Related papers: A trust-region framework for optimization using He…
We present a novel way of accelerating hybrid surrogate methods for the calculation of failure probabilities. The main idea is to use mesh refinement in order to obtain improved local surrogates of low computation cost to simulate on. These…
A surrogate-based topology optimisation algorithm for linear elastic structures under parametric loads and boundary conditions is proposed. Instead of learning the parametric solution of the state (and adjoint) problems or the optimisation…
In machine learning, we are given a dataset of the form $\{(\mathbf{x}_j,y_j)\}_{j=1}^M$, drawn as i.i.d. samples from an unknown probability distribution $\mu$; the marginal distribution for the $\mathbf{x}_j$'s being $\mu^*$. We propose…
Multi-fidelity surrogate models combining dimensionality reduction and an intermediate surrogate in the reduced space allow a cost-effective emulation of simulators with functional outputs. The surrogate is an input-output mapping learned…
This paper develops an interpretable, non-intrusive reduced-order modeling technique using regularized kernel interpolation. Existing non-intrusive approaches approximate the dynamics of a reduced-order model (ROM) by solving a data-driven…
We propose a novel framework for analyzing convergence rates of stochastic optimization algorithms with adaptive step sizes. This framework is based on analyzing properties of an underlying generic stochastic process, in particular by…
Surrogate models of numerical relativity simulations of merging black holes provide the most accurate tools for gravitational-wave data analysis. Neural network-based surrogates promise evaluation speedups, but their accuracy relies on…
We develop a Trust Region method with Regularized Barzilai-Borwein step-size obtained in a previous paper for solving large-scale unconstrained optimization problems. Simultaneously, the non-monotone technique is combined to formulate an…
We address the problem of training models with black-box and hard-to-optimize metrics by expressing the metric as a monotonic function of a small number of easy-to-optimize surrogates. We pose the training problem as an optimization over a…
In the framework of reduced basis methods, we recently introduced a new certified hierarchical and adaptive surrogate model, which can be used for efficient approximation of input-output maps that are governed by parametrized partial…
Machine learning surrogates are increasingly employed to replace expensive computational models for physics-based reliability analysis. However, their use introduces epistemic uncertainty from model approximation errors, which couples with…
We consider scattered data approximation on product regions of equal and different dimensionality. On each of these regions, we assume quasi-uniform but unstructured data sites and construct optimal sparse grids for scattered data…
Derivative-free optimization methods are numerical methods for optimization problems in which no derivative information is used. Such optimization problems are widely seen in many real applications. One particular class of derivative-free…
A trust-region algorithm is presented for finding approximate minimizers of smooth unconstrained functions whose values and derivatives are subject to random noise. It is shown that, under suitable probabilistic assumptions, the new method…
In this contribution we device and analyze improved variants of the non-conforming dual approach for trust-region reduced basis (TR-RB) approximation of PDE-constrained parameter optimization that has recently been introduced in [Keil et…
This paper develops a surrogate model refinement approach for the simulation of dynamical systems and the solution of optimization problems governed by dynamical systems in which surrogates replace expensive-to-compute state- and…
We consider the uniform approximation of the smallest eigenvalue of a large parameter-dependent Hermitian matrix by that of a smaller counterpart obtained through projections. The projection subspaces are constructed iteratively by means of…
We describe a general approach for constructing a broad class of operators approximating high-dimensional curves based on geometric Hermite data. The geometric Hermite data consists of point samples and their associated tangent vectors of…
We consider Riemannian inequality-constrained optimization problems. Such problems inherit the benefits of Riemannian approach developed in the unconstrained setting and naturally arise from applications in control, machine learning, and…
With computational models becoming more expensive and complex, surrogate models have gained increasing attention in many scientific disciplines and are often necessary to conduct sensitivity studies, parameter optimization etc. In the…