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

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. Program Title: GridapROMs.jl (version 1.0) CPC Library link to program files: https://doi.org/10.17632/h27nszy8bt.1 Developer’s repository link: https://github.com/Gridap/GridapROMs.jl Licensing provisions: MIT license Programming language: Julia Nature of problem: Numerical simulation of parameterized PDEs, including linear, nonlinear, single-field, multi-field, steady, and unsteady problems. Classical full-order models are computationally expensive, requiring intensive computations for each parameter configuration. Solution method: GridapROMs approximates the parameter-to-solution map using linear reduced order models. It constructs a reduced basis from the tangent hyperplane to the solution manifold and applies a (Petrov-)Galerkin projection to the full-order equations. Nonaffine parameter dependencies in the residual and/or Jacobian are efficiently handled using hyper-reduction techniques.