Related papers: Compressing Random Microstructures via Stochastic …

We demonstrate existence of a tile assembly system that self-assembles the statistically self-similar Sierpinski Triangle in the Winfree-Rothemund Tile Assembly Model. This appears to be the first paper that considers self-assembly of a…

Discrete rearranging patterns include cellular patterns, for instance liquid foams, biological tissues, grains in polycrystals; assemblies of particles such as beads, granular materials, colloids, molecules, atoms; and interconnected…

For uncertainty propagation of highly complex and/or nonlinear problems, one must resort to sample-based non-intrusive approaches [1]. In such cases, minimizing the number of function evaluations required to evaluate the response surface is…

This paper addresses the computational challenges in reliability-based topology optimization (RBTO) of structures associated with the estimation of statistics of the objective and constraints using standard sampling methods, and overcomes…

We propose a method based on the Wang-Landau algorithm to numerically generate the spectral densities of random matrix ensembles. The method employs Dyson's log-gas formalism for random matrix eigenvalues and also enables one to…

A topology optimization method is presented for the design of periodic microstructured materials with prescribed homogenized nonlinear constitutive properties over finite strain ranges. The mechanical model assumes linear elastic isotropic…

Disordered hyperuniform materials are an emerging class of exotic amorphous states of matter that endow them with singular physical properties. Here, we generalize the Fourier-space based numerical construction procedure for designing {\it…

We develop a supervised-learning-based approach for monitoring and diagnosing texture-related defects in manufactured products characterized by stochastic textured surfaces that satisfy the locality and stationarity properties of Markov…

Collocation has become a standard tool for approximation of parameterized systems in the uncertainty quantification (UQ) community. Techniques for least-squares regularization, compressive sampling recovery, and interpolatory reconstruction…

In this effort, we propose a convex optimization approach based on weighted $\ell_1$-regularization for reconstructing objects of interest, such as signals or images, that are sparse or compressible in a wavelet basis. We recover the…

This paper presents a novel non-linear model reduction method: Probabilistic Manifold Decomposition (PMD), which provides a powerful framework for constructing non-intrusive reduced-order models (ROMs) by embedding a high-dimensional system…

We introduce a differentiable clustering method based on stochastic perturbations of minimum-weight spanning forests. This allows us to include clustering in end-to-end trainable pipelines, with efficient gradients. We show that our method…

This paper presents a randomized algorithm for computing the near-optimal low-rank dynamic mode decomposition (DMD). Randomized algorithms are emerging techniques to compute low-rank matrix approximations at a fraction of the cost of…

Low-rank matrix approximations, such as the truncated singular value decomposition and the rank-revealing QR decomposition, play a central role in data analysis and scientific computing. This work surveys and extends recent research which…

Distributionally balanced sampling designs are low-discrepancy probability designs obtained by minimizing the expected discrepancy between the auxiliary-variable distribution of a random sample and the target population distribution.…

Topology optimization of modular structures and mechanisms enables balancing the performance of automatically-generated individualized designs, as required by Industry 4.0, with enhanced sustainability by means of component reuse. For…

We study the properties of sparse reconstruction of transformed $\ell_1$ (TL1) minimization and present improved theoretical results about the recoverability and the accuracy of this reconstruction from undersampled measurements. We then…

Unstructured pruning has the limitation of dealing with the sparse and irregular weights. By contrast, structured pruning can help eliminate this drawback but it requires complex criterion to determine which components to be pruned. To this…

The paper discusses the construction of high dimensional spatial discretizations for arbitrary multivariate trigonometric polynomials, where the frequency support of the trigonometric polynomial is known. We suggest a construction based on…

Multiscale techniques have been widely shown to potentially overcome the limitation of homogenization schemes in representing the microscopic failure mechanisms in heterogeneous media as well as their influence on their structural response…