Development and Applications of Self-learning Simulation in Finite Element Analysis

Numerical analysis such as the finite element analysis (FEA) have been widely used to solve many engineering problems. Constitutive modelling is an important component of any numerical analysis and is used to describe the material behaviour. The accuracy and reliability of numerical analysis is greatly reliant on the constitutive model that is integrated in the finite element code. In recent years, data mining techniques such as artificial neural network (ANN), genetic programming (GP) and evolutionary polynomial regression (EPR) have been employed as alternative approach to the conventional constitutive modelling. In particular, EPR offers great advantages over other data mining techniques. However, these techniques require a large database to learn and extract the material behaviour. On the other hand, the link between laboratory or field tests and numerical analysis is still weak and more investigation is needed to improve the way that they matched each other. Training a data mining technique within the self-learning simulation framework is currently considered as one of the solutions that can be utilised to accurately represent the actual material behaviour. In this thesis an EPR based machine learning technique is utilised in the heart of the self-learning framework with an automation process which is coded in MATLAB environment. The methodology is applied to simulate different material behaviour in a number of structural and geotechnical applications. Two training strategies are used to train the EPR in the developed framework, total stress-strain and incremental stress-strain strategies. The results show that integrating EPR based models in the framework allows to learn the material response during the self-learning process and provide accurate predictions to the actual behaviour. Moreover, for the first time, the behaviour of a complex material, frozen soil, is modelled based on the EPR approach. The results of the EPR model predictions are compared with the actual data and it is shown that the proposed model can capture and reproduce the behaviour of the frozen soil with a very high accuracy. The developed EPR based self-learning methodology presents a unified approach to material modelling that can also help the user to gain a deeper insight into the behaviour of the materials. The methodology is generic and can be extended to modelling different engineering materials

A genetic programming approach for economic forecasting with survey expectations

We apply a soft computing method to generate country-specific economic sentiment indicators that provide estimates of year-on-year GDP growth rates for 19 European economies. First, genetic programming is used to evolve business and consumer economic expectations to derive sentiment indicators for each country. To assess the performance of the proposed indicators, we first design a nowcasting experiment in which we recursively generate estimates of GDP at the end of each quarter, using the latest business and consumer survey data available. Second, we design a forecasting exercise in which we iteratively re-compute the sentiment indicators in each out-of-sample period. When evaluating the accuracy of the predictions obtained for different forecast horizons, we find that the evolved sentiment indicators outperform the time-series models used as a benchmark. These results show the potential of the proposed approach for prediction purposes.This research was supported by the project PID2020-118800GB-I00 from the Spanish Ministry of Science and Innovation (MCIN)/Agencia Estatal de Investigación (AEI). DOI: http://dx.doi.org/10.13039/501100011033.Peer ReviewedPostprint (published version

Search based software engineering: Trends, techniques and applications

© ACM, 2012. This is the author's version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version is available from the link below.In the past five years there has been a dramatic increase in work on Search-Based Software Engineering (SBSE), an approach to Software Engineering (SE) in which Search-Based Optimization (SBO) algorithms are used to address problems in SE. SBSE has been applied to problems throughout the SE lifecycle, from requirements and project planning to maintenance and reengineering. The approach is attractive because it offers a suite of adaptive automated and semiautomated solutions in situations typified by large complex problem spaces with multiple competing and conflicting objectives. This article provides a review and classification of literature on SBSE. The work identifies research trends and relationships between the techniques applied and the applications to which they have been applied and highlights gaps in the literature and avenues for further research.EPSRC and E

Automated Knowledge Discovery using Neural Networks

The natural world is known to consistently abide by scientific laws that can be expressed concisely in mathematical terms, including differential equations. To understand the patterns that define these scientific laws, it is necessary to discover and solve these mathematical problems after making observations and collecting data on natural phenomena. While artificial neural networks are powerful black-box tools for automating tasks related to intelligence, the solutions we seek are related to the concise and interpretable form of symbolic mathematics. In this work, we focus on the idea of a symbolic function learner, or SFL. A symbolic function learner can be any algorithm that is able to produce a symbolic mathematical expression that aims to optimize a given objective function. By choosing different objective functions, the SFL can be tuned to handle different learning tasks. We present a model for an SFL that is based on neural networks and can be trained using deep learning. We then use this SFL to approach the computational task of automating discovery of scientific knowledge in three ways. We first apply our symbolic function learner as a tool for symbolic regression, a curve-fitting problem that has traditionally been approached using genetic evolution algorithms. We show that our SFL performs competitively in comparison to genetic algorithms and neural network regressors on a sample collection of regression instances. We also reframe the problem of learning differential equations as a task in symbolic regression, and use our SFL to rediscover some equations from classical physics from data. We next present a machine-learning based method for solving differential equations symbolically. When neural networks are used to solve differential equations, they usually produce solutions in the form of black-box functions that are not directly mathematically interpretable. We introduce a method for generating symbolic expressions to solve differential equations while leveraging deep learning training methods. Unlike existing methods, our system does not require learning a language model over symbolic mathematics, making it scalable, compact, and easily adaptable for a variety of tasks and configurations. The system is designed to always return a valid symbolic formula, generating a useful approximation when an exact analytic solution to a differential equation is not or cannot be found. We demonstrate through examples the way our method can be applied on a number of differential equations that are rooted in the natural sciences, often obtaining symbolic approximations that are useful or insightful. Furthermore, we show how the system can be effortlessly generalized to find symbolic solutions to other mathematical tasks, including integration and functional equations. We then introduce a novel method for discovering implicit relationships between variables in structured datasets in an unsupervised way. Rather than explicitly designating a causal relationship between input and output variables, our method finds mathematical relationships between variables without treating any variable as distinguished from any other. As a result, properties about the data itself can be discovered, rather than rules for predicting one variable from the others. We showcase examples of our method in the domain of geometry, demonstrating how we can re-discover famous geometric identities automatically from artificially generated data. In total, this thesis aims to strengthen the connection between neural networks and problems in symbolic mathematics. Our proposed SFL is the main tool that we show can be applied to a variety of tasks, including but not limited to symbolic regression. We show how using this approach to symbolic function learning paves the way for future developments in automated scientific knowledge discovery