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Numerical simulations for flow and transport in subsurface porous media often prove computationally prohibitive due to property data availability at multiple spatial scales that can vary by orders of magnitude. A number of model order…
An algorithm is proposed for solving optimization problems arising in neural network training for supervised learning. The unique feature of the algorithm is the use of an auxiliary loss, in addition to the original loss employed for model…
In this paper we deal with verification of safety properties of parameterized systems with a tree topology. The verification problem is translated to a purely logical problem of finding a finite countermodel for a first-order formula, which…
Bayesian optimization (BO) is a sample-efficient global optimization algorithm for black-box functions which are expensive to evaluate. Existing literature on model based optimization in conditional parameter spaces are usually built on…
The central objective of this paper is to develop reduced basis methods for parameter dependent transport dominated problems that are rigorously proven to exhibit rate-optimal performance when compared with the Kolmogorov $n$-widths of the…
An alphabetic binary tree formulation applies to problems in which an outcome needs to be determined via alphabetically ordered search prior to the termination of some window of opportunity. Rather than finding a decision tree minimizing…
Many complex engineering systems consist of multiple subsystems that are developed by different teams of engineers. To analyse, simulate and control such complex systems, accurate yet computationally efficient models are required. Modular…
We present a perturbed subspace iteration algorithm to approximate the lowermost eigenvalue cluster of an elliptic eigenvalue problem. As a prototype, we consider the Laplace eigenvalue problem posed in a polygonal domain. The algorithm is…
We report our experiences for the development of a neighborhood algorithm implemented via tree-codes to optimize the performance of a discrete element method (DEM) for convex polytopes. Our implementation of the two-dimensional tree code…
Parameter-dependent models arise in many contexts such as uncertainty quantification, sensitivity analysis, inverse problems or optimization. Parametric or uncertainty analyses usually require the evaluation of an output of a model for many…
The optimization version of the cavity method for single instances, called Max-Sum, has been applied in the past to the Minimum Steiner Tree Problem on Graphs and variants. Max-Sum has been shown experimentally to give asymptotically…
In this work, we present an $\Omega\left(\min\{\log \Delta, \sqrt{\log n}\}\right)$ lower bound for Maximal Matching (MM) in $\Delta$-ary trees against randomized algorithms. By a folklore reduction, the same lower bound applies to Maximal…
In order to perform faster simulations, the model reduction is nowadays used in industrial contexts to solve large and complex problems. However, the efficiency of such an approach is sometimes cut by the interface size of the reduced model…
The reduced basis method is a powerful model reduction technique designed to speed up the computation of multiple numerical solutions of parametrized partial differential equations. We consider a quantity of interest, which is a linear…
In this contribution, we are concerned with model order reduction in the context of iterative regularization methods for the solution of inverse problems arising from parameter identification in elliptic partial differential equations. Such…
A novel multiphysics-decision tree learning algorithm is presented for (1) estimating transport properties in the variably saturated subsurface governed by explicitly coupled equations for water, heat, and solute transport; and (2)…
Automatic differentiation has become an important tool for optimization problems in computational science, and it has been applied to the Hartree-Fock method. Although the reverse-mode automatic differentiation is more efficient than the…
In order to optimally design materials, it is crucial to understand the structure-property relations in the material by analyzing the effect of microstructure parameters on the macroscopic properties. In computational homogenization, the…
Given a rooted tree and a ranking of its leaves, what is the minimum number of inversions of the leaves that can be attained by ordering the tree? This variation of the problem of counting inversions in arrays originated in mathematical…
Combining machine learning with econometric analysis is becoming increasingly prevalent in both research and practice. A common empirical strategy involves the application of predictive modeling techniques to 'mine' variables of interest…