supervised Neural Super-Resolution for Mesh-Based Simulations

TL;DR

SuperMeshNet is a semi-supervised neural framework that efficiently enhances mesh-based simulation resolution with minimal high-fidelity data, outperforming fully supervised methods.

Contribution

It introduces a semi-supervised, message passing neural network approach with inductive biases, reducing the need for high-fidelity data in super-resolution of PDE solutions.

Findings

Requires 90% less high-resolution data than fully supervised models.

Achieves lower RMSE compared to fully supervised benchmarks.

Leverages unpaired low-resolution data effectively.

Abstract

Mesh-based simulations provide high-fidelity solutions to partial differential equations (PDEs), but achieving such accuracy typically requires fine meshes, leading to substantial computational overhead. Super-resolution techniques aim to mitigate this cost by reconstructing high-resolution (HR), high-fidelity solutions from low-cost, low-resolution (LR) counterparts. However, training neural networks for super-resolution often demands large amounts of expensive HR supervision data. To address this challenge, we propose SuperMeshNet, an HR data-efficient super-resolution framework for mesh-based simulations aided by message passing neural networks (MPNNs). At its core, SuperMeshNet introduces complementary learning, a semi-supervised approach that effectively leverages both 1) a small amount of paired LR-HR data and 2) abundant unpaired LR data via two jointly trained, complementary MPNN-based models. Additionally, our model is enriched by inductive biases, which are empirically shown to further improve super-resolution performance. Extensive experiments demonstrate that SuperMeshNet requires 90% less HR data to achieve even lower root mean square error (RMSE) than that of the fully supervised benchmark without the inductive biases. The source code and datasets are available at https://github.com/jykim-git/SuperMeshNet.git.