This manuscript presents FoundPDE, a generative foundation model for symbolic discovery of partial differential equations from data.
Summary
FoundPDE maps discretized solution trajectories to symbolic PDE expressions. The broader workflow combines generative symbolic prediction with scientific feature information and coefficient refinement.
Role in my research
This is the central current manuscript in my research profile. It anchors the foundation-model side of my dissertation direction and motivates the later move toward PDEScientist, where symbolic proposal is embedded in an iterative evaluation loop.
Topics
- Symbolic PDE discovery.
- Transformer-based data-to-symbol modeling.
- Coefficient refinement.
- Sparse-data and noisy-data evaluation.
- Few-shot adaptation and compositional discovery.