A drop-in H-Bar training engine that escapes the σ-trap in neural PDE solvers via live σ/δ/α ODE integration, autonomous phase curriculum, and auto-falsification.
Neural PDE solvers (FNO, DeepONet, PINNs) are notorious for getting stuck in low-frequency, mean-predicting solutions — the σ-trap. σFlow-PDE introduces a training-time framework that:
- Live σ/δ/α ODE integration – Continuously evolves spectral coefficients during training to escape local spectral minima.
- Autonomous phase curriculum – Adaptively schedules training phases based on spectral convergence diagnostics.
- Auto-falsification – Automatically detects and rejects models that fail spectral consistency checks, ensuring robust generalization.
physics-ml · neural-operators · compositional-generalization · training-dynamics · pde-solver · h-bar-framework · ood-generalization · fno · deeponet · reproducible-ml
Distributed under the MIT License. See LICENSE for more information.