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In the ROMSOC project, we develop specially-tailored algorithmic approaches to solve the practical problems of our industry partners. The mathematical fields involved in solving these problems are as diverse as the problems themselves. Thus, our project covers a very broad range within applied mathematics: from discrete optimization to inverse problems, from deep learning to optimal control. What all these fields have in common is that error estimation is an important topic in order to quantify the quality of a computed solution. Naturally, all of them their own error measures and different ways of computing and using them. This report summarizes the state of the art methods in the respective fields concerning error measures and their usefulness in solving real-world problems., Project deliverable D4.1

In the ROMSOC project, we develop specially-tailored algorithmic approaches to solve the practical problems of our industry partners. The mathematical fields involved in solving these problems are as diverse as the problems themselves. Thus, our project covers a very broad range within applied mathematics: from discrete optimization to inverse problems, from deep learning to optimal control. What all these fields have in common is that error estimation is an important topic in order to quantify the quality of a computed solution. Naturally, all of them their own error measures and different ways of computing and using them. This report summarizes the state of the art methods in the respective fields concerning error measures and their usefulness in solving real-world problems.