Physics Intermediate Representation (PIR): A Structured Framework for Automated Physical Law Discovery

Physics Intermediate Representation (PIR) is a structured framework for automated discovery of physical laws from observational data. This paper formalises the PIR object as a six-tuple (expression, variables, dimensional signature, parameters, residual, type), defines a five-stage discovery pipeline (candidate generation, dimensional filtering, coefficient estimation, residual refinement, sparse model selection), and describes five canonical PIR types: Equation, ForceLaw, ODE, Lagrangian, and Hamiltonian. PIR bridges data-driven symbolic regression and downstream scientific reasoning by wrapping discovered expressions in typed, semantically rich objects that carry physical units, fitted parameters with uncertainties, and goodness-of-fit residuals. A comparison table shows that PIR is the only current framework providing typed output, dimensional consistency, parameter uncertainties, and Lagrangian-type identification simultaneously. The framework is grounded in the Neural Lagrangian Series (Papers 1–6), which achieved parameter recovery errors below 1.3% on scalar field and classical mechanics problems.