STORM: a nonlinear model order reduction method via symmetric tensor decomposition

Nonlinear model order reduction has always been a challenging but important task in various science and engineering fields. In this paper, a novel symmetric tensor-based orderreduction method (STORM) is presented for simulating largescale nonlinear systems. The multidimensional data structure of symmetric tensors, as the higher order generalization of symmetric matrices, is utilized for the effective capture of highorder nonlinearities and efficient generation of compact models. Compared to the recent tensor-based nonlinear model order reduction (TNMOR) algorithm [1], STORM shows advantages in two aspects. First, STORM avoids the assumption of the existence of a low-rank tensor approximation. Second, with the use of the symmetric tensor decomposition, STORM allows significantly faster computation and less storage complexity than TNMOR. Numerical experiments demonstrate the superior computational efficiency and accuracy of STORM against existing nonlinear model order reduction methods.postprin

An Efficient Two-level DC Operating Points Finder for Transistor Circuits

DC analysis, as a foundation for the simulation of many electronic circuits, is concerned with locating DC operating points. In this paper, a new and efficient algorithm to find all DC operating points is proposed for transistor circuits. The novelty of this DC operating points finder is its two-level simple implementation based on the affine arithmetic preconditioning and interval contraction method. Compared to traditional methods such as homotopy, this finder offers a dramatically faster way of computing all roots, without sacrificing any accuracy. Explicit numerical examples and comparative analysis are given to demonstrate the feasibility and accuracy of the proposed approach

Regional characterization of the long-term change in soil organic carbon under intensive agriculture

To study the change in soil organic carbon (SOC) since it was recorded during the Belgian National Soil Survey some 40 years ago, we recently revisited 939 locations still under use as arable land. The study area comprised almost the entire province of West Flanders (about 3000 km(2)) characterized by profound changes in its arable land management. Taking the increased ploughing depth (by 9.8 cm on average) into account, a significant (P = 0.001) increase of the SOC content by 0.2% on average was found, Expressed as an amount, the SOC in the topsoil rose by 9.3 t/ha on average, representing an increase of 25%. This is comparable with the conversion of arable land into grassland for 2 to 3 decades. Geostatistical tools were used to map the SOC at the two times of observation. These showed that most of the spatial variation occurred within about 4 km. Since the community level is the smallest spatial resolution on which agricultural statistics are gathered officially, a detailed modelling of the change in SOC was;as impossible. However, by selecting communities with extreme changes in SOC, we found indications that the major source of increase in SOC was due to the large increase in pig breeding

An algebraic solution of maximum likelihood function in case of Gaussian mixture distribution

Traditionally, the least-squares method has been employed as a standard technique for parameter estimation and regression fitting of models to measured points in data sets in many engineering disciplines, geoscience fields as well as in geodesy. If the model errors follow the Gaussian distribution with mean zero in linear models, the least-squares estimate is linear, unbiased and of minimum variance. However, this may not always be the case owing to contaminated data (i.e. the presence of outliers) or data from different sources with varying distributions.This study proposes an algebraic iterative method that approximates the error distribution model using a Gaussian mixture distribution, with the application of maximum likelihood estimation as a possible solution to the problem. The global maximisation of the likelihood function is carried out through the computation of the global solution of a multivariate polynomial system using numerical Groebner basis in order to considerably reduce the running time. The novelty of the proposed method is the application of the total least square (TLS) error model as opposed to ordinary least squares (OLS) and the maximisation of the likelihood function of the Gaussian mixture via an algebraic approach. Use of the TLS error model rather than OLS enables errors in all the three coordinates of the model of a 3D plane (i.e. [...]) to be considered. The proposed method is illustrated by fitting a plane to real laser-point cloud data containing outliers to test its robustness. Compared with the Random Sample Consensus and Danish robust estimation methods, the results of the proposed algebraic method indicate its efficiency in terms of computational time and its robustness in managing outliers. The proposed approach thus offers an alternative method for solving mixture distribution problems in geodesy