Related papers: The surrogate matrix methodology: A reference impl…
We consider the sample efficient estimation of failure probabilities from expensive oracle evaluations of a limit state function via importance sampling (IS). In contrast to conventional ``two stage'' approaches, which first train a…
The first step towards applying isogeometric analysis techniques to solve PDE problems on a given domain consists in generating an analysis-suitable mapping operator between parametric and physical domains with one or several patches from…
Surrogates in lieu of expensive-to-evaluate performance functions can accelerate the reliability analysis greatly. This paper proposes a new two-stage framework for surrogate-aided reliability analysis named Surrogates for Importance…
Data-driven surrogate models are widely used for applications such as design optimization and uncertainty quantification, where repeated evaluations of an expensive simulator are required. For most partial differential equation (PDE)…
Surrogate models are often used as computationally efficient approximations to complex simulation models, enabling tasks such as solving inverse problems, sensitivity analysis, and probabilistic forward predictions, which would otherwise be…
Limiting the injection rate to restrict the pressure below a threshold at a critical location can be an important goal of simulations that model the subsurface pressure between injection and extraction wells. The pressure is approximated by…
The method of geometric harmonics is adapted to the situation of incomplete data by means of the iterated geometric harmonics (IGH) scheme. The method is tested on natural and synthetic data sets with 50--500 data points and dimensionality…
The computational models for geophysical flows are computationally very expensive to employ in multi-query tasks such as data assimilation, uncertainty quantification, and hence surrogate models sought to alleviate the computational burden…
We introduce a boundary penalization technique to improve the spectral approximation of isogeometric analysis (IGA). The technique removes the outliers appearing in the high-frequency region of the approximate spectrum when using the…
Isogeometrically enriched finite elements offer efficient localized isogeometric analysis (IGA) enrichment for numerical simulations involving large computational domains. This is achieved by employing surface enriched elements to interface…
The paper addresses Bayesian inferences in inverse problems with uncertainty quantification involving a computationally expensive forward map associated with solving a partial differential equations. To mitigate the computational cost, the…
In this paper we apply the INTERNODES method to solve second order elliptic problems discretized by Isogeometric Analysis methods on non-conforming multiple patches in 2D and 3D geometries. INTERNODES is an interpolation-based method that,…
Isogeometric approach applied to Boundary Element Methods is an emerging research area. In this context, the aim of the present contribution is that of investigating, from a numerical point of view, the Symmetric Galerkin Boundary Element…
We propose a new iterative algorithm for generating a subset of eigenvalues and eigenvectors of large matrices which generalizes the method of optimal relaxations. We also give convergence criteria for the iterative process, investigate its…
Modern computational methods, involving highly sophisticated mathematical formulations, enable several tasks like modeling complex physical phenomenon, predicting key properties and design optimization. The higher fidelity in these computer…
Numerical simulations are crucial for modeling complex systems, but calibrating them becomes challenging when data are noisy or incomplete and likelihood evaluations are computationally expensive. Bayesian calibration offers an interesting…
Surrogates have been proposed as classical simulations of the pretrained quantum learning models, which are capable of mimicking the input-output relation inherent in the quantum model. Quantum hardware within this framework is used for…
We introduce a method to construct a stochastic surrogate model from the results of dimensionality reduction in forward uncertainty quantification. The hypothesis is that the high-dimensional input augmented by the output of a computational…
Bayesian optimization (BO) has well-documented merits for optimizing black-box functions with an expensive evaluation cost. Such functions emerge in applications as diverse as hyperparameter tuning, drug discovery, and robotics. BO hinges…
Immersed boundary methods are high-order accurate computational tools used to model geometrically complex problems in computational mechanics. While traditional finite element methods require the construction of high-quality boundary-fitted…