Numerical simulation of large-scale dynamical systems plays a fundamental role in studying
a wide range of complex physical phenomena; however, the inherent large-scale nature of …

Reduction strategies, such as model order reduction (MOR) or reduced basis (RB) methods,
in scientific computing may become crucial in applications of increasing complexity. In this …

This paper derives state space error bounds for the solutions of reduced systems
constructed using proper orthogonal decomposition (POD) together with the discrete …

Functions with jumps and kinks typically arising from parameter dependent or stochastic
hyperbolic PDEs are notoriously difficult to approximate. If the jump location in physical …

Reduced basis methods are projection-based model order reduction techniques for
reducing the computational complexity of solving parametrized partial differential equation …

In this work we propose and analyze a weighted reduced basis method to solve elliptic
partial differential equations (PDEs) with random input data. The PDEs are first transformed …

Abstract Physics-Informed Neural Network (PINN) has proven itself a powerful tool to obtain
the numerical solutions of nonlinear partial differential equations (PDEs) leveraging the …

The stochastic collocation method (Babuška et al. in SIAM J Numer Anal 45 (3): 1005–1034,
2007; Nobile et al. in SIAM J Numer Anal 46 (5): 2411–2442, 2008a; SIAM J Numer Anal 46 …

This work deals with the question of the resolution of nonlinear problems for many different
configurations in order to build a 'virtual chart'of solutions. The targeted problems are three …

In Bayesian inverse problems sampling the posterior distribution is often a challenging task
when the underlying models are computationally intensive. To this end, surrogates or …