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Interpolation-based methods are well-established and effective approaches for the efficient generation of accurate reduced-order surrogate models. Common challenges for such methods are the automatic selection of good or even optimal…

In computational inverse problems, it is common that a detailed and accurate forward model is approximated by a computationally less challenging substitute. The model reduction may be necessary to meet constraints in computing time when…

In this paper we develop and study adaptive empirical Bayesian smoothing splines. These are smoothing splines with both smoothing parameter and penalty order determined via the empirical Bayes method from the marginal likelihood of the…

Porous structures are intricate solid materials with numerous small pores, extensively used in fields like medicine, chemical engineering, and aerospace. However, the design of such structures using computer-aided tools is a time-consuming…

Kernel smoothing is a widely used nonparametric method in modern statistical analysis. The problem of efficiently conducting kernel smoothing for a massive dataset on a distributed system is a problem of great importance. In this work, we…

Model-based iterative reconstruction (MBIR) techniques have demonstrated many advantages in X-ray CT image reconstruction. The MBIR approach is often modeled as a convex optimization problem including a data fitting function and a penalty…

Surface reconstruction from magnetic resonance (MR) imaging data is indispensable in medical image analysis and clinical research. A reliable and effective reconstruction tool should: be fast in prediction of accurate well localised and…

In this paper we investigate the convergence of the Policy Iteration Algorithm (PIA) for a class of general continuous-time entropy-regularized stochastic control problems. In particular, instead of employing sophisticated PDE estimates for…

We present a cost-efficient and versatile method to map an unknown 3D freeform surface using only sparse measurements while the end-effector of a robotic manipulator moves along the surface. The geometry is locally approximated by a plane,…

Acquiring an anatomical map from position data is important for medical applications where catheters interact with soft tissues. To improve autonomous navigation in these settings, we require information beyond nonparametric maps typically…

Optimization of Reconfigurable Intelligent Surfaces (RIS) via a previously introduced method is effective, but time-consuming, because multiport impedance or scatter matrices are required for each transmitter and receiver position, which…

We develop a novel randomized conjugate gradient least squares (RCGLS) method for solving least-squares problems, in which iterative sketching is employed at each step to reduce the dimension and hence the computational cost. In particular,…

In this paper we consider a family of algorithms for approximate implicitization of rational parametric curves and surfaces. The main approximation tool in all of the approaches is the singular value decomposition, and they are therefore…

Poisson surface reconstruction (PSR) remains a popular technique for reconstructing watertight surfaces from 3D point samples thanks to its efficiency, simplicity, and robustness. Yet, the existing PSR method and subsequent variants work…

Computing a quasi-developable strip surface bounded by design curves finds wide industrial applications. Existing methods compute discrete surfaces composed of developable lines connecting sampling points on input curves which are not…

Sampling-based controllers, such as Model Predictive Path Integral (MPPI) methods, offer substantial flexibility but often suffer from high variance and low sample efficiency. To address these challenges, we introduce a hybrid…

This paper presents an adaptive discretization strategy for level set topology optimization of structures based on hierarchical B-splines. This work focuses on the influence of the discretization approach and the adaptation strategy on the…

B\'ezier splines are widely available in various systems with the curves and surface designs. In general, the B\'ezier spline can be specified with the B\'ezier curve segments and a B\'ezier curve segment can be fitted to any number of…

Least squares is by far the simplest and most commonly applied computational method in many fields. In almost all applications, the least squares objective is rarely the true objective. We account for this discrepancy by parametrizing the…

Recently, the influence of potentially present symmetries has begun to be studied in complex networks. A typical way of studying symmetries is via the automorphism group of the corresponding graph. Since complex networks are often subject…