Feature Description
This feature adds a Topological Monitor for Fourier Neural Operators (FNOs) in PINA. It tracks Betti numbers (β₀, β₁) during validation to detect structural hallucinations (ghost islands) that standard MSE loss misses.
Motivation
FNOs are spectrally accurate but topologically blind. By truncating high frequencies (n_modes), they smooth out sharp features, often generating non-physical disconnected components. This monitor gives engineers real-time visibility into structural health.
Proposed Implementation
TopologyMonitor: PyTorch Lightning callback using GUDHI's CubicalComplexTopologicalProfiler: Lazy-loaded profiler with state consistencyGudhiBackend: Persistent homology with persistence filtering- Tutorial notebook demonstrating on Darcy Flow
Dependencies
- Requires
gudhi (optional, installed via pip install gudhi)
Additional Context
I have already implemented this feature and will submit a PR once this issue is created.
Feature Description
This feature adds a Topological Monitor for Fourier Neural Operators (FNOs) in PINA. It tracks Betti numbers (β₀, β₁) during validation to detect structural hallucinations (ghost islands) that standard MSE loss misses.
Motivation
FNOs are spectrally accurate but topologically blind. By truncating high frequencies (
n_modes), they smooth out sharp features, often generating non-physical disconnected components. This monitor gives engineers real-time visibility into structural health.Proposed Implementation
TopologyMonitor: PyTorch Lightning callback using GUDHI's CubicalComplexTopologicalProfiler: Lazy-loaded profiler with state consistencyGudhiBackend: Persistent homology with persistence filteringDependencies
gudhi(optional, installed viapip install gudhi)Additional Context
I have already implemented this feature and will submit a PR once this issue is created.