This research direction studies how to recover symbolic partial differential equations from observed or simulated solution data. The goal is not only to predict a trajectory, but to recover a compact equation that can be inspected, tested, and reused.
For me, the important distinction is between learning a good simulator and discovering a scientific object. A black-box model can be useful, but a symbolic PDE gives a hypothesis that can be checked against known physics, transferred to new settings, and revised when it fails.
Current emphasis
- Learning from spatiotemporal solution fields.
- Handling sparse, noisy, or heterogeneous data.
- Distinguishing symbolic correctness from downstream trajectory accuracy.
- Building evaluation loops that make failures diagnosable.
Questions I care about
- When does a model recover the right symbolic family rather than a numerically convenient surrogate?
- How much data are needed before the governing terms become identifiable?
- How should coefficient fitting, derivative estimation, and residual scoring be separated from symbolic proposal?
- What failure modes are caused by the model, and what failures are really caused by the evaluator or data representation?
Why it matters
Scientific machine learning becomes more useful when the output is an interpretable scientific object, not only a black-box predictor. Symbolic PDE discovery is one version of that problem: the model should produce a governing equation that a scientist can read.
Related work on this site
- FoundPDE studies direct data-to-symbol PDE prediction.
- PDEScientist studies iterative, evaluator-guided PDE discovery.
- PDE Evaluation Loops focuses on scoring contracts and trace-based diagnosis.