Symbolic regression finds equations that fit data. The problem in engineering is that fitting data isn't enough — the equation must also satisfy physical laws. A constitutive model for rubber that fits the experimental stress-strain curve but violates thermodynamic consistency will predict impossible material behavior outside the calibration range.
The approach here uses large language models as physics-informed agents. The LLM doesn't just search the space of mathematical expressions. It zero-shot synthesizes executable physical constraints — specifically thermodynamic consistency and frame indifference — and uses them to prune the search space before fitting. The constitutive law must be convex, must be frame-invariant, must satisfy the second law. These aren't post-hoc checks. They're built into the candidate generation.
The result is a novel hybrid constitutive model combining a Mooney-Rivlin linear base with a rational locking term. It achieves high accuracy across multiple deformation modes, guarantees unconditional convexity, and maintains numerical stability under severe compression — exactly where industry-standard models fail. The model doesn't extrapolate dangerously because it was never allowed to learn a shape that would.
The general principle: constraining the search space by physics produces better results than searching freely and filtering afterward. The constraints aren't obstacles to discovery. They're navigation aids. The LLM's contribution isn't finding the answer — it's encoding the domain knowledge that defines which answers are physically admissible.