At its essence, computational mechanics provides numerical solutions to problems that arise from observations of engineered systems or natural phenomena. Partial differential equations commonly govern the resulting mathematical descriptions. Discretization of the problem al- lows for the approximation of a solution using computational methods. The long-established finite element method and the method of finite differences are among the most popular approaches. However, with problems of increasing complexity, conventional methods often result in exponential growth in the computational effort, thus motivating the search for al- ternatives. Increased accessibility of deep learning techniques has inspired recent research into investigating their application in physics and engineering. Most publications have em- ployed neural networks to approximate the hidden solution of problems described by partial differential equations. The distinct idea behind those approaches is to incorporate domain knowledge into the learning model to outweigh the usual data scarceness in physical systems. The first promising results have motivated the pursuit of this line of study in the context of computational mechanics. Therefore, this work elaborates on the fundamentals of machine learning and neural networks, and the current literature on learning-based methods in com- putational mechanics is reviewed. The focus lies on applications of physics-enriched surrogate models. Subsequently, a physics-informed neural network is employed to predict the solution of a heat transfer example. By documenting the implementation and related obstacles, this thesis intends to inform future research on the subject. A discussion on the advantages and drawbacks of learning-based algorithms in the engineering context concludes the thesis.     «

At its essence, computational mechanics provides numerical solutions to problems that arise from observations of engineered systems or natural phenomena. Partial differential equations commonly govern the resulting mathematical descriptions. Discretization of the problem al- lows for the approximation of a solution using computational methods. The long-established finite element method and the method of finite differences are among the most popular approaches. However, with problems of increasin...     »