In recent years, we have witnessed a significant shift toward ever-more complex and ever-
larger-scale systems in the majority of the grand societal challenges tackled in applied …

In many situations across computational science and engineering, multiple computational
models are available that describe a system of interest. These different models have varying …

Data-driven discovery is revolutionizing how we model, predict, and control complex
systems. Now with Python and MATLAB®, this textbook trains mathematical scientists and …

Nearly all model-reduction techniques project the governing equations onto a linear
subspace of the original state space. Such subspaces are typically computed using methods …

This paper considers the creation of parametric surrogate models for applications in science
and engineering where the goal is to predict high-dimensional output quantities of interest …

A reduced basis method based on a physics-informed machine learning framework is
developed for efficient reduced-order modeling of parametrized partial differential equations …

To overcome the limitations associated with purely physics-based and data-driven modeling
methods, hybrid, physics-based data-driven models have been developed, with improved …

Numerical simulation of parametrized differential equations is of crucial importance in the
study of real-world phenomena in applied science and engineering. Computational methods …

A data-driven framework is proposed towards the end of predictive modeling of complex
spatio-temporal dynamics, leveraging nested non-linear manifolds. Three levels of neural …

This work presents an optimal model management strategy that exploits multifidelity
surrogate models to accelerate the estimation of statistics of outputs of computationally …