research
A Foundation Model Writes the Equation Behind the Data
FoundPDE maps observed trajectories to symbolic partial differential equations and exposes where noise breaks recovery.
Summary
FoundPDE maps observed trajectories to symbolic partial differential equations and exposes where noise breaks recovery.
FoundPDE turns discretized space-time trajectories into symbolic equations, combining a transformer with Fourier and derivative features plus coefficient refinement. On 20 clean in-domain PDE families, the authors report 97.50 percent type recognition; with a 2 percent multiplicative-noise level, 94.43 percent, falling to 52.09 percent at 10 percent noise. Few-shot tuning recovered more than 90 percent on four held-out composite families. The model is a discovery aid whose equations still require scientific validation.
Why it matters
FoundPDE maps observed trajectories to symbolic partial differential equations and exposes where noise breaks recovery.
Limits and context
No additional limitation was separately recorded.
Key claims
FoundPDE maps observed trajectories to symbolic partial differential equations and exposes where noise breaks recovery.
Evidence: source-2026-10-21-008
Sources
- arXiv preprint 2610.26963, original v1arXiv · primary research
Corrections
No corrections have been recorded for this story.