Nonintrusive Nonlinear Reduced Order Models for Structures in Large Deformations: Validations to Atypical Structures and Basis Construction Aspects

The focus of this investigation is on reduced order models (ROMs) of the nonlinear geometric response of structures that are built nonintrusively, i.e., from standard outputs of commercial finite element codes. Several structures with atypical loading, boundary conditions, or geometry are considered to not only support the broad applicability of these ROMs but also to exemplify the different steps involved in determining an appropriate basis for the response. This basis is formed here as a combination of linear vibration modes and dual modes, and some of the steps involved follow prior work; others are novel aspects, all of which are covered in significant detail to minimize the expertise needed to develop these ROMs. The comparisons of the static and dynamic responses of these structures predicted by the ROMs and by the underlying finite element models demonstrate the high accuracy that can be achieved with the ROMs, even in the presence of significant nonlinearity.

Examples of computation of level lines of polynomials in a plane

Here we present a theory and 3 nontrivial examples of level lines calculating of real polynomials in the real plane. For this case we implement the following programs of computational algebra: factorization of a polynomial, calculation of the Grobner basis, construction of Newton's polygon, representation of an algebraic curve in a plane. Furthermore, it is shown how to overcome computational difficulties.

Gradient Boosts the Approximate Vanishing Ideal

In the last decade, the approximate vanishing ideal and its basis construction algorithms have been extensively studied in computer algebra and machine learning as a general model to reconstruct the algebraic variety on which noisy data approximately lie. In particular, the basis construction algorithms developed in machine learning are widely used in applications across many fields because of their monomial-order-free property; however, they lose many of the theoretical properties of computer-algebraic algorithms. In this paper, we propose general methods that equip monomial-order-free algorithms with several advantageous theoretical properties. Specifically, we exploit the gradient to (i) sidestep the spurious vanishing problem in polynomial time to remove symbolically trivial redundant bases, (ii) achieve consistent output with respect to the translation and scaling of input, and (iii) remove nontrivially redundant bases. The proposed methods work in a fully numerical manner, whereas existing algorithms require the awkward monomial order or exponentially costly (and mostly symbolic) computation to realize properties (i) and (iii). To our knowledge, property (ii) has not been achieved by any existing basis construction algorithm of the approximate vanishing ideal.

Quantity assessment method for the sustainability of a construction company

Introduction. Professional construction customers (investors) often face the problem of selecting a reliable contractor, when they have to assess construction companies for potential involvement in their projects guided, among other things, by a directly non-measurable emergent indicator of sustainability (from now on referred to as sustainability of a construction company). The given problem is of particular concern as most construction companies are now financially unstable. Materials and methods. The article defines the sustainability of a construction company. It also evaluates the sustainability of a construction company indicator by a number of statistical estimate iterations. The study proposes an evaluation method for quantitative integrated synthetic aggregators of sustainability of a construction company and identifies several private indicators Xj characterizing a construction company’s stable condition. Results. The advantages of the proposed evaluation method for the sustainability of a construction company are as follows: a unified information basis (construction operations indicators) for the assessment of qualitative and quantitative integrated synthetic aggregators of sustainability. This method is based on unified evaluation indicators of construction operations: technical, technological, organizational, and economical. The proposed method has an advantage of the versatility of the resultant own and comparative assessments of the sustainability of construction companies, visual clarity of obtained results, and relative ease of calculation procedures. Conclusions. This study illustrates a procedure developed for evaluating quantitative indicators of the sustainability of a construction company. This procedure offers a high level of accuracy in determining the reasons contributing to the lower sustainability of a construction company and identifying symptoms indicative of loss of sustainability. An integral indicator is formed that assesses the stability of the construction company according to the results of statistical analysis and represents a weighted sum of the values of the initial indicators of construction operations and activities of the enterprise. In this way, businesses can assess both their own condition and the condition of proposed contractors.

Accelerating many-nucleon basis generation for high performance computing enabled ab initio nuclear structure studies

We present the problem of generating a many-nucleon basis in [Formula: see text]-scheme for ab initio nuclear structure calculations in a symmetry-adapted no-core shell model framework. We first discuss and analyze the basis construction algorithm whose baseline implementation quickly becomes a significant bottleneck for large model spaces and heavier nuclei. The outcomes of this analysis are utilized to propose a new scalable version of the algorithm. Its performance is consequently studied empirically using the Blue Waters supercomputer. The measurements show significant acceleration achieved with over two orders of magnitude speedups realized for larger model spaces.