Shared-structure sparse identification for parametric reduced-order modelling

Parametric reduced-order modelling plays an important role in engineering applications, where repeated simulations under varying parameters can make direct high-fidelity computation prohibitively expensive. To achieve both computational efficiency and interpretability, one appealing strategy is to identify explicit dynamical systems in a low-dimensional latent space. However, latent dynamical system identification remains challenging in the parametric setting, since complex models tend to be numerically unstable, whereas sparse models identified independently at different parameter values often fail to generalise because the active terms vary across the parameter domain. To address these issues, we propose a parametric non-intrusive reduced-order modelling framework based on shared-structure sparse regression (SSSR), which extends our previous sparse latent dynamical system identification framework Lin et al. (2025) to parametric problems. Proper orthogonal decomposition is used to obtain a low-dimensional latent representation, and SSSR is developed to identify latent governing equations with a common support across the parameter domain. Radial basis function interpolation and neural networks are then employed to learn the mapping from physical parameters to the coefficients of the identified latent system. In addition, a theoretical analysis is provided to show the residual monotonicity of SSSR and to relate the coefficient prediction error to the latent-state prediction error. By enforcing a shared sparse structure, the proposed method reduces model complexity, improves interpretability, and makes the parameter-to-coefficient mapping more reliable. Numerical results on four parametric PDE benchmark problems show that the proposed method yields accurate predictions and robust generalisation to unseen parameters.