Mesh-Free Convolution: Learned Spectral Attenuation and Transport
Learning solution operators for partial differential equations (PDEs) requires models that can represent spatial structure across grids and scales. This becomes especially important in time-dependent problems, where the learned operator is often used autoregressively: each predicted state is fed back as input to predict future states. In this setting, small spatial errors can be repeatedly propagated through the learned dynamics, leading to instability and drift, vitiating long-term solution fidelity. We propose Mesh-Free Convolutions (MFCs), filters defined in continuous space and discretized only at evaluation time. This allows the same learned filters to be applied across resolutions. ...
| Authors | Niloufar Zakariaei, Manav Manav, Eldad Haber |
|---|---|
| Primary category | cs.LG |
| Published | 11 October 2026 |
| Last updated at source | 11 October 2026 |
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