Käänteisanalyysi

Käänteisanalyysi, meaning inverse analysis in Finnish, is a problem-solving technique used to determine the unknown causes or parameters of a system based on observed effects or outputs. Instead of the typical forward analysis where inputs are known and outputs are predicted, käänteisanalyysi starts with the observed outcome and works backward to deduce the initial conditions or system properties that must have produced it.

This method is employed across various scientific and engineering disciplines. For instance, in geophysics, it can be used to infer the structure of the Earth's interior from seismic wave data. In medical imaging, käänteisanalyysi helps reconstruct internal body structures from external measurements. In materials science, it can be used to determine material properties from experimental responses. In engineering, it might involve finding the required design parameters of a component given its performance requirements.

The core challenge in käänteisanalyysi often lies in its ill-posed nature. Unlike well-posed problems where a unique solution exists and is stable with respect to small changes in the input, inverse problems frequently lack a unique solution or are highly sensitive to noise in the observed data. This often necessitates the use of regularization techniques to find a stable and meaningful solution. These techniques introduce additional constraints or assumptions to guide the solution towards a physically plausible outcome. The success of käänteisanalyysi depends on the quality of the observed data and the appropriate selection of mathematical models and solution methods.