Reducing Parametric Problems With Discontinuities Using Deep Learning

ABSTRACT

Model order reduction becomes necessary when dealing with large‐scale engineering problems governed by parametric Partial Differential Equations (PDEs). Conventional projection based reduced basis methods, e.g., based on proper orthogonal decomposition, are not only intrusive in nature but may also demand tailored strategies to efficiently deal with non‐linearities induced by the problem parameters. Reducing the order of non‐affine parametric problems while ensuring an efficient offline–online decomposition becomes more complicated if the solutions exhibit discontinuities. The nature of the problem itself, the type of parameters that is geometrical or physical, and the extent of their variations affect the complexity and reducibility of the problem. In this contribution, we investigate non‐intrusive and data‐driven methods to construct reduced order models that can be queried numerous times within few seconds while addressing the aforementioned issues. We are interested in scenarios with geometric and physical parameters, while targeting problems in fracture mechanics and inhomogeneous elasticity. Spline based discretizations to some parametric problems exhibiting the above‐mentioned properties are used to benchmark the efficiency and accuracy of the reduced order models to be presented.