相关论文: The surrogate matrix methodology: Low-cost assembl…
The combination of the Reduced Basis and the Empirical Interpolation Method (EIM) approaches have produced outstanding results in many disciplines. In particular, in gravitational wave (GW) science these results range from building…
We consider and discretize a mixed formulation for linear elasticity with weakly imposed symmetry in two and three dimensions. Whereas existing methods mainly deal with simplicial or polygonal meshes, we take advantage of isogeometric…
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…
This work is in the context of blackbox optimization where the functions defining the problem are expensive to evaluate and where no derivatives are available. A tried and tested technique is to build surrogates of the objective and the…
The advent of multi-material additive manufacturing and automated composite manufacturing has enabled the design of structures featuring complex curvilinear anisotropy. To take advantage of the new design space, efficient computational…
Recent advances in the field of machine learning open a new era in high performance computing. Applications of machine learning algorithms for the development of accurate and cost-efficient surrogates of complex problems have already…
Surrogate models are used for global approximation of responses generated by expensive computer experiments like CFD applications. In this paper, we make use of structural similarities which are shared by a class of related problems. We…
We compare convergence of isogeometric analysis (IGA), a spline modification of finite element method (FEM), with FEM in the context of our real space code for ab-initio electronic structure calculations of non-periodic systems. The…
AI-driven surrogate modeling has become an increasingly effective alternative to physics-based simulations for 3D design, analysis, and manufacturing. These models leverage data-driven methods to predict physical quantities traditionally…
Multi-material problems often exhibit complex geometries along with physical responses presenting large spatial gradients or discontinuities. In these cases, providing high-quality body-fitted finite element analysis meshes and obtaining…
Gaussian processes (GPs) serve as flexible surrogates for complex surfaces, but buckle under the cubic cost of matrix decompositions with big training data sizes. Geospatial and machine learning communities suggest pseudo-inputs, or…
In this paper, we focus on solving a sequence of linear systems with an identical (or similar) coefficient matrix. For this type of problems, we investigate the subspace correction and deflation methods, which use an auxiliary matrix…
The present paper proposes a Bayesian framework for inverse problems that seamlessly integrates optimization and inversion to enable rapid surrogate modeling, accurate parameter inference, and rigorous uncertainty quantification. Bayesian…
This work presents an efficient quadrature rule for shell analysis fully integrated in CAD by means of Isogeometric Analysis (IGA). General CAD-models may consist of trimmed parts such as holes, intersections, cut-offs etc. Therefore, IGA…
Inverse problems are prevalent in both scientific research and engineering applications. In the context of Bayesian inverse problems, sampling from the posterior distribution can be particularly challenging when the forward models are…
This paper presents a novel learning-based approach to construct a surrogate problem that approximates a given parametric nonconvex optimization problem. The surrogate function is designed to be the minimum of a finite set of functions,…
The study of quantum three-body problems has been centered on low-energy states that rely on accurate numerical approximation. Recently, isogeometric analysis (IGA) has been adopted to solve the problem as an alternative but more robust…
A Skeleton-stabilized IsoGeometric Analysis (SIGA) technique is proposed for incompressible viscous flow problems with moderate Reynolds number. The proposed method allows utilizing identical finite dimensional spaces (with arbitrary…
In this paper we discuss the numerical solution on a simple 2D domain of the Helmoltz equation with mixed boundary conditions. The so called radiation problem depends on the wavenumber constant parameter k and it is inspired here by medical…
A new algorithm is developed to tackle the issue of sampling non-Gaussian model parameter posterior probability distributions that arise from solutions to Bayesian inverse problems. The algorithm aims to mitigate some of the hurdles faced…