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Isogeometric analysis was proposed to bridge the gap between computer-aided design and numerical discretization. However, standard multi-patch isogeometric analysis mandates conformal discretizations across patch interfaces, posing…
We present a fully explicit dynamic formulation for geometrically exact shear-deformable beams. The starting point of this work is an existing isogeometric collocation (IGA-C) formulation which is explicit in the strict sense of the time…
Near isometric orthogonal embeddings to lower dimensions are a fundamental tool in data science and machine learning. In this paper, we present the construction of such embeddings that minimizes the maximum distortion for a given set of…
The numerical simulation of additive manufacturing techniques promises the acceleration of costly experimental procedures to identify suitable process parameters. We recently proposed Floating Isogeometric Analysis (FLIGA), a new…
Discrete optimization belongs to the set of $\mathcal{NP}$-hard problems, spanning fields such as mixed-integer programming and combinatorial optimization. A current standard approach to solving convex discrete optimization problems is the…
The development of materials with specific structural properties is of huge practical interest, for example, for medical applications or for the development of light weight structures in aeronautics. In this article, we combine shape…
In this work we investigate the practicality of stochastic gradient descent and recently introduced variants with variance-reduction techniques in imaging inverse problems. Such algorithms have been shown in the machine learning literature…
Many recent successes of machine learning went hand in hand with advances in optimization. The exchange of ideas between these fields has worked both ways, with machine learning building on standard optimization procedures such as gradient…
We consider elliptic problems in multipatch isogeometric analysis (IGA) where the patch parameterizations may be singular. Specifically, we address cases where certain dimensions of the parametric geometry diminish as the singularity is…
The matrix formation associated to high-order discretizations is known to be numerically demanding. Based on the existing procedure of interpolation and lookup, we design a multiscale assembly procedure to reduce the exorbitant assembly…
Statistical design of experiments is widely used in scientific and industrial investigations. A generalized minimum aberration (GMA) orthogonal array is optimum under the well-established, so-called GMA criterion, and such an array can…
It is classical that, when the small deformation is assumed, the incremental analysis problem of an elastoplastic structure with a piecewise-linear yield condition and a linear strain hardening model can be formulated as a convex quadratic…
Physics-informed neural networks (PINNs) have effectively been demonstrated in solving forward and inverse differential equation problems, but they are still trapped in training failures when the target functions to be approximated exhibit…
Finding tight bounds on the optimal solution is a critical element of practical solution methods for discrete optimization problems. In the last decade, decision diagrams (DDs) have brought a new perspective on obtaining upper and lower…
This paper presents a novel variational formulation to simulate linear free-surface flow. The variational formulation is suitable for higher-order finite elements and higher-order and higher-continuity shape functions as employed in…
Physics-informed neural networks (PINNs) formulate the solution of partial differential equations as residual minimization problems over neural network parameterizations. Although highly flexible, optimization of PINNs using modern variants…
Implicit Neural representations (INRs) are widely used for scientific data reduction and visualization by modeling the function that maps a spatial location to a data value. Without any prior knowledge about the spatial distribution of…
The problems of Lasso regression and optimal design of experiments share a critical property: their optimal solutions are typically \emph{sparse}, i.e., only a small fraction of the optimal variables are non-zero. Therefore, the…
We provide explicit expressions for quadrature rules on the space of $C^1$ cubic splines with non-uniform, symmetrically stretched knot sequences. The quadrature nodes and weights are derived via an explicit recursion that avoids an…
The design of fusion devices is typically based on computationally expensive simulations. This can be alleviated using high aspect ratio models that employ a reduced number of free parameters, especially in the case of stellarator…