GridapROMs.jl: Efficient reduced order modelling in the Julia programming language

Abstract: In this paper, we introduce GridapROMs, a Julia-based library for the numerical approximation of parameterized partial differential equations (PDEs) using a comprehensive suite of linear reduced order models (ROMs). The library is designed to be extendable and productive, leveraging an expressive high-level API built on the Gridap PDE solver backend, while achieving high performance through Julia's just-in-time compiler and advanced lazy evaluation techniques. GridapROMs is PDE-agnostic, enabling its application to a wide range of problems, including linear, nonlinear, single-field, multi-field, steady, and unsteady equations. This work details the library's key innovations, implementation principles, and core components, providing usage examples and demonstrating its capabilities by solving a fluid dynamics problem modeled by the Navier-Stokes equations in a 3D geometry.