A meshfree exterior calculus for generalizable and data-efficient learning of physics from point clouds

1. 1Build a meshfree exterior calculus framework using sparse Schur complement solves to equip ε-ball graphs with virtual node and edge measures
2. 2Apply the MEEC framework to point clouds to learn structure-preserving descriptions of physics
3. 3Configure MEEC-Net, a data-efficient surrogate model, to transfer across resolutions, geometries, and physical parameters
4. 4Test the generalizability of MEEC-Net on various physics problems and datasets
5. 5Compare the performance of MEEC-Net with other state-of-the-art methods for learning physics from point clouds

Researchers and engineers working on physics-informed neural networks, computational physics, and geometric deep learning can benefit from this approach to improve model generalizability and data efficiency

💡 Meshfree exterior calculus enables the creation of data-efficient and generalizable models for learning physics from point clouds, allowing for transferability across different resolutions, geometries, and physical parameters

🌐 Introducing meshfree exterior calculus for data-efficient learning of physics from point clouds! 🚀 Generalizable and transferable models across resolutions and geometries 📈