Disentangling Invariant Structures from Parameter Variations for Parameterized Equation Discovery

While Symbolic Regression (SR) excels at discovering mathematical expressions from data, it traditionally treats numerical coefficients as fixed, recovering isolated mathematical instances. However, many scientific applications require Parameterized Equation Discovery (PED): identifying an invariant symbolic skeleton alongside instance-specific parameters across multiple parameter-varying environments. A fundamental challenge in PED is parameter-induced structural ambiguity, where parameter variations can drastically alter the data distribution of a single skeleton or cause distinct skeletons to become observationally aliased. Existing multi-environment SR methods rely heavily on heuristic search and post-hoc aggregate fitness evaluation, lacking a data-driven prior to separate structural invariants from parameter variations. In this work, we propose DisPV (Disentangling invariant structures from Parameter Variations), the first pre-training framework specifically designed for PED. DisPV designs a dual-stream architecture that explicitly disentangles universal mathematical structures from environment-specific constants at the representation level. Through a cross-environment contrastive learning strategy, the skeleton stream isolates invariant structural features, while the parallel constant stream predicts instance-specific parameters. By learning structural invariance directly from parameter-varying data representations, DisPV provides a highly accurate structural prior. Extensive experiments on synthetic and physics-inspired benchmarks demonstrate that DisPV, coupled with genetic programming refinement, significantly outperforms state-of-the-art search-based baselines with an average $R^2=0.9$.