A PGD-based multiscale formulation for non-linear solid mechanics under small deformations

Model reduction techniques have became an attractive and a promising field to be applied in multiscale methods. The main objective of this work is to formulate a multiscale procedure for non-linear problems based on parametrized microscale models. The novelty of this work relies in the implementation of the model reduction technique known as Proper Generalized Decomposition for solving the high dimensional parametrized problem resulting from the microscale model. The multiscale framework here proposed is formulated to non-linear problems, specifically to material non-linearities, where material response is governed by a strain dependent evolution law. Two strategies to deal with this kind of problem under small deformations are detailed in this work. Both strategies based on parametrized microscale models solved by PGD have been applied to a problem with a rate-dependent isotropic damage model. First, a procedure where the problem is solved by uncoupling the equilibrium equation to the state variable expression has been explored. In order, to alleviate the parametrized microscale problem, a second strategy for problems with material non-linearity has been proposed, incorporating a parametrized microscale problem at each macroscale increment (FE-PGD). The basis of those procedures are described and compared, highlighting the solution accuracy and computer time consumption in comparison to a traditional finite element analysis

Prediction and identification of physical systems by means of physically-guided neural networks with meaningful internal layers

Substitution of well-grounded theoretical models by data-driven predictions is not as simple in engineering and sciences as it is in social and economic fields. Scientific problems suffer many times from paucity of data, while they may involve a large number of variables and parameters that interact in complex and non-stationary ways, obeying certain physical laws. Moreover, a physically-based model is not only useful for making predictions, but to gain knowledge by the interpretation of its structure, parameters, and mathematical properties. The solution to these shortcomings seems to be the seamless blending of the tremendous predictive power of the data-driven approach with the scientific consistency and interpretability of physically-based models. We use here the concept of Physically-Guided Neural Networks (PGNN) to predict the input-output relation in a physical system, while, at the same time, fulfilling the physical constraints. With this goal, the internal hidden state variables of the system are associated with a set of internal neuron layers, whose values are constrained by known physical relations, as well as any additional knowledge on the system. Furthermore, when having enough data, it is possible to infer knowledge about the internal structure of the system and, if parameterized, to predict the state parameters for a particular input-output relation. We show that this approach, besides getting physically-based predictions, accelerates the training process, reduces the amount of data required to get similar accuracy, partly filters the intrinsic noise in the experimental data and improves its extrapolation capacity. (C) 2021 ElsevierB.V. All rights reserved

An unsupervised data completion method for physically-based data-driven models

Data-driven methods are an innovative model-free approach for engineering and sciences, still in process of maturation. The idea behind is the combination of data analytics techniques, to handle the huge amount of data derived from continuous monitoring or experimental measurements, and of the constraints imposed by universal physical laws, particular to the field in hands. A well-known problem in the former corresponds to the quality and completeness of the available data that, sometimes, are so poor that make the predictions useless. In data-driven simulation-based engineering and sciences (DDSBES), the intrinsic physical constraints may help in completing the missing data in a more precise manner, by forcing them to remain in the manifold defined by the physical laws. In this work, a suitable imputation method to complete incomplete data that preserves the data context-dependent structure is presented. This is accomplished by enforcing the data to fulfill the set of physical constraints, specific to the problem. For this purpose, a generalization of the weighted mean concept is proposed, where the distance to the admissible points (in a physical sense) is used as a weighting function to get the optimal candidate. The method is evaluated in a classical regression problem, where it is compared with other standard methods, showing better results. Then, its application is illustrated in two data-driven problems, where no filling data procedure has been yet proposed, showing good predictive capability, provided that the data are close enough to the actual system state

A multiscale data-driven approach for bone tissue biomechanics

The data-driven methodology with application to continuum mechanics relies upon two main pillars: (i) experimental characterization of stress–strain pairs associated to different loading states, and (ii) numerical elaboration of the elasticity equations as an optimization (searching) algorithm using compatibility and equilibrium as constraints. The purpose of this work is to implement a multiscale data-driven approach using experimental data of cortical bone tissue at different scales. First, horse cortical bone samples are biaxially loaded and the strain fields are recorded over a region of interest using a digital image correlation technique. As a result, both microscopic strain fields and macroscopic strain states are obtained by a homogenization procedure, associated to macroscopic stress loading states which are considered uniform along the sample. This experimental outcome is here referred as a multiscale dataset. Second, the proposed multiscale data-driven methodology is implemented and analyzed in an example of application. Results are presented both in the macroscopic and microscopic scales, with the latter considered just as a post-process step in the formulation. The macroscopic results show non-smooth strain and stress patterns as a consequence of the tissue heterogeneity which suggest that a preassumed linear homogeneous orthotropic model may be inaccurate for bone tissue. Microscopic results show fluctuating strain fields – as a consequence of the interaction and evolution of the microconstituents – an order of magnitude higher than the averaged macroscopic solution, which evidences the need of a multiscale approach for the mechanical analysis of cortical bone, since the driving force of many biological bone processes is local at the microstructural level. Finally, the proposed multiscale data-driven technique may also be an adequate strategy for the solution of intractable large size multiscale FE2 computational approaches since the solution at the microscale is obtained as a postprocessing. As a main conclusion, the proposed multiscale data-driven methodology is a useful alternative to overcome limitations in the continuum mechanical study of the bone tissue. This methodology may also be considered as a useful strategy for the analysis of additional biological or technological hierarchical multiscale materials

Patología endodóntica periodontal. Revisión bibliográfica

Los procesos patológicos que afectan a las estructuras del periodonto pueden tener diversos orígenes y cursar con una sintomatología parecida. No hay signos ni síntomas patognomónicos que nos indiquen una etiología concreta. Por tanto, es preciso utilizar todas las pruebas diagnósticas disponibles para descubrir el origen de la afectación, e instaurar el tratamiento apropiado, Sólo así se evitarán fracasos diagnósticos y terapéuticos. En este trabajo se revisan las comunicaciones existentes entre la pulpa y el periodonto, la patogenia de las lesiones endoperiodontales, su pronóstico, su tratamiento y se hace especial hincapié en el diagnóstico y diagnóstico diferencial de dichas lesiones

Analysis of the parametric correlation in mathematical modeling of in vitro glioblastoma evolution using copulas

Modeling and simulation are essential tools for better understanding complex biological processes, such as cancer evolution. However, the resulting mathematical models are often highly non-linear and include many parameters, which, in many cases, are difficult to estimate and present strong correlations. Therefore, a proper parametric analysis is mandatory. Following a previous work in which we modeled the in vitro evolution of Glioblastoma Multiforme (GBM) under hypoxic conditions, we analyze and solve here the problem found of parametric correlation. With this aim, we develop a methodology based on copulas to approximate the multidimensional probability density function of the correlated parameters. Once the model is defined, we analyze the experimental setting to optimize the utility of each configuration in terms of gathered information. We prove that experimental configurations with oxygen gradient and high cell concentration have the highest utility when we want to separate correlated effects in our experimental design. We demonstrate that copulas are an adequate tool to analyze highly-correlated multiparametric mathematical models such as those appearing in Biology, with the added value of providing key information for the optimal design of experiments, reducing time and cost in in vivo and in vitro experimental campaigns, like those required in microfluidic models of GBM evolution

Evaluation of dimensionality reduction methods applied to numerical weather models for solar radiation forecasting

The interest in solar radiation prediction has increased greatly in recent times among the scientific community. In this context, Machine Learning techniques have shown their ability to learn accurate prediction models. The aim of this paper is to go one step further and automatically achieve interpretability during the learning process by performing dimensionality reduction on the input variables. To this end, three non standard multivariate feature selection approaches are applied, based on the adaptation of strong learning algorithms to the feature selection task, as well as a battery of classic dimensionality reduction models. The goal is to obtain robust sets of features that not only improve prediction accuracy but also provide more interpretable and consistent results. Real data from the Weather Research and Forecasting model, which produces a very large number of variables, is used as the input. As is to be expected, the results prove that dimensionality reduction in general is a useful tool for improving performance, as well as easing the interpretability of the results. In fact, the proposed non standard methods offer important accuracy improvements and one of them provides with an intuitive and reduced selection of features and mesoscale nodes (around 10% of the initial variables centered on three specific nodes).This work has been partially supported by the projects TIN2014-54583-C2-2-R, TEC2014-52289-R and TEC2016-81900-REDT of the Spanish Interministerial Commission of Science and Technology (MICYT), and by Comunidad Autónoma de Madrid, under project PRICAM P2013ICE-2933

Bio-inspired computation: where we stand and what's next

In recent years, the research community has witnessed an explosion of literature dealing with the adaptation of behavioral patterns and social phenomena observed in nature towards efficiently solving complex computational tasks. This trend has been especially dramatic in what relates to optimization problems, mainly due to the unprecedented complexity of problem instances, arising from a diverse spectrum of domains such as transportation, logistics, energy, climate, social networks, health and industry 4.0, among many others. Notwithstanding this upsurge of activity, research in this vibrant topic should be steered towards certain areas that, despite their eventual value and impact on the field of bio-inspired computation, still remain insufficiently explored to date. The main purpose of this paper is to outline the state of the art and to identify open challenges concerning the most relevant areas within bio-inspired optimization. An analysis and discussion are also carried out over the general trajectory followed in recent years by the community working in this field, thereby highlighting the need for reaching a consensus and joining forces towards achieving valuable insights into the understanding of this family of optimization techniques

A Genetic Tuning to Improve the Performance of Fuzzy Rule-Based Classification Systems with Interval-Valued Fuzzy Sets: Degree of Ignorance and Lateral Position

Fuzzy Rule-Based Systems are appropriate tools to deal with classification problems due to their good properties. However, they can suffer a lack of system accuracy as a result of the uncertainty inherent in the definition of the membership functions and the limitation of the homogeneous distribution of the linguistic labels. The aim of the paper is to improve the performance of Fuzzy Rule-Based Classification Systems by means of the Theory of Interval-Valued Fuzzy Sets and a post-processing genetic tuning step. In order to build the Interval-Valued Fuzzy Sets we define a new function called weak ignorance for modeling the uncertainty associated with the definition of the membership functions. Next, we adapt the fuzzy partitions to the problem in an optimal way through a cooperative evolutionary tuning in which we handle both the degree of ignorance and the lateral position (based on the 2-tuples fuzzy linguistic representation) of the linguistic labels. The experimental study is carried out over a large collection of data-sets and it is supported by a statistical analysis. Our results show empirically that the use of our methodology outperforms the initial Fuzzy Rule-Based Classification System. The application of our cooperative tuning enhances the results provided by the use of the isolated tuning approaches and also improves the behavior of the genetic tuning based on the 3-tuples fuzzy linguistic representation.Spanish Government TIN2008-06681-C06-01 TIN2010-1505