FoundPDE studies symbolic PDE discovery as a generative modeling problem. The model maps discretized solution trajectories to symbolic PDE expressions, then refines numerical coefficients after the symbolic form is proposed.
The project treats equation discovery as a data-to-symbol task. Instead of fitting a library of candidate terms from scratch for every dataset, the model learns across many PDE families and then predicts the symbolic structure of a new system.
What the project does
- Uses transformer-based sequence modeling for data-to-symbol prediction.
- Adds scientific feature information such as derivative and Fourier-style features.
- Refines coefficients using numerical optimization.
- Studies robustness under sparse data, noisy data, and few-shot adaptation.
Research questions
- Can a pre-trained model recover the correct symbolic PDE family from limited spatiotemporal data?
- How much do scientific features and coefficient refinement help beyond pure sequence prediction?
- Does few-shot adaptation help the model move beyond its pretraining distribution?
- Can the model recover composite equations by assembling simpler learned structures?
Current status
This is the current manuscript-level project. It is the foundation-model anchor of my dissertation direction and the starting point for the more iterative PDEScientist line of work.
Role in the broader agenda
FoundPDE is the foundation-model component of my current research arc. It establishes a direct generative approach before moving to more iterative, tool-using systems.