Surrogate modeling and uncertainty quantification tasks for PDE systems are most often
considered as supervised learning problems where input and output data pairs are used for …

Reduced order modeling is an important and fast-growing research field in computational
science and engineering, motivated by several reasons, of which we mention just a few …

In this book we consider solution branches and bifurcations in nonlinear partial differential
equations (PDEs) as models from science (and some economics). Given a nonlinear PDE …

This work deals with optimal control problems as a strategy to drive bifurcating solution of
nonlinear parametrized partial differential equations towards a desired branch. Indeed, for …

We present and distribute a parallel finite-element toolbox written in the free software
FreeFEM for computing the Bogoliubov-de Gennes (BdG) spectrum of stationary solutions to …

In this paper we combine concepts from Riemannian optimization P.-A. Absil, R. Mahony,
and R. Sepulchre, Optimization Algorithms on Matrix Manifolds, Princeton University Press …

Topology optimization problems often support multiple local minima due to a lack of
convexity. Typically, gradient-based techniques combined with continuation in model …

Rotational Bose-Einstein condensates can exhibit quantized vortices as topological
excitations. In this study, the ground and excited states of the rotational Bose-Einstein …

Recently, a novel bifurcation technique known as deflated continuation was applied to the
single-component nonlinear Schrödinger (NLS) equation with a parabolic trap in two spatial …

We propose a constrained high-index saddle dynamics (CHiSD) method to search for index-
k saddle points of an energy functional subject to equality constraints. With Riemannian …