This review discusses Operator Inference, a nonintrusive reduced modeling approach that
incorporates physical governing equations by defining a structured polynomial form for the …

This article addresses the inference of physics models from data, from the perspectives of
inverse problems and model reduction. These fields develop formulations that integrate data …

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 …

Dynamical systems are at the core of computational models for a wide range of complex
phenomena and, as a consequence, the simulation of dynamical systems has become a …

This paper presents a physics-based data-driven method to learn predictive reduced-order
models (ROMs) from high-fidelity simulations and illustrates it in the challenging context of a …

Recently developed reduced-order modeling techniques aim to approximate nonlinear
dynamical systems on low-dimensional manifolds learned from data. This is an effective …

A method for the nonintrusive and structure-preserving model reduction of canonical and
noncanonical Hamiltonian systems is presented. Based on the idea of operator inference …

We present a new scientific machine learning method that learns from data a
computationally inexpensive surrogate model for predicting the evolution of a system …

A projection-based formulation is presented for non-linear model reduction of problems with
extreme scale disparity. The approach allows for the selection of an arbitrary, but complete …

We discuss model order reduction (MOR) for large-scale quadratic-bilinear (QB) systems
based on balanced truncation. The method for linear systems mainly involves the …