1 Introduction -- 1.1 Recurrent issues in numerical simulation -- 1.2 Model reduction: information versus relevant information -- 1.3 PGD at a glance -- 1.4 Revisiting the simulation challenges -- 1.5 A brief state of the art on PGD-based model order reduction -- 2 Multiscale modelling -- 2.1 From quantum mechanics to kinetic theory -- 2.2 Advanced solvers for multi-dimensional models -- 2.3 Numerical examples -- 2.4 Conclusions -- 3 Homogenization -- 3.1 Homogenization of linear heterogenous models -- 3.2 Non-concurrent nonlinear homogenization -- 3.3 Numerical examples -- 3.4 Conclusions -- 4 Coupled models -- 4.1 Efficient coupling of global and local models -- 4.2 Fully globalized local models -- 4.3 Heterogeneous time integration -- 4.4 Numerical example -- 4.5 Discussion -- 5 Parametric models in evolving domains -- 5.1 Evolving domains issues -- 5.2 PGD in evolving domains -- 5.3 Separated representation constructor -- 5.4 Numerical test -- 5.5 Towards parametric modeling in evolving domains -- 5.6 Numerical test involving parametric modeling -- 5.7 Conclusions -- 6 Space separation -- 6.1 In-plane/out-of-plane separated representation -- 6.2 Laminates -- 6.3 Conclusions -- 7 Process optimization -- 7.1 Parametric boundary conditions -- 7.2 Parametric modeling of pultrusion -- 7.3 Optimization strategy -- 7.4 Conclusion 8 Shape optimization -- 8.1 Introduction -- 8.2 Geometrical parameters as extra-coordinates -- 8.3 Numerical results -- 8.4 Conclusions -- 9 DDDAS -- 9.1 Introduction to DDDAS -- 9.2 PGD solution of a flowing process -- 9.3 Simulating a breakdown scenario -- 9.4 Post-processing in a smartphone -- 9.5 Conclusions -- 10 Inverse analysis -- 10.1 PGD based parameter identification -- 10.2 PGD based Cauchy’s problem -- 10.3 Parameter identification examples -- 10.4 Cauchy’s problem example -- 10.5 Conclusions -- 11 Tape placement -- 11.1 Parametric modeling -- 11.2 ATP thermal model -- 11.3 ATP mechanical modeling -- 11.4 Numerical results -- 11.5 Conclusions -- 12 Augmented learning -- 12.1 Towards augmented learning -- 12.2 Examples of augmented learning -- 12.3 Conclusions -- References -- Index.