Complex engineering systems described by parameteric partial differential equations often render high-fidelity simulations computationally prohibitive, making model oder reduction indispensable. Projection-based reduced-order modeling (ROM) techniques that rely on proper orthogonal decomposition (POD), are typically of intrusive nature [1]. Complex time-dependent parametric problems as well as static problems involving discontinuities are challenging to reduce. In particular,the complexity and reducibility of a problem highly depend on its inherent characteristics and on the type of parametrization. POD in combination with neural networks can be used as a non-intrusive data-driven ROM able to output numerous solutions within few seconds [2]. The goal of this contribution is to enhance such ROMs using networks with B-splines functions [4] and to investigate their capabilities for a wider range of problems. We further extend the ROM to non-linear dimensionality reduction [3] to tackle problems with non-linear manifolds. We target problems with geometrical and physical parameterization in fracture mechanics, inhomogeneous elasticity and binary phase separation process modelled using the Cahn-Hilliard equation. The reduced order models are benchmarked in comparison with the high-fidelity models generated using spline-based discretization. REFERENCES [1] Margarita Chasapi, Pablo Antolin and Annalisa Buffa, A localized reduced basis approach for unfitted domain methods on parameterized geometries, Computer Methods in Applied Mechanics and Engineering, 410, 115997, 2023. [2] Jan S. Hesthaven and Stefano Ubbiali, Non-intrusive reduced order modeling of nonlinear problems using neural networks, Journal of Computational Physics, 363, 55-78, 2018. [3] Nicola Franco, Andrea Manzoni and Paolo Zunino, A deep learning approach to reduced order modelling of parameter dependent partial differential equations, Mathematics of Computation, 92.340, 483-524, 2023. [4] Pakshal Bohra, Joaquim Campos, Harshit Gupta, Shayan Aziznejad, and Michael Unser, Learning activation functions in deep (spline) neural networks, IEEE Open Journal of Signal Processing ,1, 295-309, 2020.