5 papers
On the sample complexity of the active subspace method
Fabio Nobile, Matteo Raviola, Raúl Tempone
Active subspaces identify low-dimensional linear structure in high-dimensional parameter-to-output maps by estimating the dominant eigenspace of a gradient covariance operator. In…
Dirac-Frenkel dynamics with inertia for nonlinearly parametrized solutions of evolution problems
Matteo Raviola, Benjamin Peherstorfer
Even when Dirac-Frenkel dynamics determine a well-defined evolution in function space, the corresponding parameter dynamics can be non-unique or ill-conditioned for redundant nonli…
A Dirac-Frenkel-Onsager principle: Instantaneous residual minimization with gauge momentum for nonlinear parametrizations of PDE solutions
Matteo Raviola, Benjamin Peherstorfer
Dirac-Frenkel instantaneous residual minimization evolves nonlinear parametrizations of PDE solutions in time, but ill-conditioning can render the parameter dynamics non-unique. We…
Stochastic gradient with least-squares control variates
Fabio Nobile, Matteo Raviola, Nathan Schaeffer
The stochastic gradient descent (SGD) method is a widely used approach for solving stochastic optimization problems, but its convergence is typically slow. Existing variance reduct…
A function approximation algorithm using multilevel active subspaces
Fabio Nobile, Matteo Raviola, Raul Tempone
The Active Subspace (AS) method is a widely used technique for identifying the most influential directions in high-dimensional input spaces that affect the output of a computationa…