Title: Neural Super-Resolution for Mesh-Based Simulations under Scarce Supervision
Primary area: applications to physical sciences (physics, chemistry, biology, etc.)
Keywords: Mesh-Based Simulation; Super-Resolution; Semi-Supervised Learning

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, posing a major practical limitation. 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). As its core, SuperMeshNet introduces complementary learning that effectively leverages both a small amount of paired LR-HR data and abundant unpaired LR data via two jointly trained, complementary MPNN-based models. Theses models are enriched by task-specific inductive biases that emphasize local variations critical for accurate super-resolution. Extensive experiments demonstrate that SuperMeshNet–an MPNN-based model with inductive biases trained on a dataset with 10% paired LR--HR data and 90% unpaired LR data–achieves an even lower root mean square error (RMSE) than the same MPNN without inductive biases trained on 100% of LR-HR pairs, while in turn requiring 90% less HR data. The source code and datasets are available at https://anonymous.4open.science/r/SuperMeshNet/README.md.