Databased prediction models are used to estimate a possible outcome for previously unknown production parameters. These forward models enable to test new production designs and parameters virtually before applying them in the real world. Cause-effect networks are one way to generate such a prediction model. Multiple inputs and stages are being connected to one large prediction model. The functional behaviour and correlation of inputs as well as outputs is obtained through data based learning. In general, these models are non-linear and not invertible, especially for micro cold forming processes. While already being useful in process design, such models have their highest impact if inverted to find process parameters for a given output. Combining methods from the mathematical field of inverse problems as well as machine learning, a generalized inverse can be approximated. This allows finding process parameters for a given output without inverting the model directly but still using inherit information of the forward model. In this work, Tikhonov functionals are used to perform a parameter identification. The classical approach is altered by changing the discrepancy term to incorporate tolerances. Thereby, small deviations of a certain pattern are being neglected and the parameter finding process is being stabilized. In addition, different types of regularization are taken into consideration. Besides theoretical aspects of this method, examples are provided to demonstrate advantages and boundaries of an application for the process design in micro cold forming processes.

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Tikhonov functionals are a well known method for solving inverse problems. They consist of a discrepancy and a penalty term. The first term evaluates the deviation of simulated data from measured data. We alternate this term by incorporating tolerances, which neglects small deviations from the data within a prescribed tolerance. This approach adapts ideas from support vector regression, which utilizes such a tolerance for identity operators and semi discrete problems. Furthermore, the application for inverse problems is motivated by applications where such tolerances naturally occur, e.g. application with multiple measurements. In this case instead of one measurement a confidence interval for the measurement can be used.In this work we provide an overview on the necessary analysis and alternation of Tikhonov functionals incorporating tolerances. In addition, an example of applications are shown and discussed.