A study of machine learning approaches to mechanics problems

Machine learning (ML) is an umbrella term for solving problems for which development of algorithms by human programmers would be cost-prohibitive, and instead the problems are solved by helping machines 'discover' their 'own' algorithms, without needing to be explicitly told what to do by any human-developed algorithms. Recently, generative artificial neural networks have been able to surpass results of many previous approaches. Machine learning approaches have been applied to large language models, computer vision, speech recognition, email filtering, agriculture and medicine, where it is too costly to develop algorithms to perform the needed tasks. The mathematical foundations of ML are provided by mathematical optimization methods. Data mining is a related (parallel) field of study, focusing on exploratory data analysis through unsupervised learning. ML is known in its application across business problems under the name predictive analytics. Although not all machine learning is statistically-based, computational statistics is an important source of the field's methods. Machine learning tools represent key enablers for empowering material scientists and engineers to accelerate the development of novel materials, processes and techniques. One of the aims of using such approaches in the field of materials science is to achieve high-throughput identification and quantification of essential features along the process-structure-property-performance chain. In this contribution, machine learning and statistical learning approaches are reviewed in terms of their successful application to specific problems in the field of continuum materials mechanics. They are categorized with respect to their type of task designated to be either descriptive, predictive or prescriptive; thus to ultimately achieve identification, prediction or even optimization of essential characteristics. The respective choice of the most appropriate machine learning approach highly depends on the specific use-case, type of material, kind of data involved, spatial and temporal scales, formats, and desired knowledge gain as well as affordable computational costs. Different examples are reviewed involving case-by-case dependent application of different types of artificial neural networks and other data-driven approaches such as support vector machines, decision trees and random forests as well as Bayesian learning, and model order reduction procedures such as principal component analysis, among others. These techniques are applied to accelerate the identification of material parameters or salient features for materials characterization, to support rapid design and optimization of novel materials or manufacturing methods, to improve and correct complex measurement devices, or to better understand and predict fatigue behavior, among other examples. Besides experimentally obtained datasets, numerous studies draw required information from simulation-based data mining. Altogether, it is shown that experiment- and simulation-based data mining in combination with machine leaning tools provide exceptional opportunities to enable highly reliant identification of fundamental interrelations within materials for characterization and optimization in a scale-bridging manner. Potentials of further utilizing applied machine learning in materials science and empowering significant acceleration of knowledge output are pointed out.

کلیدواژه ها:

neural networks (NNs) ، elasticity ، failure mechanics ، phase-field modeling