Missing value imputation in a data matrix using the regularised singular value decomposition.

Some statistical analysis techniques may require complete data matrices, but a frequent problem in the construction of databases is the incomplete collection of information for different reasons. One option to tackle the problem is to estimate and impute the missing data. This paper describes a form of imputation that mixes regression with lower rank approximations. To improve the quality of the imputations, a generalisation is proposed that replaces the singular value decomposition (SVD) of the matrix with a regularised SVD in which the regularisation parameter is estimated by cross-validation. To evaluate the performance of the proposal, ten sets of real data from multienvironment trials were used. Missing values were created in each set at four percentages of missing not at random, and three criteria were then considered to investigate the effectiveness of the proposal. The results show that the regularised method proves very competitive when compared to the original method, beating it in several of the considered scenarios. As it is a very general system, its application can be extended to all multivariate data matrices. •The imputation method is modified through the inclusion of a stable and efficient computational algorithm that replaces the classical SVD least squares criterion by a penalised criterion. This penalty produces smoothed eigenvectors and eigenvalues that avoid overfitting problems, improving the performance of the method when the penalty is necessary. The size of the penalty can be determined by minimising one of the following criteria: the prediction errors, the Procrustes similarity statistic or the critical angles between subspaces of principal components.

Proposal of an open-source computational toolbox for solving PDEs in the context of chemical reaction engineering using FEniCS and complementary components.

In this contribution, an open-source computational toolbox composed of FEniCS and complementary packages is introduced to the chemical and process engineering field by addressing two case studies. First, the oxidation of o-xylene to phthalic anhydride is modelled and used as a FEniCS' proof-of-concept based on a comparison with the software Aspen Custom Modeler (ACM). The results show a maximum absolute error of 2% and thus a good FEniCS/ACM agreement. Second, synthetic natural gas (SNG) production through CO2 methanation is covered in further detail. In this instance, a parametric study is performed for a tube bundle fixed-bed reactor employing a two-dimensional and transient pseudo-homogeneous model. An operating window for critical variables is evaluated, discussed, and successfully contrasted with the literature. Therefore, the computational toolbox methodology and the consistency of the results are validated, strengthening FEniCS and complements as an interesting alternative to solve mathematical models concerning chemical reaction engineering.